Chapter 1 Review Questions 1. What do we mean by a geocentric universe? In broad terms, contrast a geocentric universe with our modern view of the universe. geocentric universe ancient belief in The idea that the Earth is the center of the entire universe. 2. Describe the major levels of structure in the universe. stars filled with helium gas and hydrogen gas. dust. planets 3. What do we mean when we say that the universe is expanding? Why does an expanding universe suggest a beginning in what we call the Big Bang? telescopic observations of distant galaxies show that the entire universe is expanding. That is, average distances between galaxies are increasing with time. If the universe is expanding, everything must have been closer together in the past. From the observed rate of expansion, astronomers estimate that the expansion started somewhere between 12 billion and 16 billion years ago. Astronomers call this beginning the Big Bang. The universe has continued to expand ever since the Big Bang, but not always at the same rate. Until about a decade ago, astronomers assumed that the expansion rate slowed with time because of gravity, which attracts all objects to all other objects. 4. Summarize our cosmic origins and explain what Carl Sagan meant when he said that we are "star stuff." Our cosmic origins: All the matter and energy in the universe was created in the Big Bang. the elements from which we are made were produced in stars that shined long ago, and these elements formed the Earth, thanks to the recycling role played by our galaxy. 5. Explain the statement The farther away we look in distance, the further back we look in time. 6. What do we mean by the observable universe? 7. Describe key features of our solar system as they would appear on a scale of 1 to 10 billion. 8. How do the distances to the stars compare to distances within our solar system? Give a few examples to put the comparison in perspective. 9. Describe at least two ways to put the scale of the Milky Way Galaxy in perspective. 10. How many galaxies are in the observable universe? How many stars are in the observable universe? Put these numbers in perspective. A galaxy is a great island of stars in space, containing from a few hundred million to a trillion or more stars. The Milky Way Galaxy is relatively large, containing more than 100 billion stars. 11. Imagine describing the cosmic calendar to friends. In your own words, give them a feel for how the human race fits into the scale of time. No one knows exactly when the earliest life arose on Earth, but it certainly was within the first billion years, or by mid-September on the cosmic calendar. For most of the Earth's history, living organisms remained relatively primitive and microscopic in size. Larger invertebrate life arose only about 600 million years ago, or about December 13 on the cosmic calendar. The age of the dinosaurs began shortly after midnight on Christmas (December 25) on the cosmic calendar. The dinosaurs vanished abruptly around 1:00 a.m. on December 30 (65 million years ago in real time),probably due to the impact of an asteroid or comet [Section 12.6]. With the dinosaurs gone, small furry mammals inherited the Earth. Some 60 million years later, or around 9:00 p.m. on December 31 of the cosmic calendar, the earliest hominids (human ancestors) walked upright. Most of the major events of human history took place within the final seconds of the final minute of the final day on the cosmic calendar. Agriculture arose about 30 seconds ago. The Egyptians built the pyramids about 13 seconds ago. The cosmic calendar compresses the history of the universe into 1 year; this version assumes that the universe is 12 billion years old, so that each month represents about 1 billion years. It is only within the last few seconds of the last day that human civilization has taken shape. 12. Briefly summarize the major motions of the Earth through the universe. The Earth rotates on its axis once each day. The axis is a line joining the North and South Poles and passing through the center of the Earth. The Earth revolves around the Sun once each year, following an orbit that is not quite circular. 13. What is an astronomical unit? What is the ecliptic plane? The average distance of the Earth from the Sun is called an astronomical unit, or AU (more technically, an astronomical unit is the semimajor axis of the Earth's orbit): 1 AU @ 150 million km (93 million miles) the Earth Sun distance varies between 147.1 million and 152.1 million kilometers. The average distance, which defines 1 astronomical unit (AU), is 149.6 million kilometers. The plane of the Earth's orbit around the Sun is called the ecliptic plane. The Earth's rotation axis happens to be tilted by 23½° from a line perpendicular to the ecliptic plane, pointing nearly in the direction of Polaris, the North Star. Viewed from above the North Pole, the Earth both rotates and revolves counterclockwise. 14. Describe the cause of the Earth's seasons, and explain why the seasons are opposite in the Northern and Southern Hemispheres. Seasons The combination of the Earth's rotation and its revolution around the Sun explains why we have seasons. Because the Earth's rotation axis remains pointed in the same direction toward Polaris throughout the year, its orientation relative to the Sun changes as it orbits the Sun. The familiar seasonal changes longer and warmer days in summer, and shorter and cooler days in winter arise because of changes in how directly the Sun's rays strike a particular location on Earth. When the rays are fairly direct, the Sun's path through the sky is long and high and the days are warm. When the Sun's rays strike less directly, the Sun's path is short and low through the sky and the days are cool. Notice that the Sun's rays strike the Northern Hemisphere more directly on the side of the orbit near point 2 in Figure 1.13, while they strike the Southern Hemisphere more directly on the side of the orbit near point 4. That is why the seasons are opposite in the Northern and Southern Hemispheres. 15. What is precession, and how does it affect the appearance of our sky? Precession Although the Earth's axis will remain pointed toward Polaris throughout our lifetimes, it has not always been so and will not always remain so. The reason is a gradual motion called precession. Like the axis of a spinning top, the Earth's axis also sweeps out a circle (precesses) much more slowly (Figure 1.14). Note that the axis tilt remains close to 23½° throughout the cycle; only the axis orientation changes. Each cycle of the Earth's precession takes about 26,000 years. precession The gradual wobble of the axis of a rotating object around a vertical line. 16. Briefly describe the motion of the Sun relative to stars in the local solar neighborhood and to the entire Milky Way Galaxy. Given the relatively high speeds of stars relative to us, why don't we notice them racing around the sky? the local solar neighborhood is only a tiny portion of the Milky Way Galaxy. The stars in the local solar neighborhood actually move quite fast relative to our solar system, but the enormous distances between stars make this motion barely detectable on human time scales. The entire Milky Way Galaxy is rotating. Stars at different distances from the galactic center take different amounts of time to complete an orbit. Our solar system, located about 28,000 light-years from the galactic center, completes one orbit of the galaxy in about 230 million years 17. Describe the raisin cake model of the universe, and explain how it shows that a uniform expansion would lead us to see more distant galaxies moving away from us at higher speeds. If you now imagine the Local Raisin to represent our Local Group of galaxies and the other raisins to represent more distant galaxies or clusters of galaxies, you have a basic picture of the expansion of the universe. That is, space itself is growing, and more distant galaxies move away from us faster because they are carried along with this expansion like raisins in an expanding cake. And, just as the raisins themselves do not expand, the individual galaxies and clusters of galaxies do not expand (because they are bound together by gravity). The effects of expansion would appear basically the same viewed from any place in the universe. 18. Briefly describe how astronomy is interwoven with social and technological change. the development of space travel and the computer revolution have helped fuel tremendous progress in astronomy. We've learned a lot about our solar system by sending probes to the planets, and many of our most powerful observatories, including the Hubble Space Telescope, reside in space. On the ground, computer design and control have led to tremendous growth in the size and power of telescopes, particularly in the past decade. We spin around the Earth's axis as we revolve around the Sun. Our solar system moves among the stars of the local solar neighborhood, while this entire neighborhood orbits the center of the Milky Way Galaxy. Our galaxy, in turn, moves among the other galaxies of the Local Group, while the Local Group is carried along with the overall expansion of the universe. Table 1.2 lists the motions and their associated speeds. Spaceship Earth is indeed carrying us on a remarkable journey. Discussion Questions 1. Vast Orbs. The chapter-opening quotation from Christiaan Huygens suggests that humans might be less inclined to wage war if everyone appreciated the Earth's place in the universe. Do you agree? Defend your opinion. 2. Infant Species. In the last few tenths of a second before midnight on December 31 of the cosmic calendar, we have developed an incredible civilization and learned a great deal about the universe, but we also have developed technology through which we could destroy ourselves. The midnight bell is striking, and the choice for the future is ours. How far into the next cosmic year do you think our civilization will survive? Defend your opinion. 3. A Human Adventure. How important do you think astronomical discoveries have been to our social development? Defend your opinion with examples drawn from your knowledge of history. Problems (Quantitative problems are marked with an asterisk.) Sensible Statements? For problems 1–8, decide whether the statement is sensible and explain why it is or is not. Example: I walked east from our base camp at the North Pole. Solution: The statement does not make sense because east has no meaning at the North Pole—all directions are south from the North Pole. 1. The universe is between 10 billion and 16 billion years old. 2. The universe is between 10 billion and 16 billion light-years old. 3. It will take me light-years to complete this homework assignment! 4. Someday we may build spaceships capable of traveling at a speed of 1 light-minute per hour. 5. Astronomers recently discovered a moon that does not orbit a planet. 6. NASA plans soon to launch a spaceship that will leave the Milky Way Galaxy to take a photograph of the galaxy from the outside. 7. The observable universe is the same size today as it was a few billion years ago. 8. Photographs of distant galaxies show them as they were when they were much younger than they are today. 9. No Axis Tilt. Suppose the Earth's axis had no tilt. Would we still have seasons? Why or why not? 10. Tour Report. A friend asks you the following questions concerning your tour of a scale-model solar system. Answer each question in one paragraph. 1. Is the Sun really much bigger than the Earth? 2. Is it true that the Sun uses nuclear energy? 3. Would it be much harder to send humans to Mars than to the Moon? 4. In elementary school, I heard that Neptune is farther from the Sun than Pluto. Is this true? 5. I read that Pluto is not really a planet. What's the story? 6. Why didn't they have any stars besides the Sun in the scale model? 7. What was the most interesting thing you learned during your tour? 11. Raisin Cake Universe. Suppose that all the raisins in a cake are 1 centimeter apart before baking and after baking they are 4 centimeters apart. 1. Draw diagrams to represent the cake before and after baking. 2. Identify one raisin as the Local Raisin on your diagrams. Construct a table showing the distances and speeds of other raisins as seen from the Local Raisin. 3. Briefly explain how your expanding cake is similar to the expansion of the universe. 12. Scaling the Local Group of Galaxies. Both the Milky Way Galaxy and the Great Galaxy in Andromeda (M31) have a diameter of about 100,000 light-years. The distance between the two galaxies is about 2.5 million light-years. 1. Using a scale on which 1 centimeter represents 100,000 light-years, draw a sketch showing both galaxies and the distance between them to scale. 2. How does the separation between galaxies compare to the separation between stars? Based on your answer, discuss the likelihood of galactic collisions in comparison to the likelihood of stellar collisions. 13. Distances by Light. Just as a light-year is the distance that light can travel in 1 year, we define a light-second as the distance that light can travel in 1 second, a light-minute as the distance that light can travel in 1 minute, and so on. Following the method of Mathematical Insight 1.1, calculate the distance in kilometers represented by each of the following: 1 light-second; 1 light-minute; 1 light-hour; 1 light-day. 14. Driving to the Planets (and Stars). Imagine that you could drive your car in space at a constant speed of 100 km/hr (62 mi/hr). (In reality, the law of gravity would make driving through space at a constant speed all but impossible.) 1. How long would it take to circle the Earth in low orbit? (Hint: Use the Earth's circumference of approximately 40,000 km.) 2. Suppose you started driving from the Sun. How long would it take to reach Earth? How long would it take to reach Pluto? Use the data in Table 1.1. 3. How long would it take to drive the 4.4 light-years to Alpha Centauri? (Hint: You'll need to convert the distance to kilometers.) 4. The Voyager 2 spacecraft is traveling at about 50,000 km/hr. At this speed, how long would it take to reach Alpha Centauri (if it were headed in the right direction, which it is not)? 15. Speed Calculations. Calculate each of the following speeds in both kilometers per hour and miles per hour. In each case, assume a circular orbit; recall that the formula for the circumference of a circle is 2 X p X radius. (Hint: Divide the distance traveled in the circular orbit by the time it takes to complete one orbit.) 1. The speed of the Earth going around the Sun; use the average Earth–Sun distance of 149.6 million km. 2. The speed of our solar system around the center of our galaxy; assume that we are located 28,000 light-years from the center and that each orbit takes 230 million years. Web Projects Find useful links for Web projects on the text Web site. 1. Astronomy on the Web. The Web contains a vast amount of astronomical information. Starting from the links on the textbook Web site, spend at least an hour exploring astronomy on the Web. Write two or three paragraphs summarizing what you learned from your Web surfing. What was your favorite astronomical Web site, and why? 2. Voyage. Visit the Web site for the Voyage scalemodel solar system on the National Mall. Write a one-page summary of what you learn from your virtual tour. 3. NASA Missions. Visit the NASA Web site to learn about upcoming missions that concern astronomy. Write a one-page summary of the mission you feel is most likely to give us new astronomical information during the time you are enrolled in your astronomy course. Chapter 2 Review Questions 1. What is a constellation? How is a constellation related to a pattern of stars in the sky? The patterns of stars seen in the sky are usually called constellations. Astronomers, however, use the term constellation to refer to a specific region of the sky. Any place in the sky belongs to some constellation; familiar patterns of stars merely help locate particular constellations. For example, the constellation Orion includes all the stars in the familiar pattern of the hunter, along with the region of the sky in which these stars are found 2. What is the celestial sphere? Describe the major features shown on a model of the celestial sphere. The point directly above the Earth's North Pole is called the north celestial pole (NCP), and the point directly above the Earth's South Pole is called the south celestial pole. The celestial equator represents an extension of the Earth's equator into space celestial sphere is The imaginary sphere on which objects in the sky appear to reside when observed from Earth. 3. What is the ecliptic, and how is it related to the ecliptic plane? ecliptic is the Sun's apparent annual path among the constellations. ecliptic plane is The plane of the Earth's orbit around the Sun. The Sun, however, appears to slowly circle the celestial sphere on a simple annual path called the ecliptic; this apparent path is the projection of the ecliptic plane into space. A model of the celestial sphere typically shows the patterns of the stars, the borders of the 88 official constellations, the ecliptic, and the celestial equator and poles. 4. What is the Milky Way in our sky, and how is it related to the Milky Way Galaxy? As your eyes adapt to darkness at a dark site, you'll begin to see the whitish band of light called the Milky Way. It is from this band of light that our Milky Way Galaxy gets its name. You can see only part of the Milky Way at any particular time, but it stretches all the way around the celestial sphere. If you look carefully, you will notice that the Milky Way varies in width and has dark fissures running through it. The band of light called the Milky Way bears an important relationship to the Milky Way Galaxy: It traces the galactic plane as it appears from our location in the outskirts of the galaxy (Figure 2.6). Recall that the Milky Way Galaxy is shaped like a thin pancake with a bulge in the middle. When we look in any direction within the plane of the galaxy, we see countless stars, along with interstellar gas and dust. These stars and glowing clouds of gas form the band of light we call the Milky Way. 5. Why does the local sky look like a dome? Define horizon, zenith, and meridian. Describe how you can locate an object in the local sky by its altitude and its direction along the horizon. Picture yourself standing in a flat, open field. The sky appears to take the shape of a dome, making it easy to understand why people of many ancient cultures believed we lived on a flat Earth lying under a great dome that encompassed the world. Today, we use the appearance of a dome to define the local sky—the sky as seen from wherever you happen to be standing (Figure 2.9). The boundary between Earth and sky is what we call the horizon. The point directly overhead is your zenith. Your meridian is an imaginary half–circle stretching from your horizon due south, through your zenith, to your horizon due north. horizontal branch The horizontal line of stars that represents helium-burning stars on an H–R diagram for a cluster of stars. zenith is the point directly overhead, which has an altitude of 90. meridian is A half-circle extending from your horizon (altitude 0) due south, through your zenith, to your horizon due north. Your meridian is an imaginary half–circle stretching from your horizon due south, through your zenith, to your horizon due north. 6. Explain why we can measure only angular sizes and distances for objects in the sky. What are arcminutes and arcseconds? Because of our lack of depth perception in the sky, we cannot tell the true sizes of objects or the true distances between objects just by looking at them. For example, the Sun and the Moon look about the same size in our sky, but the Sun is actually about 400 times larger than the Moon in diameter. We can, however, measure angles in the sky. The angular size of an object like the Sun or the Moon is the angle it appears to span in your field of view. The angular distance between a pair of objects is the angle that appears to separate them. arcminutes One arcminute is 1/60 of 1. arcseconds One arcsecond is 1/60 of an arcminute, or 1/3,600 of 1. 7. Briefly describe how and why the sky varies with latitude. If you stay in one place, you'll see the same set of stars following the same paths through your sky from one year to the next. But if you travel north or south, you'll notice somewhat different sets of stars moving through the sky on somewhat different paths. This observation convinced ancient scientists that the sky must be more than a simple dome. 8. Briefly describe how and why the sky changes with the seasons. the sky changes with travel north or south. east–west travel does not change the stars visible in the sky. Seasonal Changes in the Sky The basic patterns of motion in the sky remain the same from one day to the next: The Sun, Moon, planets, and stars trace daily circles around the sky. However, if you observe the sky night after night, you will notice changes that cannot be seen over a single night. One pattern that becomes obvious after a few months is that the constellations visible at a particular time change with the seasons. For example, Orion is prominent in the evening sky in February, but by September it is visible only if you look shortly before dawn. The nighttime constellations change with the seasons because of the Earth's orbit around the Sun. As shown in Figure 2.15, at different times of year we view the Sun from different places in our orbit. As a result, the Sun appears to move steadily eastward along a circular path through the constellations each year; we've already identified this path as the ecliptic (Figure 2.4). The constellations along the ecliptic are called the constellations of the zodiac. When the Sun appears north of the celestial equator, the Sun's daily path is long and high for the Northern Hemisphere (making the long, hot days of summer) but short and low for the Southern Hemisphere (making the short, cool days of winter). The situation for the two hemispheres is reversed when the Sun appears south of the celestial equator. At any particular location, you can notice this annual change by observing the Sun's position in your sky at the same time each day 9. Describe the Moon's cycle of phases and explain why we see phases of the Moon. each day the Moon rises in the east and sets in the west. Like the Sun, the Moon also moves gradually eastward through the constellations of the zodiac. However, it takes the Moon only about a month to make a complete circuit around the celestial sphere. If you carefully observe the Moon's position relative to bright stars over just a few hours, you can notice the Moon's drift among the constellations. As the Moon moves through the sky, both its appearance and the time at which it rises and sets change with the cycle of lunar phases. Each complete cycle from one new moon to the next takes about 2½ days. We see lunar phases for the same reason. Half of the Moon is always illuminated by the Sun, but the amount of this illuminated half that we see from Earth depends on the Moon's position in its orbit. The time of day during which the Moon is visible also depends on its phase. For example, full moon occurs when the Moon is opposite the Sun in the sky, so the full moon rises around sunset, reaches the meridian at midnight, and sets around sunrise. The phases of the Moon depend on its location relative to the Sun in its orbit. 10. Why don't we see an eclipse at every new and full moon? Describe the conditions that must be met to see a solar or lunar eclipse. the lunar phases, a new moon would always block our view of the Sun, and the Earth would always prevent sunlight from reaching a full moon. if the Moon's shadow should fall on Earth during new moon and that Earth's shadow should fall on the Moon during full moon. Any time one astronomical object casts a shadow on another, we say that an eclipse is occurring. the Moon always shows nearly the same face to Earth. 11. Why are eclipses so difficult to predict? Explain the importance of eclipse seasons and the saros cycle to eclipse prediction. Any time one astronomical object casts a shadow on another, we say that an eclipse is occurring. we should have an eclipse with every new moon and every full moon—but we don't. an eclipse can occur only when the Earth, Moon, and Sun lie along a straight line, two conditions must be met simultaneously for an eclipse to occur: The nodes of the Moon's orbit must be nearly aligned with the Earth and the Sun. The phase of the Moon must be either new or full. There are two basic types of eclipse. A lunar eclipse occurs when the Moon passes through the Earth's shadow and therefore can occur only at full moon. 12. What is the apparent retrograde motion of the planets? Why was it difficult for ancient astronomers to explain but easy for us to explain? Like the Sun and the Moon, the planets appear to move slowly through the constellations of the zodiac. the Sun and the Moon always appear to move eastward relative to the stars, the planets occasionally reverse course and appear to move westward through the zodiac. A period during which a planet appears to move westward relative to the stars is called a period of apparent retrograde motion (retrograde means "backward"). a period of apparent retrograde motion for Jupiter. apparent retrograde motion Refers to the apparent motion of a planet, as viewed from Earth, during the period of a few weeks or months when it moves westward relative to the stars in our sky. Ancient astronomers could easily "explain" the daily paths of the stars through the sky by imagining that the celestial sphere was real and that it really rotated around the Earth each day. But the apparent retrograde motion of the planets posed a far greater mystery: What could cause the planets sometimes to go backwardthe ancient Greeks came up with some very clever ways to explain the occasional backward motion of the planets. But these ideas never allowed them to predict planetary positions in the sky with great accuracy (though the accuracy was sufficient for their needs at that time), because they were wedded to the incorrect idea of an Earth–centered universe. 13. What is stellar parallax? Describe the role it played in making ancient astronomers believe in an Earth-centered universe. stellar parallax is the apparent shift in the position of a nearby star (relative to distant objects) that occurs as we view the star from different positions in the Earth's orbit of the Sun each year. there were many reasons for the historic reluctance to abandon the idea of an Earth–centered universe, perhaps the most prominent involved the inability of ancient peoples to detect something called stellar parallax. Extend your arm and hold up one finger. If you keep your finger still and alternately close your left eye and right eye, your finger will appear to jump back and forth against the background. This apparent shifting, called parallax, occurs simply because your two eyes view your finger from opposite sides of your nose. Note that if you move your finger closer to your face, the parallax increases. In contrast, if you look at a distant tree or flagpole instead of your finger, you probably cannot detect any parallax by alternately closing your left eye and right eye. Thus, parallax depends on distance, with nearer objects exhibiting greater parallax than more distant objects. Discussion Questions 1. Geocentric Language. Many common phrases reflect the ancient Earth-centered view of our universe. For example, the phrase "the Sun rises each day" implies that the Sun is really moving over the Earth. In fact, the Sun only appears to rise as the rotation of the Earth carries us to a place where we can see the Sun in our sky. Identify other common phrases that imply an Earth-centered viewpoint. 2. Flat Earth Society. Believe it or not, there is an organization called the Flat Earth Society, whose members hold that the Earth is flat and that all indications to the contrary (such as pictures of the Earth from space) are fabrications made as part of a conspiracy to hide the truth from the public. Discuss the evidence for a round Earth and how you can check it for yourself. In light of the evidence, is it possible that the Flat Earth Society is correct? Defend your opinion. Problems Sensible Statements? For problems 1-8, decide whether the statement is sensible and explain why it is or is not. (For an example, see Chapter 1 problems.) 1. If you had a very fast spaceship, you could travel to the celestial sphere in about a month. 2. The constellation Orion didn't exist when my grandfather was a child. 3. When I looked into the dark fissure of the Milky Way with my binoculars, I saw what must have been a cluster of distant galaxies. 4. Last night the Moon was so big that it stretched for a mile across the sky. 5. I live in the United States, and during my first trip to Argentina I saw many constellations that I'd never seen before. 6. Last night I saw Jupiter right in the middle of the Big Dipper. (Hint: Is the Big Dipper part of the zodiac?) 7. Last night I saw Mars move westward through the sky in its apparent retrograde motion. (Hint: How long does it take to notice apparent retrograde motion?) 8. Although all the known stars appear to rise in the east and set in the west, we might someday discover a star that will appear to rise in the west and set in the east. 9. View from Afar. Describe how the Milky Way Galaxy would look in the sky of someone observing from a planet around a star in M31. 10. Your View. 1. Find your latitude and longitude, and state the source of your information. 2. Describe the altitude and direction in your sky at which the north or south celestial pole appears. 3. Is Polaris a circumpolar star in your sky? Explain. 4. Describe the path of the meridian in your sky. 5. Describe the path of the celestial equator in your sky. (Hint: Study Figure 2.12.) 11. View from the Moon. Suppose you lived on the Moon, near the center of the face that we see from Earth. 1. During the phase of full moon, what phase would you see for Earth? Would it be daylight or dark where you live? 2. On Earth, we see the Moon rise and set in our sky each day. If you lived on the Moon, would you see the Earth rise and set? Why or why not? (Hint: Remember that the Moon always keeps the same face toward Earth.) 3. What would you see when people on Earth were experiencing an eclipse? Answer for both solar and lunar eclipses. 12. A Farther Moon. Suppose the distance to the Moon was twice its actual value. Would it still be possible to have a total solar eclipse? An annular eclipse? A total lunar eclipse? Explain. 13. A Smaller Earth. Suppose the Earth was smaller in size. Would solar eclipses be any different? If so, how? What about lunar eclipses? Explain. 14. Observing Planetary Motion. Find out what planets are currently visible in your evening sky. At least once a week, observe the planets and draw a diagram showing the position of each visible planet relative to stars in a zodiac constellation. From week to week, note how the planets are moving relative to the stars. Can you see any of the apparently "erratic" features of planetary motion? Explain. 15. A Connecticut Yankee. Find the book A Connecticut Yankee in King Arthur's Court, by Mark Twain. Read the portion that deals with the Connecticut Yankee's prediction of an eclipse (or read the entire book). In a one- to two-page essay, summarize the episode and how it helps the Connecticut Yankee gain power. Web Projects Find useful links for Web projects on the text Web site. 1. Sky Information. Search the Web for sources of daily information about sky phenomena (such as lunar phases, times of sunrise and sunset, and unusual sky events). Identify and briefly describe your favorite source. 2. Constellations. Search the Web for information about the constellations and their mythology. Write a short report about one or more constellations. 3. Upcoming Eclipse. Find information about an upcoming solar or lunar eclipse that you might have a chance to witness. Write a short report about how you could best witness the eclipse, including any necessary travel to a viewing site, and what you can expect to see. Bonus: Describe how you could photograph the eclipse. Chapter 3 Review Questions 1. In what ways is scientific thinking a fundamental part of human nature? What characteristics does the modern scientific method possess that go beyond this everyday type of thinking? Through power of observation. Observing, and thinking when a helium balloon is inflated and rises into the sky. experience with falling objects and balloons exemplifies scientific thinking, which, in essence, is a way of learning about nature through careful observation and trial-and-error experiments. Rather than thinking differently than other people, modern scientists simply are trained to organize this everyday thinking in a way that makes it easier for them to share their discoveries and employ their collective wisdom. 2. Explain how the people of central Africa predicted the weather by observing the Moon. Our exploration begins in central Africa, where people of many indigenous societies predict the weather with reasonable accuracy by making careful observations of the Moon. The Moon begins its monthly cycle as a crescent in the western sky just after sunset. Through long traditions of sky watching, central African societies learned that the orientation of the crescent "horns" relative to the horizon is closely tied to rainfall patterns. Africans first developed the ability to predict weather using the lunar crescent. But the earliest-known written astronomical record comes from central Africa near the border of modern-day Congo and Uganda. It consists of an animal bone (known as the Ishango bone) etched with patterns that appear to be part of a lunar calendar, probably carved around 6500 b.c. 3. How are the names of the seven days of the week related to astronomical objects? Our 24-hour day is the time it takes the Sun to circle our sky. The length of a month comes from the lunar cycle, and our calendar year is based on the cycle of the seasons. The days of the week are named after the seven naked-eye objects that appear to move among the constellations: the Sun, the Moon, and the five planets recognized in ancient times The positions of the stars also indicate the time if you know the approximate date. For example, in December the constellation Orion rises around sunset, reaches the meridian around midnight, and sets around sunrise. if it is winter and Orion is setting, dawn must be approaching. Most ancient peoples probably were adept at estimating the time of night, although written evidence is sparse. Determining the Time of Day In the daytime, ancient peoples could tell time by observing the Sun's path through the sky. Many cultures probably used the shadows cast by sticks as simple sundials [Section S1.2]. The ancient Egyptians built huge obelisks, often inscribed or decorated in homage to the Sun, that probably also served as simple clocks 4. Briefly explain how the ancient Egyptians determined the time of day or night. By about 1500 b.c., Egyptians had abandoned star clocks in favor of clocks that measure time by the flow of water through an opening of a particular size, just as hourglasses measure time by the flow of sand through a narrow neck.(*footnote) These water clocks had the advantage of being useful even when the sky was cloudy, and they eventually became the primary timekeeping instruments for many cultures, including the Greeks, Romans, and Chinese. The water clocks, in turn, were replaced by mechanical clocks in the 1600s and by electronic clocks in the twentieth century. Despite the availability of other types of clocks, sundials remained in use throughout ancient times and are still popular today both for their decorative value and as reminders that the Sun and stars once were our only guides to time. The Egyptian "hours" were not a fixed amount of time because the amount of daylight varies during the year. For example, "summer hours" were longer than "winter hours," because one-twelfth of the daylight lasts longer in summer than in winter. Only much later in history did the hour become a fixed amount of time, subdivided into 60 equal minutes, each consisting of 60 equal seconds. The Egyptians also divided the night into 12 equal parts, and early Egyptians used the stars to determine the time at night. Egyptian star clocks, often found painted on the coffin lids of Egyptian pharaohs, essentially cataloged where particular stars appear in the sky at particular times of night and particular times of year. By knowing the date from their calendar and observing the positions of particular stars in the sky, the Egyptians could use the star clocks to estimate the time of night. 5. Briefly describe the astronomical uses of each of the following: Stonehenge, the Templo Mayor, the Sun Dagger, the Mayan observatory at Chichén Itzá, lines in the Nazca desert, Pawnee lodges, the Big Horn Medicine Wheel. Many cultures built structures to help them mark the seasons. One of the oldest standing human-made structures served such a purpose: Stonehenge in southern England, which was constructed in stages from about 2750 b.c. to about 1550 b.c. Observers standing in its center see the Sun rise directly over the Heel Stone only on the summer solstice. Stonehenge also served as a social gathering place and probably as a religious site; no one knows whether its original purpose was social or astronomical. Perhaps it was built for both—in ancient times, social rituals and practical astronomy probably were deeply intertwined. scale model shows the Templo Mayor and the surrounding plaza as they are thought to have looked before Aztec civilization was destroyed by the Conquistadors. One of the most spectacular structures used to mark the seasons was the Templo Mayor in the Aztec city of Tenochtitlán, located on the site of modern-day Mexico City (Figure 3.4). Twin temples surmounted a flat-topped, 150-foot-high pyramid. From the location of a royal observer watching from the opposite side of the plaza, the Sun rose directly through the notch between the twin temples on the equinoxes. Like Stonehenge, the Templo Mayor served important social and religious functions in addition to its astronomical role. Before it was destroyed by the Conquistadors, other Spanish visitors reported stories of elaborate rituals, sometimes including human sacrifice, that took place at the Templo Mayor at times determined by astronomical observations. The Sun Dagger is an arrangement of rocks that shape the Sun's light into a dagger, with a spiral carved on a rock face behind them. The dagger pierces the center of the carved spiral each year at noon on the summer solstice.b The Sun Dagger is located on a vertical cliff face high on this butte in New Mexico. Many cultures also made careful observations of the planets and stars. Mayan observatories in Central America, such as the one still standing at Chichen Itza had windows strategically placed for observations of Venus. Observational aids could also mark the rising and setting of the stars. More than 800 lines, some stretching for miles, are etched in the dry desert sand of Peru between the Ingenio and Nazca Rivers. Many of these lines may simply have been well-traveled pathways, but others are aligned in directions that point to places where bright stars or the Sun rose at particular times of year. In addition to the many straight lines, the desert features many large figures of animals, which may be representations of constellations made by the Incas who lived in the region Structures for astronomical observation also were popular in North America. Lodges built by the Pawnee people in Kansas featured strategically placed holes for observing the passage of constellations that figured prominently in their folklore. In the northern plains of the United States, Native American Medicine Wheels probably were designed for astronomical observations. The "spokes" of the Medicine Wheel at Big Horn, Wyoming, were aligned with the rising and setting of bright stars, as well as with the rising and setting of the Sun on the equinoxes and solstices (Figure 3.9). The 28 spokes of the Medicine Wheel probably relate to the month of the Native Americans, which they measured as 28 days (rather than 29 or 30 days) because they did not count the day of the new moon. Aerial and ground view of the Big Horn Medicine Wheel in Wyoming. Note the 28 "spokes" radiating out from the center. These spokes probably relate to the month of the Native Americans. Before a structure such as Stonehenge could be built, careful observations had to be made and repeated over and over to ensure their validity. Careful, repeatable observations also underlie the modern scientific method. To this extent, elements of modern science were present in many early human cultures. 6. Explain why the Muslim fast of Ramadan occurs earlier with each subsequent year. 7. What is the Metonic cycle? How does the Jewish calendar follow the Metonic cycle? How does this influence the date of Easter? The Metonic cycle can be used to keep lunar calendars fairly closely synchronized with solar calendars, but only if the lunar calendar has 7 extra lunar months in every 19 years. To see why, recall that each cycle of lunar phases takes an average of 29.53 days the synodic month. A 12-month lunar calendar has 12 X 29.53 = 354.36 days, or about 11 days less than our 365-day solar calendar. If the new year on a 12-month lunar calendar occurs this year on October 1, next year it will occur 11 days earlier, on September 20; the following year it will occur 11 days before that, on September 9; and so on. Without using the Metonic cycle, over many years the lunar new year would move all the way around the solar calendar. The Metonic cycle is a period of 19 years on a solar calendar, which is almost precisely 235 months on a lunar calendar. For a lunar calendar roughly synchronized to remain a solar calendar, it must have exactly 235 months in each 19-year period. Because a 12-month lunar calendar has a total of only 19 X 12 = 228 months in 19 years, the lunar calendar needs 7 extra months to reach the required 235 months. One way to accomplish this is to have 7 years with a thirteenth lunar month in every 19-year cycle, as is the case for the Jewish calendar. The Jewish calendar follows the Metonic cycle, adding a thirteenth month in the third, sixth, eighth, eleventh, fourteenth, seventeenth, and nineteenth years of each cycle. This also explains why the date of Easter changes each year: The New Testament ties the date of Easter to the Jewish festival of Passover, which has its date set by the Jewish lunar calendar. In a slight modification of the original scheme, most Western Christians now celebrate Easter on the first Sunday after the first full moon after March 21; if the full moon falls on Sunday, Easter is the following Sunday. (Eastern Orthodox churches calculate the date of Easter differently, because they base the date on the Julian rather than the Gregorian calendar. 8. What role did the Navigator play in Polynesian society? Perhaps the people most dependent on knowledge of the stars were the Polynesians, who lived and traveled among the many islands of the mid- and South Pacific. Because the next island in a journey usually was too distant to be seen, poor navigation meant becoming lost at sea. As a result, the most esteemed position in Polynesian culture was that of the Navigator, a person who had acquired the detailed knowledge necessary to navigate great distances among the islands. The Navigators employed a combination of detailed knowledge of astronomy and equally impressive knowledge of the patterns of waves and swells around different islands. The stars provided their broad navigational sense, pointing them in the correct direction of their intended destination. As they neared a destination, the wave and swell patterns guided them to their precise landing point. The Navigator memorized all his skills and passed them to the next generation through a well-developed program for training future Navigators. Unfortunately, with the advent of modern navigational technology, many of the skills of the Navigators have been lost. 9. What was the Library of Alexandria? What role did it play in the ancient empires of Greece and Rome? Great Hall and a scroll room of the Library of Alexandria. the Library of Alexandria held more than a half million books, handwritten on papyrus scrolls. As the invention of the printing press was far in the future, most of the scrolls probably were original manuscripts or the single copies of original manuscripts. When the library was destroyed, most of its storehouse of ancient wisdom was lost forever. 10. What do we mean by a model of nature? Explain how the celestial sphere represents such a model. the Greeks soon learned that the simple idea of a celestial sphere could not explain all the phenomena they saw in the sky (particularly the apparent retrograde motion of the planets). They therefore added spheres for the Sun, the Moon, and each of the planets and continued to change their ideas of how the spheres moved in an ongoing attempt to make the model agree with reality. 11. Who was Ptolemy? Briefly describe how the Ptolemaic model of the universe explains apparent retrograde motion while preserving the idea of an Earth-centered universe. The culmination of this ancient modeling came with the work of Claudius Ptolemy (c. a.d. 100–170), pronounced tol-e-mee. Ptolemy's model of the universe is a tribute to human ingenuity in that it made reasonably accurate predictions despite being built on the flawed premise of an Earth-centered universe. Following a Greek tradition dating back to Plato (428–348 b.c.), Ptolemy imagined that all heavenly motions must proceed in perfect circles. To explain the apparent retrograde motion of planets, Ptolemy used an idea first suggested by Apollonius (c. 240–190 b.c.) and further developed by Hipparchus (c. 190–120 b.c.). This idea held that each planet moved along a small circle that, in turn, moved around a larger circle (Figure 3.16). As seen from Earth, this "circle upon circle" motion meant that a planet usually moved eastward relative to the stars but sometimes moved westward in apparent retrograde motion. This diagram shows several key features of Ptolemy's model of the motions of the Sun, Moon, and planets around the Earth. The planets move around the small circles at the same time that these circles move around the Earth. By careful selection of the sizes of the circles and the rates at which planets moved, along with a few other adjustments, this model was used to predict planetary positions, including apparent retrograde motion, for 1,500 years. In order to show the circle-upon-circle idea clearly, this diagram exaggerates several features of the true Ptolemaic model; for example, for each retrograde loop, Mars moves much farther in the actual model than shown here. 12. Briefly describe the role played by Islamic scholars of the Middle Ages in the development of modern science. The Babylonians invented methods of writing on clay tablets and developed arithmetic to serve in commerce and later in astronomical calculations. the Greek astronomer and geographer Eratosthenes (c. 276–196 b.c.) estimated the size of the Earth in about 240 b.c. He did it by comparing the altitude of the Sun on the summer solstice in the Egyptian cities of Syene (modern-day Aswan) and Alexandria 13. Describe the basic process of the scientific method. What is the role of a model in this method? What do we mean by facts when discussing science? Theories can be proved false, however, if they fail to account for observed or experimental facts. Theories can be proved false, however, if they fail to account for observed or experimental facts. Birds fly up into the air but eventually come back down. some rockets are launched into space and never return to Earth. What goes up must come down. 14. Briefly describe how science differs from pseudoscience and nonscience. The word science comes from the Latin scientia, meaning "knowledge"; it is also the root of the words conscience (related to the idea of self-knowledge or self-awareness) and omniscience (the quality of being all-knowing). Today, science connotes a special kind of knowledge: the kind that makes predictions that can be confirmed by rigorous observations and experiments. In brief, the modern scientific method is an organized approach to explaining observed facts with a model of nature, subject to the constraint that any proposed model must be testable and the provision that the model must be modified or discarded if it fails these tests. science The search for knowledge that can be used to explain or predict natural phenomena in a way that can be confirmed by rigorous observations or experiments. pseudoscience Something that purports to be science or may appear to be scientific but that does not adhere to the testing and verification requirements of the scientific method. By pseudoscience we mean attempts to search for knowledge in ways that may at first seem scientific but do not adhere to the testing and verification requirements of the scientific method; the prefix pseudo means "false." For example, at the beginning of each year you can find tabloid newspapers offering predictions made by people who claim to be able to "see" the future. Because they make specific predictions, we can test their claims by checking whether their predictions come true, and numerous studies have shown that their predictions come true no more often than would be expected by pure chance. But these seers seem unconcerned with the results of such studies. The fact that they make testable claims but then ignore the results of the tests marks their claimed ability to see the future as pseudoscience. 15. Briefly explain how science as a whole can be objective even while individual scientists have personal biases and beliefs. the scientific method begins with a set of observed facts. A fact is supposed to be a statement that is objectively true. For example, we consider it a fact that the Sun rises each morning, that the planet Mars appeared in a particular place in our sky last night, and that the Earth rotates. Facts are not always obvious, as illustrated by the case of the Earth's rotation—for most of human history, the Earth was assumed to be stationary at the center of the universe. facts often are based on beliefs about the world that others might not share. For example, when we say that the Sun rises each morning, we assume that it is the same Sun day after day—an idea that might not have been accepted by ancient Egyptians, whose mythology held that the Sun died with every sunset and was reborn with every sunrise. Nevertheless, facts are the raw material that scientific models seek to explain, so it is important that scientists agree on the facts. In the context of science, a fact must therefore be something that anyone can verify for himself or herself, at least in principle. scientists eventually made plenty of observations to verify the planetary positions predicted by his model. In that sense, the scientific method represents an ideal prescription for judging objectively whether a proposed model of nature is close to the truth. For example, in the late nineteenth and early twentieth centuries, some astronomers claimed to see networks of "canals" in their blurry telescopic images of Mars, and they hypothesized that Mars was home to a dying civilization that used the canals to transport water to thirsty cities. Because no such canals actually exist, these astronomers apparently were allowing their beliefs to influence how they interpreted blurry images. It was, in essence, a form of cheating—even though it certainly was not intentional. 16. Briefly describe the international character of modern astronomy. The abundance of new data is disseminated worldwide via the Internet, and new data are collected at international observatories in many different countries and in space. The result is that, after a few centuries during which advances in astronomy were made primarily in Europe and the United States, astronomy is once again a worldwide endeavor. Just as the ancient civilizations of Egypt and Mesopotamia benefited from the cross-fertilization of ideas brought by people of many different cultures, astronomy today is benefiting from the great variety of perspectives of scientists from all over the world. 17. What is the basic tenet of astrology? Why might this idea have seemed quite reasonable in ancient times? What role did astrology play in the development of astronomy? astrology played an important role in the historical development of astronomy. In brief, the basic tenet of astrology is that human events are influenced by the apparent positions of the Sun, Moon, and planets among the stars in our sky. The origins of this idea are easy to understand. After all, there is no doubt that the position of the Sun in the sky influences our lives it determines the seasons and the times of planting and harvesting, of warmth and cold, and of daylight and darkness. Similarly, the Moon determines the tides, and the cycle of lunar phases coincides with many biological cycles. Because the planets also appear to move among the stars, it seemed reasonable that planets also influence our lives, even if these influences were much more difficult to discover. Astrology's Role in Astronomical History Because forecasts of the seasons and forecasts of human events were imagined to be closely related, astrologers and astronomers usually were one and the same in the ancient world. For example, in addition to his books on astronomy, Ptolemy published a treatise on astrology called Tetrabiblios that remains the foundation for much of astrology today. Interestingly, Ptolemy himself recognized that astrology stood upon a far shakier foundation than astronomy. In the introduction to Tetrabiblios, Ptolemy compared astronomical and astrological predictions: Astronomy, which is first both in order and effectiveness, is that whereby we apprehend the aspects of the movements of sun, moon, and stars in relation to each other and to the earth. I shall now give an account of the second and less sufficient method of prediction astrology in a proper philosophical way, so that one whose aim is the truth might never compare its perceptions with the sureness of the first, unvarying science. Other ancient scientists probably likewise recognized that their astrological predictions were far less reliable than their astronomical ones. 18. How do we make scientific tests of astrology? What have such tests found? Scientific Tests of Astrology Today, different astrologers follow different practices, which makes it difficult even to define astrology. Some astrologers no longer claim any ability to make testable predictions and therefore are practicing a form of nonscience—which modern science can say nothing about. However, for most astrologers the business of astrology is casting horoscopes. Horoscopes often are cast for individuals and either predict future events in the person's life or describe characteristics of the person's personality and life. If the horoscope predicts future events, it can be evaluated by whether the predictions come true. If it describes the person's personality and life, the description can be checked for accuracy. A scientific test of astrology requires evaluating many horoscopes and comparing their accuracy to what would be expected by pure chance. For example, suppose a horoscope states that a person's best friend is female. Because that is true of roughly half the population in the United States, an astrologer who casts 100 such horoscopes would be expected by pure chance to be right about 50 times. Thus, we would be impressed with the predictive ability of the astrologer only if he or she were right much more often than 50 times out of 100. In hundreds of scientific tests, astrological predictions have never proved to be accurate by a substantially greater margin than expected from pure chance.(*footnote) Similarly, in tests in which astrologers are asked to cast horoscopes for people they have never met, the horoscopes fail to correctly match personalities any more often than expected by chance. The verdict is clear: The methods of astrology are useless for predicting the past, the present, or the future. What about newspaper horoscopes, which often appear to ring true? If you read them carefully, you will find that these horoscopes generally are so vague as to be untestable. For example, a horoscope that says "It is a good day to spend time with your friends" doesn't offer much for testing. Indeed, if you read the horoscopes for all 12 astrological signs, you'll probably find that several of them apply equally well to you. In science, observations and experiments are the ultimate judge of any idea. Astrology also places great importance on the positions of the planets among the constellations. The planets revolve rotate around the sun star. Discussion Questions 1. The Impact of Science. The modern world is filled with ideas, knowledge, and technology that developed through science and application of the scientific method. Discuss some of these things and how they affect our lives. Which of these impacts do you think are positive? Which are negative? Overall, do you think science has benefited the human race? Defend your opinion. 2. The Importance of Ancient Astronomy. Why was astronomy important to people in ancient times? Discuss both the practical importance of astronomy and the importance it may have had for religious or other traditions. Which do you think was more important in the development of ancient astronomy, its practical or its philosophical role? Defend your opinion. 3. Secrecy and Science. The text mentions that some historians believe that Chinese science and technology fell behind that of Europe because of the Chinese culture of secrecy. Do you agree that secrecy can hold back the advance of science? Why or why not? For the past 200 years, the United States has allowed a greater degree of free speech than most other countries in the world. How great a role do you think this has played in making the United States the world leader in science and technology? Defend your opinion. 4. Lunar Cycles. We have now discussed four distinct lunar cycles: the 29½-day cycle of phases, the 18-year-11 1/3 -day saros cycle, the 19-year Metonic cycle, and the 18.6-year cycle over which a full moon rises at its most southerly place along the horizon. Discuss how each of these cycles can be observed and the role each cycle has played in human history. 5. Astronomy and Astrology. Why do you think astrology remains so popular around the world even though it has failed all scientific tests of its validity? Do you think the popularity of astrology has any positive or negative social consequences? Defend your opinions. Problems True Statements? For problems 1–6, decide whether the statements are true or false and clearly explain how you know. 1. If we defined hours as the ancient Egyptians did, we'd have the longest hours on the summer solstice and the shortest hours on the winter solstice. 2. The date of Christmas (December 25) is set each year according to a lunar calendar. 3. When navigating in the South Pacific, the Polynesians found their latitude with the aid of the pointer stars of the Big Dipper. 4. The Ptolemaic model reproduced apparent retrograde motion by having planets move sometimes counterclockwise and sometimes clockwise in their circles. 5. In science, saying that something is a theory means that it is really just a guess. 6. Ancient astronomers were convinced of the validity of astrology as a tool for predicting the future. 7. Cultural Astronomy. Choose a particular culture of interest to you, and research the astronomical knowledge and accomplishments of that culture. Write a two- to three-page summary of your findings. 8. Astronomical Structures. Choose an ancient astronomical structure of interest to you (e.g., Stonehenge, Nazca lines, Pawnee lodges) and research its history. Write a two- to three-page summary of your findings. If possible, also build a scale model of the structure or create detailed diagrams to illustrate how the structure was used. 9. Venus and the Mayans. The planet Venus apparently played a particularly important role in Mayan society. Research the evidence and write a one- to two-page summary of current knowledge about the role of Venus in Mayan society. 10. Scientific Test of Astrology. Find out about at least one scientific test that has been conducted to test the validity of astrology. Write a short summary of how the test was conducted and what conclusions were reached. 11. Your Own Astrological Test. Devise your own scientific test of astrology. Clearly define the methods you will use in your test and how you will evaluate the results. Then carry out the test. Web Projects Find useful links for Web projects on the text Web site. 1. Easter. Find out when Easter is celebrated by different sects of Christianity. Then research how and why different sects set different dates for Easter. Summarize your findings in a one- to two-page report. 2. Greek Astronomers. Many ancient Greek scientists had ideas that, in retrospect, seem well ahead of their time. Choose one or more of the following ancient Greek scientists, and learn enough about their work in science and astronomy to write a one- to two-page "scientific biography." Thales Anaximander Pythagoras Anaxagoras Empedocles Democritus Meton Plato Eudoxus Aristotle Callipus Aristarchus Archimedes Eratosthenes Apollonius Hipparchus Seleucus Ptolemy Hypatia 3. The Ptolemaic Model. This chapter gives only a very brief description of Ptolemy's model of the universe. Investigate the model in greater depth. Using diagrams and text as needed, give a two- to three-page description of the model Chapter 4 Review Questions 1. Briefly describe and differentiate between kinetic energy, potential energy, and radiative energy. kinetic energy is a Energy of motion, given by the formula mv2. potential energy Energy stored for later conversion into kinetic energy; includes gravitational potential energy, electrical potential energy, and chemical potential energy. radiative energy Energy carried by light; the energy of a photon is Planck's constant times its frequency, or hf. First, whenever matter is moving, it has energy of motion, or kinetic energy (kinetic comes from a Greek word meaning "motion"). Falling rocks, the moving blades on an electric mixer, a car driving down the highway, and the molecules moving in the air around us are all examples of objects with kinetic energy. The second basic category of energy is potential energy, or energy being stored for later conversion into kinetic energy. A rock perched on a ledge has gravitational potential energy because it will fall if it slips off the edge. Gasoline contains chemical potential energy, which a car engine converts to the kinetic energy of the moving car. Power companies supply electrical potential energy, which we use to run dishwashers and other appliances. The third basic category is energy carried by light, or radiative energy (the word radiation is often used as a synonym for light). Plants directly convert the radiative energy of sunlight into chemical potential energy through the process of photosynthesis. Radiative energy is fundamental to astronomy, because telescopes collect the radiative energy of light from distant stars. 2. What is the formula for the kinetic energy of an object? Based on this formula, explain why (a) a 4-ton truck moving at 100 km/hr has 4 times as much kinetic energy as a 1-ton car moving at 100 km/hr; (b) a 1-ton car moving at 100 km/hr has the same kinetic energy as a 4-ton truck moving at 50 km/hr. Kinetic Energy We can calculate the kinetic energy of any moving object with a very simple formula: Kinetic Energy = 1 mv 2 2 where m is the mass of the object and v is its speed (v for velocity). If we measure the mass in kilograms and the speed in meters per second, the resulting answer will be in joules. energy has units of a mass times a velocity squared, so 1 joule = 1 (kg X m2)/s2. The kinetic energy formula is easy to interpret. The m in the formula tells us that kinetic energy is proportional to mass: A 5-ton truck has 5 times the kinetic energy of a 1-ton car moving at the same speed. The v 2 tells us that kinetic energy increases with the square of the velocity: If you double your speed (e.g., from 30 km/hr to 60 km/hr), your kinetic energy becomes 22 = 4 times greater. 3. What does temperature measure? How is it related to kinetic energy? What is thermal energy? How hot the water is. How cold the water is. Three temperature scales are commonly used today (Figure 4.2). In the United States, we usually use the Fahrenheit scale, defined so that water freezes at 32°F and boils at 212°F. Internationally, temperature is usually measured on the Celsius scale, which places the freezing point of water at 0°C and the boiling point at 100°C. Scientists measure temperature on the Kelvin scale, which is the same as the Celsius scale except for its zero point. A temperature of 0 K is the coldest possible temperature, known as absolute zero; it is equivalent to –273.15°C. (The degree symbol ° is not used when writing temperatures on the Kelvin scale.) any particular temperature has a Kelvin value that is numerically 273.15 larger than its Celsius value. Using T to stand for temperature. To find the conversion between Fahrenheit and Celsius, note that the Fahrenheit scale has 180° (212°F – 32°F = 180°F) between the freezing and boiling points of water, whereas the Celsius scale has only 100° between these points. Thermal Energy Suppose we want to know about the kinetic energy of the countless tiny particles (atoms and molecules) inside a rock or of the countless particles in the air or in a distant star. Each of these tiny particles has its own motion relative to surrounding particles, and these motions constantly change as the particles jostle one another. The result is that the particles inside a substance appear to move randomly: Any individual particle may be moving in any direction with any of a wide range of speeds. Despite the seemingly random motion of particles within a substance, it's easy to measure the average kinetic energy of the particles—temperature is a measure of this average. A higher temperature simply means that, on average, the particles have more kinetic energy are moving faster. Kinetic energy depends on both mass and speed, but for a particular set of particles, greater kinetic energy means higher speeds. The speeds of particles within a substance can be surprisingly fast. For example, the air molecules around you move at typical speeds of about 500 meters per second (about 1,000 miles per hour). The energy contained within a substance as measured by its temperature is often called thermal energy. thermal energy Represents the collective kinetic energy, as measured by temperature, of the many individual particles moving within a substance. 4. Briefly describe how a 500°F oven and a pot of boiling water illustrate the difference between temperature and heat. How is this difference important to astronauts in Earth orbit? Suppose you heat your oven to 500°F. Then you open the oven door, quickly thrust your arm inside (without touching anything), and immediately remove it. What will happen to your arm? Not much. Now suppose you boil a pot of water. Although the temperature of boiling water is only 212°F, you would be badly burned if you put your arm in the pot, even for an instant. Thus, the water in the pot transfers more thermal energy to your arm than does the air in the oven, even though it has a lower temperature. That is, your arm heats more quickly in the water. This is because thermal energy content depends on both the temperature and the total number of particles, which is much larger in a pot of water. The oven is hotter than the boiling pot of water. FIGURE 4.4 (click image to enlarge) Both boxes have the same temperature, but the box on the right contains more thermal energy because it contains more particles. 5. What is gravitational potential energy? How does an object's gravitational potential energy depend on its mass, the distance it has to fall, and the strength of gravity? Gravitational Potential EnergyGravitational potential energy is extremely important in astronomy. The conversion of gravitational potential energy into kinetic (or thermal) energy helps explain everything from the speed at which an object falls to the ground to the formation processes of stars and planets. The mathematical formula for gravitational potential energy can take a variety of forms, but in words the idea is simple: The amount of gravitational potential energy released as an object falls depends on its mass, the strength of gravity, and the distance it falls. This statement explains the obvious fact that falling from a 10-story building hurts more than falling out of a chair. Your gravitational potential energy is much greater on top of the 10-story building than in your chair because you can fall much farther. Because your gravitational potential energy will be converted to kinetic energy as you fall, you'll have a lot more kinetic energy by the time you hit the ground after falling from the building than after falling from the chair, which means you'll hit the ground much harder. Gravitational potential energy also helps us understand how the Sun became hot enough to sustain nuclear fusion. Before the Sun formed, its matter was contained in a large, cold, diffuse cloud of gas. Most of the individual gas particles were far from the center of this large cloud and therefore had considerable amounts of gravitational potential energy. As the cloud collapsed under its own gravity, the gravitational potential energy of these particles was converted to thermal energy, eventually making the center of the cloud hot enough to ignite nuclear fusion. astronauts working in Earth orbit (e.g., outside the Space Shuttle) tend to get very cold and therefore use heated space suits and gloves. The astronauts feel cold despite the high temperature because the extremely low density of space means that relatively few particles are available to transfer thermal energy to an astronaut. (You may wonder how the astronauts become cold given that the low density also means the astronauts cannot transfer much of their own thermal energy to the particles in space. It turns out that they lose their body heat by emitting thermal radiation. 6. What do we mean by mass-energy? Explain the meaning of the formula E = mc 2 and what it has to do with the Sun, nuclear bombs, and particle accelerators. mass-energy is the potential energy of mass, which has an amount E = mc2. Mass-EnergyAlthough matter and energy seem very different in daily life, they are intimately connected. Einstein showed that mass itself is a form of potential energy, often called mass-energy. The mass-energy of any piece of matter is given by the formula E = mc 2 where E is the amount of potential energy, m is the mass of the object, and c is the speed of light. If the mass is measured in kilograms and the speed of light in meters per second, the resulting mass-energy has units of joules. Note that the speed of light is a large number (c = 3 X 108 m/s) and the speed of light squared is much larger still (c 2 = 9 X 1016 m2/s2). Thus, Einstein's formula implies that a relatively small amount of mass represents a huge amount of mass-energy. Mass-energy can be converted to other forms of energy 7. What is the law of conservation of energy? Your body is using energy right now to keep you alive. Where does this energy come from? Where does it go? Conservation of Energy A fundamental principle in science is that, regardless of how we change the form of energy, the total quantity of energy never changes. This principle is called the law of conservation of energy. It has been carefully tested in many experiments, and it is a pillar upon which modern theories of the universe are built. Because of this law, the story of the universe is a story of the interplay of energy and matter: All actions in the universe involve exchanges of energy or the conversion of energy from one form to another. For example, imagine that you've thrown a baseball so that it is moving and has kinetic energy. Where did this kinetic energy come from? The baseball got its kinetic energy from the motion of your arm as you threw it; that is, some of the kinetic energy of your moving arm was transferred to the baseball. Your arm, in turn, got its kinetic energy from the release of chemical potential energy stored in your muscle tissues. Your muscles got this energy from the chemical potential energy stored in the foods you ate. The energy stored in the foods came from sunlight, which plants convert into chemical potential energy through photosynthesis. The radiative energy of the Sun was generated through the process of nuclear fusion, which releases some of the mass-energy stored in the Sun's supply of hydrogen. Thus, the ultimate source of the energy of the moving baseball is the mass-energy stored in hydrogen—which was created in the Big Bang. The process of nuclear fusion in the core of the Sun converts some of the Sun's mass into energy, ultimately generating the sunlight that sustains most life on Earth. In nuclear reactors, the splitting (fission) of elements such as uranium or plutonium converts some of the mass-energy of these materials into heat, which is then used to generate electrical power. In an H-bomb, nuclear fusion similar to that in the Sun uses a small amount of the mass-energy in hydrogen to devastating effect. Incredibly, a 1-megaton H-bomb that could destroy a major city requires the conversion of only about 0.1 kilogram of mass about 3 ounces into energy. 8. Briefly define atom, element, and molecule. How was Democritus's idea of atoms similar to the modern concept of atoms? How was it different? atoms Consist of a nucleus made from protons and neutrons surrounded by a cloud of electrons. element (chemical) A substance made from individual atoms of a particular atomic number. molecule Technically the smallest unit of a chemical element or compound; in this text, the term refers only to combinations of two or more atoms held together by chemical bonds. two basic properties of matter on Earth from everyday experience. First, matter can exist in different phases: as a solid, such as ice or a rock; as a liquid, such as flowing water or oil; or as a gas, such as air. Second, even in a particular phase, matter exists in a great variety of different substances. What is matter, and why does it have so many different forms? Let's follow the lead of the ancient Greek philosopher Democritus (c. 470–380 b.c.), who wondered what would happen if we broke a piece of matter, such as a rock, into ever smaller pieces. Democritus believed that the rock would eventually break into particles so small that nothing smaller could be possible. He called these particles atoms, a Greek term meaning "indivisible." (By modern definition, atoms are not indivisible because they are composed of smaller particles.) Building upon the beliefs of earlier Greek scientists, Democritus thought that all materials were composed of just four basic elements: fire, water, earth, and air. He proposed that the different properties of the elements could be explained by the physical characteristics of their atoms. Democritus suggested that atoms of water were smooth and round, so water flowed and had no fixed shape, while burns were painful because atoms of fire were thorny. He imagined atoms of earth to be rough and jagged, like pieces of a three-dimensional jigsaw puzzle, so that they could stick together to form a solid substance. He even explained the creation of the world with an idea that sounds uncannily modern, suggesting that the universe began as a chaotic mix of atoms that slowly clumped together to form the Earth. Although Democritus was wrong about there being only four types of atoms and about their specific properties, his general idea was right. Today, we know that all ordinary matter is composed of atoms and that each different type of atom corresponds to a different chemical element. 9. What is electrical charge? What type of electrical charge is carried by protons, neutrons, and electrons? Under what circumstances do electrical charges attract? Under what circumstances do they repel? The properties of an atom depend mainly on the amount of electrical charge in its nucleus. Electrical charge is a fundamental physical property that is always conserved, just as energy is always conserved. Electrons carry a negative electrical charge of –1, protons carry a positive electrical charge of +1, and neutrons are electrically neutral. Oppositely charged particles attract one another, and similarly charged particles repel one another. The attraction between the positively charged protons in the nucleus and the negatively charged electrons that surround it is what holds an atom together. Ordinary atoms have identical numbers of electrons and protons, making them electrically neutral overall. electron-volt (eV) A unit of energy equivalent to 1.60 10–19 joule. electroweak era The era of the universe during which only three forces operated (gravity, strong force, and electroweak force), lasting from 10–38 second to 10–10 second after the Big Bang. electroweak force The force that exists at high energies when the electromagnetic force and the weak force exist as a single force. 10. Briefly describe the structure of an atom. How big is an atom? How big is the nucleus in comparison to the entire atom? electrons can be thought of as tiny particles, they are not quite like tiny grains of sand, and they don't really orbit the nucleus as planets orbit the Sun. Instead, the electrons in an atom are "smeared out," forming a kind of cloud that surrounds the nucleus and gives the atom its apparent size. The electrons aren't really cloudy; it's just that it is impossible to pinpoint their positions. An atomic nucleus is very tiny, even compared to the atom itself: If we imagine an atom on a scale on which its nucleus is the size of your fist, its electron cloud would be many miles wide. Nearly all the atom's mass resides in its nucleus, because protons and neutrons are each about 2,000 times more massive than an electron. Figure 4.6 shows the structure of a typical atom. The structure of a typical atom. 11. Define and distinguish between atomic number and atomic mass. Under what conditions are two atoms different isotopes of the same element? atomic number is The number of protons in an atom. atomic mass is The combined number of protons and neutrons in an atom. Each different chemical element contains a different number of protons in its nucleus called its atomic number. For example, a hydrogen nucleus contains just one proton, so its atomic number is 1; a helium nucleus contains two protons, so its atomic number is 2. The combined number of protons and neutrons in an atom is called its atomic mass (or atomic weight). The atomic mass of ordinary hydrogen is 1 because its nucleus is just a single proton. Helium usually has two neutrons in addition to its two protons, giving it an atomic mass of 4. Carbon usually has six protons and six neutrons, giving it an atomic mass of 12. Sometimes, the same element can have varying numbers of neutrons. For example, in rare cases a hydrogen nucleus contains a neutron in addition to its proton, making its atomic mass 2; hydrogen with atomic mass 2 is often called deuterium. The different forms of hydrogen are called isotopes of one another. A third isotope of hydrogen, 12. What do we mean by a phase of matter? Briefly describe how the idea of bonds between atoms (or molecules) explains the difference between the solid, liquid, and gas phases. phase (of matter) Describes the way in which atoms or molecules are held together; the common phases are solid, liquid, and gas. gas phase The phase of matter in which atoms or molecules can move essentially independently of one another. liquid phase The phase of matter in which atoms or molecules are held together but move relatively freely. solid phase The phase of matter in which atoms or molecules are held rigidly in place. 13. Briefly explain why a few atoms (or molecules) are always in gas phase around any solid or liquid. Then explain how sublimation and evaporation are similar and how they are different. even in a particular phase, matter exists in a great variety of different substances. atoms are not indivisible because they are composed of smaller particles. 14. Explain why, at sufficiently high temperatures, molecules undergo molecular dissociation and atoms undergo ionization. As the temperature rises, the molecules move faster, making collisions among them more violent. These collisions eventually split the water molecules into their component atoms of hydrogen and oxygen. The process by which the bonds that hold the atoms of a molecule together are broken is called molecular dissociation. At still higher temperatures, collisions can break the bonds holding electrons around the nuclei of individual atoms, allowing the electrons to go free. The loss of one or more negatively charged electrons leaves a remaining atom with a net positive charge. Such charged atoms are called ions, and the process of stripping electrons from atoms is called ionization. molecular dissociation is The process by which a molecule splits into its component atoms. ionization The process of stripping an electron from an atom. at high temperatures, what once was water becomes a hot gas consisting of freely moving electrons and positively charged ions of hydrogen and oxygen. This type of hot gas, in which atoms have become ionized, is called a plasma, sometimes referred to as "the fourth phase of matter." Other chemical substances go through similar phase changes, but the temperatures at which phase changes occur depend on the types of atom or molecules involved. neutral hydrogen contains only one electron, which balances the single positive charge of the one proton in its nucleus. 15. What is a plasma? Explain why, at very high temperatures, all matter is in this "fourth phase of matter." plasma is A gas consisting of ions and electrons. ionizartion at high temperatures, what once was water becomes a hot gas consisting of freely moving electrons and positively charged ions of hydrogen and oxygen. This type of hot gas, in which atoms have become ionized, is called a plasma, sometimes referred to as "the fourth phase of matter." Other chemical substances go through similar phase changes, but the temperatures at which phase changes occur depend on the types of atom or molecules involved. 16. Describe the three basic ways in which atoms can contain energy. In what way does an atom in an excited state contain more energy than an atom in the ground state? two different ways in which atoms have energy. First, by virtue of their mass, they possess mass-energy in the amount mc 2. Second, they possess kinetic energy by virtue of their motion. Atoms also contain energy in a third way: as electric potential energy in the distribution of their electrons around their nuclei. The simplest case is that of hydrogen, which has only one electron. Remember that an electron tends to be "smeared out" into a cloud around the nucleus. When the electron is "smeared out" to the minimum extent that nature allows, the atom contains its smallest possible amount of electric potential energy; we say that the atom is in its ground state. If the electron somehow gains energy, then it becomes "smeared out" over a greater volume, and we say that the atom is in an excited state. If the electron gains enough energy, it can escape the atom completely, in which case the atom has been ionized. ground state (of an atom) The lowest possible energy state of the electrons in an atom. excited state (of an atom) Any arrangement of electrons in an atom that has more energy than the ground state. 17. How are the possible energy levels of electrons in atoms similar to the possible gravitational potential energies of a person on a ladder? How are they different? electrons in atoms can have only particular energies (which correspond to particular sizes and shapes of the electron cloud). As a simple analogy, suppose you're washing windows on a building. If you use an adjustable platform to reach high windows, you can stop the platform at any height above the ground. if you use a ladder, you can stand only at particular heights—the heights of the rungs of the ladder—and not at any height in between The possible energies of electrons in atoms are like the possible heights on a ladder. Only a few particular energies are possible, and energies between these special few are not possible. The possible energy levels of the electron in hydrogen are represented like the steps of a ladder in Figure 4.11. The ground state, or level 1, is the bottom rung of the ladder; its energy is labeled zero because the atom has no excess electrical potential energy to lose. Each subsequent rung of the ladder represents a possible excited state for the electron. Each level is labeled with the electron's energy above the ground state in units of electron-volts, or eV (1 eV = 1.60 X 10–19 joule). For example, the energy of an electron in energy level 2 is 10.2 eV greater than that of an electron in the ground state. That is, an electron must gain 10.2 eV of energy to "jump" from level 1 to level 2. Similarly, jumping from level 1 to level 3 requires gaining 12.1 eV of energy. unlike a ladder built for climbing, the rungs on the electron's energy ladder are closer together near the top. The top itself represents the energy of ionization—if the electron gains this much energy, 13.6 eV above the ground state in the case of hydrogen, the electron breaks free from the atom. (Any excess energy beyond that needed for ionization becomes kinetic energy of the free-moving electron.) Because energy is always conserved, an electron cannot jump to a higher energy level unless its atom gains the energy from somewhere else. Discussion Questions 1. Knowledge of Mass-Energy. Einstein's discovery that energy and mass are equivalent has led to technological developments both beneficial and dangerous. Discuss some of these developments. Overall, do you think the human race would be better or worse off if we had never discovered that mass is a form of energy? Defend your opinion. 2. Perpetual Motion Machines. Every so often, someone claims to have built a machine that can generate energy perpetually from nothing. Why isn't this possible according to the known laws of nature? Why do you think claims of perpetual motion machines sometimes receive substantial media attention? 3. Indoor Pollution. Given that sublimation and evaporation are very similar processes, why is sublimation generally much more difficult to notice? Discuss how sublimation, particularly from plastics and other human-made materials, can cause "indoor pollution." 4. Democritus and the Path of History. Besides his belief in atoms, Democritus held several other strikingly modern notions. For example, he maintained that the Moon was a world with mountains and valleys and that the Milky Way was composed of countless individual stars—ideas that weren't generally accepted until the time of Galileo, more than 2,000 years later. Unfortunately, we know of Democritus's work only secondhand because none of the 72 books he is said to have written survived the destruction of the Library of Alexandria. How do you think history might have been different if the work of Democritus had not been lost? Problems Sensible Statements? For Problems 1–4, decide whether the statement is sensible and explain why it is or is not. 1. The sugar in my soda will provide my body with about a million joules of energy. 2. When I drive my car at 30 miles per hour, it has three times as much kinetic energy as it does at 10 miles per hour. 3. If you put an ice cube outside the Space Station, it would take a very long time to melt, even though the temperature in Earth orbit is several thousand degrees (Celsius). 4. Someday soon, scientists are likely to build an engine that produces more energy than it consumes. 5. Gravitational Potential Energy. 1. Why does a bowling ball perched on a cliff ledge have more gravitational potential energy than a baseball perched on the same ledge? 2. Why does a diver on a 10-meter platform have more gravitational potential energy than a diver on a 3-meter diving board? 3. Why does a 100-kg satellite orbiting Jupiter have more gravitational potential energy than a 100-kg satellite orbiting the Earth, assuming both satellites orbit at the same distance from the planet centers? 6. Einstein's Famous Formula. 1. What is the meaning of the formula E = mc 2? Be sure to define each variable. 2. How does this formula explain the generation of energy by the Sun? 3. How does this formula explain the destructive power of nuclear bombs? 7. Atomic Terminology Practice. 1. The most common form of iron has 26 protons and 30 neutrons in its nucleus. State its atomic number, atomic mass, and number of electrons if it is electrically neutral. 2. Consider the following three atoms: Atom 1 has 7 protons and 8 neutrons; atom 2 has 8 protons and 7 neutrons; atom 3 has 8 protons and 8 neutrons. Which two are isotopes of the same element? 3. Oxygen has atomic number 8. How many times must an oxygen atom be ionized to create an O+5 ion? How many electrons are in an O+5 ion? 4. Consider fluorine atoms with 9 protons and 10 neutrons. What are the atomic number and atomic mass of this fluorine? Suppose we could add a proton to this fluorine nucleus. Would the result still be fluorine? Explain. What if we added a neutron to the fluorine nucleus? 5. The most common isotope of gold has atomic number 79 and atomic mass 197. How many protons and neutrons does the gold nucleus contain? If it is electrically neutral, how many electrons does it have? If it is triply ionized, how many electrons does it have? 6. The most common isotope of uranium is 238U, but the form used in nuclear bombs and nuclear power plants is 235U. Given that uranium has atomic number 92, how many neutrons are in each of these two isotopes of uranium? 8. The Fourth Phase of Matter. 1. Explain why nearly all the matter in the Sun is in the plasma phase. 2. Based on your answer to part (a), explain why plasma is the most common phase of matter in the universe. 3. Given that plasma is the most common phase of matter in the universe, why is it so rare on Earth? 9. Energy Level Transitions. The labeled transitions below represent an electron moving between energy levels in hydrogen. Answer each of the following questions and explain your answers. 1. Which transition could represent an electron that gains 10.2 eV of energy? 2. Which transition represents an electron that loses 10.2 eV of energy? 3. Which transition represents an electron that is breaking free of the atom? 4. Which transition, as shown, is not possible? 5. Describe the process taking place in transition A. 10. Energy Comparisons. Use the data in Table 4.1 to answer each of the following questions. 1. Compare the energy of a 1-megaton hydrogen bomb to the energy released by a major earthquake. 2. If the United States obtained all its energy from oil, how much oil would be needed each year? 3. Compare the Sun's annual energy output to the energy released by a supernova. 11. Moving Candy Bar. Metabolizing a candy bar releases about 106 joules. How fast must the candy bar travel to have the same 106 joules in the form of kinetic energy? (Assume the candy bar's mass is 0.2 kg.) Is your answer faster or slower than you expected? 12. Calculating Densities. Find the average density of the following objects in grams per cubic centimeter. 1. A rock with volume 15 cm3 and mass 50 g. 2. Earth, with its mass of 6 1024 kg and radius of about 6,400 km. (Hint: The formula for the volume of a sphere is 4/3 radius3.) 3. The Sun, with its mass of 2 1030 kg and radius of about 700,000 km. 13. Spontaneous Human Combustion. Suppose that, through a horrific act of an angry god (or a very powerful alien, if you prefer), all the mass in your body was suddenly converted into energy according to the formula E = mc 2. How much energy would be produced? Compare this to the energy released by a 1-megaton hydrogen bomb (see Table 4.1). What effect would your disappearance have on the surrounding region? (Hint: Multiply your mass in kilograms by c 2.) 14. Fusion Power. No one has yet succeeded in creating a commercially viable way to produce energy through nuclear fusion. However, suppose we could build fusion power plants using the hydrogen in water as a fuel. Based on the data in Table 4.1, how much water would we need each minute in order to meet U.S. energy needs? Could such a reactor power the entire United States with the water flowing from your kitchen sink? Explain. (Hint: Use the annual U.S. energy consumption to find the energy consumption per minute; then divide by the energy yield from fusing 1 liter of water to figure out how many liters would be needed each minute.) Web Projects Find useful links for Web projects on the text Web site. 1. Energy Comparisons. Using information from the Energy Information Administration Web site, choose some aspect of U.S. or world energy use that interests you. Write a short report on this issue. 2. Nuclear Power. There are two basic ways to generate energy from atomic nuclei: through nuclear fission (splitting nuclei) and through nuclear fusion (combining nuclei). All current nuclear reactors are based on fission, but fusion would have many advantages if we could develop the technology. Research some of the advantages of fusion and some of the obstacles to developing fusion power. Do you think fusion power will be a reality in your lifetime? Explain. Chapter 5 Review Questions 1. How does speed differ from velocity? Give an example in which you can be traveling at constant speed but not at constant velocity. speed The rate at which an object moves. Its units are distance divided by time, such as m/s or km/hr. velocity The combination of speed and direction of motion; it can be stated as a speed in a particular direction, such as 100 km/hr due north. The concepts we use to determine the trajectory of a ball, a rocket, or a planet are familiar to you from driving a car. The speedometer indicates your speed, usually in units of both miles per hour (mi/hr) and kilometers per hour (km/hr); for example, 100km/hr is a speed. Your velocity is your speed in a certain direction; "100 km/hr going due north" describes a velocity. It is possible to change your velocity without changing your speed, for example, by maintaining a steady 60 km/hr as you drive around a curve. Because your direction is changing as you round the curve, your velocity is also changing—even though your speed is constant. 2. What do we mean by acceleration? Explain the units of acceleration. acceleration The rate at which an object's velocity changes. Its standard units are m/s2. Whenever your velocity is changing, you are experiencing acceleration. You are undoubtedly familiar with the term acceleration as it applies to increasing speed. 3. What is the acceleration of gravity on Earth? If you drop a rock from very high, how fast will it be falling after 4 seconds (neglecting air resistance)? The Acceleration of Gravity One of the most important types of acceleration is that caused by gravity, which makes objects accelerate as they fall. In a famous (though probably apocryphal) experiment that involved dropping weights from the Leaning Tower of Pisa, Galileo demonstrated that gravity accelerates all objects by the same amount, regardless of their mass. This fact may be surprising because it seems to contradict everyday experience: A feather floats gently to the ground, while a rock plummets. However, this difference is caused by air resistance. If you dropped a feather and a rock on the Moon, where there is no air, both would fall at exactly the same rate. 4. What is momentum? How can momentum be affected by a force? What do we mean when we say that momentum will be changed only by a net force? momentum is The product of an object's mass and velocity. In transferring some of its momentum to your car, the truck (or bug) exerts a force on your car. More generally, a force is anything that can cause a change in momentum. You are familiar with many types of force besides collisional force. For example, if you shift into neutral while driving along a flat stretch of road, the forces of air resistance and road friction will continually sap your car's momentum (transferring it to molecules in the air and the pavement), slowing your velocity until you come to a stop. You probably are also familiar with forces arising from gravity, electricity, and magnetism. The mere presence of a force does not always cause a change in momentum. force is Anything that can cause a change in momentum. 5. What is the difference between mass and weight? mass is A measure of the amount of matter in an object. weight is The net force that an object applies to its surroundings; in the case of a stationary body on the surface of the Earth, weight = mass acceleration of gravity. Your mass refers to the amount of matter in your body, which is different from your weight. Imagine standing on a scale in an elevator (Figure 5.2). When the elevator is stationary or moving at constant velocity, the scale reads your "normal" weight. When the elevator is accelerating upward, the floor exerts an additional force that makes you feel heavier, and the scale verifies your greater apparent weight.(*footnote) Note that your weight is greater than its "normal" value only while the elevator is accelerating, not while it is moving at constant velocity. When the elevator accelerates downward, the floor and the scale are dropping away, so your weight is reduced. 6. What is free-fall, and why does it make you weightless? Briefly describe why astronauts are weightless in the Space Station. free-fall Refers to conditions in which an object is falling without resistance; objects are weightless when in free-fall. there's plenty of gravity in space; even at the distance of the Moon, the Earth's gravity is strong enough to hold the Moon in orbit. In fact, in the low-Earth orbit of the Space Station, the acceleration of gravity is scarcely less than it is on the Earth's surface. Why, then, are the astronauts weightless? Because the Space Station and all other orbiting objects are in a constant state of free-fall, and any time you are in free-fall you are weightless. Imagine being an astronaut. You'd have the sensation of free-fall—just as when falling from a diving board—the entire time you were in orbit. This constantly falling sensation makes most astronauts sick to their stomach when they first experience weightlessness. Fortunately, they quickly get used to the sensation, which allows them to work hard and enjoy the view. Free-Fall, Weightlessness, and Orbit If the cable breaks so that the elevator is in free-fall, the floor drops away at the same rate that you fall. You lose contact with the scale, so your apparent weight is zero and you feel weightless. In fact, you are in free-fall whenever nothing is preventing you from falling. For example, you are in free-fall when you jump off a chair or spring from a diving board or trampoline. Surprising as it may seem, you have therefore experienced weightlessness many times in your life and can experience it right now simply by jumping off your chair. Of course, your weightlessness lasts for only the very short time until you hit the ground. Astronauts are weightless for much longer periods because orbiting spacecraft are in a constant state of free-fall. To understand why, imagine a cannon that shoots a ball horizontally from a tall mountain. 7. Why does a spaceship require a high speed to achieve orbit? What would happen if it were launched with a speed greater than the Earth's escape velocity? escape velocity The speed necessary for an object to completely escape the gravity of a large body such as a moon, planet, or star. If an orbiting object travels at the escape velocity or faster, it can completely escape from the Earth, never to return. (It will still be weightless as long as it does not fire any engines, because it is still in free-fall—only now "falling" in response to the gravity of the Sun, planets, and other objects.) The escape velocity from the Earth's surface is about 40,000 km/hr (25,000 mi/hr). 8. State each of Newton's three laws of motion. For each law, give an example of its application. Newton's First Law of Motion Newton's first law of motion deals with situations in which no net force is acting on an object. It states: In the absence of a net force, an object moves with constant velocity. Newton's second law of motion tells us what happens to an object when a net force is present. We have already said that a net force changes an object's momentum, accelerating it in the direction of the force. This law explains why you can throw a baseball farther than you can throw a shot-put. For both the baseball and the shot-put, the force delivered by your arm equals the product of mass and acceleration. Because the mass of the shot-put is greater than that of the baseball, the same force from your arm gives the shot-put a smaller acceleration. Due to its smaller acceleration, the shot-put leaves your hand with less speed than the baseball and thus travels a shorter distance before hitting the ground. Newton's Third Law of Motion Think for a moment about standing still on the ground. The force of gravity acts downward on you, so if this force were acting alone Newton's second law would demand that you be accelerating downward. The fact that you are not falling means that the ground must be pushing back up on you with exactly the right amount of force to offset gravity. This fact is embodied in Newton's third law of motion: For any force, there always is an equal and opposite reaction force. According to this law, your body exerts a gravitational force on the Earth identical to the one the Earth exerts on you, except that it acts in the opposite direction. In this mutual pull, the ground just happens to be caught in the middle. newton The standard unit of force in the metric system: Newton's first law of motion States that, in the absence of a net force, an object moves with constant velocity. Newton's laws of motion Three basic laws that describe how objects respond to forces. Newton's second law of motion States how a net force affects an object's motion. Specifically: force = rate of change in momentum, or force = mass acceleration. Newton's third law of motion States that, for any force, there is always an equal and opposite reaction force. 9. What is angular momentum? What kind of force can cause a change in angular momentum? Explain. angular momentum Momentum attributable to rotation or revolution. The angular momentum of an object moving in a circle of radius r is the product mvr. Just as momentum can be changed only by a force, the angular momentum of any object can be changed only by a twisting force, or torque. For example, opening a door requires rotating the door on its hinges. Making it rotate means giving it some angular momentum, which you can do by applying a torque the torque depends not only on how much force you use to push on the door, but also on where you push. The farther out from the hinges you push, the more torque you can apply and the easier it is to open the door. 10. What is the law of conservation of angular momentum? How can a skater use this principle to vary his or her rate of spin? When no net torque is present, a law very similar to Newton's first law applies—the law of conservation of angular momentum: In the absence of net torque (twisting force), the total angular momentum of a system remains constant. A spinning ice skater illustrates this law. Because there is so little friction on ice, the ice skater essentially keeps a constant angular momentum. When she pulls in her extended arms, she effectively decreases her radius. Therefore, for the product m X v X r to remain unchanged, her velocity of rotation must increase. The law of conservation of angular momentum arises frequently in astronomy, because gravity is often the only significant force and gravity rarely acts as a twisting force.(*footnote) For example, angular momentum is generally conserved for rotating planets, planets orbiting a star, and rotating galaxies. Indeed, conservation of angular momentum explains why the Earth doesn't need any fuel to make it rotate: In the absence of any torque to stop the rotation, the Earth would keep rotating forever. Earth's rotation gradually slows, due to a torque caused by tides. 11. Was Copernicus the first person to suggest a Sun-centered solar system? What advantages did his model have over the Ptolemaic model? In what ways did it fail to improve on the Ptolemaic model? No Ptolemy, whose complex model had planets spinning on circles upon circles around the Earth. tables of planetary motion based on the Ptolemaic model of the universe were noticeably inaccurate. Copernicus concluded that planetary motion could be explained more simply in a Sun-centered solar system, as had been suggested by Aristarchus some 1,800 years earlier and he began developing a Sun-centered system for predicting planetary positions. In addition to its aesthetic advantages, the Sun-centered system of Copernicus allowed him to discover a mathematical relationship between a planet's true orbital period around the Sun and the time between successive appearances of the planet at opposition in the sky He was also able to use geometrical techniques to estimate the distances of the planets from the Sun in terms of the Earth–Sun distance (i.e., distances in astronomical units). However, the model published by Copernicus did not predict planetary positions substantially more accurately than did the old Ptolemaic model. 12. How were Tycho Brahe's observations important to the development of modern astronomy? In 1563, Tycho decided to observe a widely anticipated conjunction of Jupiter and Saturn. To his surprise, the conjunction occurred nearly two days later than Copernicus had predicted. He resolved to improve the state of astronomical prediction and set about compiling careful observations of stellar and planetary positions in the sky. Tycho's fame grew after he observed what he called a nova, meaning "new star," in 1572 and proved that it was at a distance much farther away than the Moon. (He compared observations made by other astronomers at other locations on Earth to his own, proving that the nova had no observable parallax and must be more distant than the Moon.) Today, we know that Tycho saw a supernova—the explosion of a distant star. In 1577, Tycho observed a comet and proved that it too lay in the realm of the heavens. 13. State Kepler's three laws of motion, and explain the meaning of each law. Kepler's first law States that the orbit of each planet about the Sun is an ellipse with the Sun at one focus. Kepler's laws of planetary motion Three laws discovered by Kepler that describe the motion of the planets around the Sun. Kepler's second law States that, as a planet moves around its orbit, it sweeps out equal areas in equal times. This tells us that a planet moves faster when it is closer to the Sun (near perihelion) than when it is farther from the Sun (near aphelion) in its orbit. Kepler's third law States that the square of a planet's orbital period is proportional to the cube of its average distance from the Sun (semimajor axis), which tells us that more distant planets move more slowly in their orbits. In its original form, written p2 = a3. See also Newton's version of Kepler's third law. 14. Describe how Galileo helped spur acceptance of Kepler's Sun-centered model of the solar system. Galileo (1564–1642), a contemporary and correspondent of Kepler, answered all three objections. Galileo defused the first objection with experiments that almost single-handedly overturned the Aristotelian view of physics. His demonstration that gravity accelerates all objects by the same amount directly contradicted Aristotle's claim that heavier objects would fall to the ground faster. Aristotle also had taught that the natural tendency of any object was to come to rest. Galileo demonstrated that a moving object remains in motion unless a force acts to stop it, an idea now codified in Newton's first law of motion. he concluded that objects such as birds, falling stones, and clouds that are moving with the Earth should stay with the Earth unless some force knocks them away. This same idea explains why passengers in an airplane stay with the moving airplane even when they leave their seats. 15. What is the universal law of gravitation? Summarize what this law says in words, and then state the law mathematically. Define each variable in the formula. universal law of gravitation is The law expressing the force of gravity (Fg) between two objects, given by the formula 16. Describe how Newton's laws of motion and law of universal gravitation explain why each of Kepler's three laws is true. Newton's laws of motion Three basic laws that describe how objects respond to forces. Newton's universal law of gravitation See universal law of gravitation. Newton's first law of motion States that, in the absence of a net force, an object moves with constant velocity. Newton's second law of motion States how a net force affects an object's motion. Specifically: force = rate of change in momentum, or force = mass acceleration. Newton's third law of motion States that, for any force, there is always an equal and opposite reaction force. 17. What do we mean by bound and unbound orbits? bound orbits are Orbits on which an object travels repeatedly around another object; bound orbits are elliptical in shape. unbound orbits are Orbits on which an object comes in toward a large body only once, never to return; unbound orbits may be parabolic or hyperbolic in shape. 18. Why is Newton's version of Kepler's third law so important to our understanding of the universe? Newton's version of Kepler's third law This generalization of Kepler's third law can be used to calculate the masses of orbiting objects from measurements of orbital period and distance. Usually written as: 19. Explain how the Moon creates tides on the Earth. How do tides vary with the phase of the Moon? Why? 20. What is tidal friction? Briefly describe how tidal friction has affected the Earth and the Moon. tidal force A force that is caused when the gravity pulling on one side of an object is larger than that on the other side, causing the object to stretch. tidal friction Friction within an object that is caused by a tidal force. tidal heating A source of internal heating created by tidal friction. It is particularly important for satellites with eccentric orbits such as Io and Europa. 21. What is synchronous rotation, and what causes it? Describe the synchronous rotation of Pluto and Charon. Describe the variation on synchronous rotation that applies to Mercury. synchronous rotation Describes the rotation of an object that always shows the same face to an object that it is orbiting because its rotation period and orbital period are equal. 22. Explain why orbits cannot change spontaneously. How can atmospheric drag cause an orbit to change? How can a gravitational encounter cause an orbit to change? Discussion Questions 1. Kepler's Choice. Casting aside the idea that orbits must be perfect circles meant going against deeply entrenched beliefs, and Kepler said that it shook his deep religious faith. Given that only two of Tycho's observations disagreed with a perfectly circular orbit—and only by 8 arcminutes—do you think that most other people would have made the choice Kepler made to abandon perfect circles? Have you ever performed an experiment that disagreed with theory? Which did you question, the theory or your experiment? Why? 2. Aristotle and Modern English. Aristotle believed that the Earth was made from the four elements fire, water, earth, and air, while the heavens were made from ether (literally, "upper air"). The literal meaning of quintessence is "fifth element," and the literal meaning of ethereal is "made of ether." Look up these words in the dictionary. Discuss how their modern meanings are related to Aristotle's ancient beliefs. 3. Tidal Complications. The ocean tides on Earth are much more complicated than they might at first seem from the simple physics that underlies tides. Discuss some of the factors that make the real tides so complicated and how these factors affect the tides. Some factors to consider: the distribution of land and oceans; the Moon's varying distance from Earth in its orbit; the fact that the Moon's orbital plane is not perfectly aligned with the ecliptic and neither the Moon's orbit nor the ecliptic is aligned with the Earth's equator. Problems Sensible Statements? For problems 1–4, decide whether the statement is sensible and explain why it is or is not. 1. If you could go shopping on the Moon to buy a pound of chocolate, you'd get a lot more chocolate than if you bought a pound on Earth. 2. Upon its publication in 1543, the Copernican model was immediately accepted by most scientists because its predictions of planetary positions were essentially perfect. 3. Newton's version of Kepler's third law allows us to calculate the mass of Saturn from orbital characteristics of its moon Titan. 4. If an asteroid passed by Earth at just the right distance, it would be captured by the Earth's gravity and become our second moon. 5. Understanding Acceleration. 1. Some schools have an annual ritual that involves dropping a watermelon from a tall building. Suppose it takes 6 seconds for the watermelon to fall to the ground (which would mean it's dropped from about a 60-story building). If there were no air resistance so that the watermelon would fall with the acceleration of gravity, how fast would it be going when it hit the ground? Give your answer in m/s, km/hr, and mi/hr. 2. As you sled down a steep, slick street, you accelerate at a rate of 4 m/s2. How fast will you be going after 5 seconds? Give your answer in m/s, km/hr, and mi/hr. 3. You are driving along the highway at a speed of 70 miles per hour when you slam on the brakes. If your acceleration is at an average rate of –20 miles per hour per second, how long will it take to come to a stop? 6. Spinning Skater. Suppose an ice skater wants to start spinning. Explain why she won't start spinning if she simply stomps her foot straight down on the ice. How should she push off on the ice to start spinning? Why? What should she do when she wants to stop spinning? 7. New Comet. Imagine that a new comet is discovered and studies of its motion indicate that it orbits the Sun with a period of 1,000 years. What is the comet's average distance (semimajor axis) from the Sun? (Hint: Use Kepler's third law in its original form.) 8. The Gravitational Law. Use the universal law of gravitation to answer each of the following questions. 1. How does tripling the distance between two objects affect the gravitational force between them? 2. Compare the gravitational force between the Earth and the Sun to that between Jupiter and the Sun. The mass of Jupiter is about 318 times the mass of the Earth. 3. Suppose the Sun were magically replaced by a star with twice as much mass. What would happen to the gravitational force between the Earth and the Sun? 9. Head-to-Foot Tides. You and the Earth attract each other gravitationally, so you should also be subject to a tidal force resulting from the difference between the gravitational attraction felt by your feet and that felt by your head (at least when you are standing). Explain why you can't feel this tidal force. 10. Eclipse Frequency in the Past. Over billions of years, the Moon has gradually been moving farther from the Earth. Thus, the Moon used to be substantially nearer the Earth than it is today. 1. How would the Moon's past angular size in our sky compare to its present angular size? Why? 2. How would the length of a lunar month in the past compare to the length of a lunar month today? Why? (Hint: Think about Kepler's third law as it would apply to the Moon orbiting the Earth.) 3. Based on your answers to parts (a) and (b), would eclipses (both solar and lunar) have been more or less common in the past? Why? 11. Geostationary Orbit. A satellite in geostationary orbit appears to remain stationary in the sky as seen from any particular location on Earth. 1. Briefly explain why a geostationary satellite must orbit the Earth in 1 sidereal day, rather than 1 solar day. 2. Communications satellites, such as those used for television broadcasts, are often placed in geostationary orbit. The transmissions from such satellites are received with satellite dishes, such as those that can be purchased for home use. In one or two paragraphs, explain why geostationary orbit is a convenient orbit for communications satellites. 12. Elevator to Orbit. Suppose that someday we build a giant elevator from the Earth's surface to geosynchronous orbit. The top of the elevator would then have the same orbital distance and period as any satellite in geosynchronous orbit. 1. Suppose you were to drop an object out of the elevator at its top. Explain why the object would appear to float right next to the elevator rather than falling. 2. Briefly explain why (not counting the huge costs for construction) the elevator would make it much cheaper and easier to put satellites in orbit or to launch spacecraft into deep space. 13. Understanding Kepler's Third Law. Use Newton's version of Kepler's third law to answer the following questions. (Hint: The calculations for this problem are so simple that you will not need a calculator.) 1. Imagine another solar system, with a star of the same mass as the Sun. Suppose there is a planet in that solar system with a mass twice that of Earth orbiting at a distance of 1 AU from the star. What is the orbital period of this planet? Explain. 2. Suppose a solar system has a star that is four times as massive as our Sun. If that solar system has a planet the same size as Earth orbiting at a distance of 1 AU, what is the orbital period of the planet? Explain. 14. Gees. Acceleration is sometimes measured in gees, or multiples of the acceleration of gravity: 1 gee (1g) means 1 X g, or 9.8 m/s2; 2 gees (2g) means 2 X g, or 2 X 9.8 m/s2 = 19.6 m/s2; and so on. Suppose you experience 6 gees of acceleration in a rocket. 1. What is your acceleration in meters per second squared? 2. You will feel a compression force from the acceleration. How does this force compare to your normal weight? 3. Do you think you could survive this acceleration for long? Explain. 15. Measuring Masses. Use Newton's version of Kepler's third law to answer each of the following questions. 1. The Moon orbits the Earth in an average of 27.3 days at an average distance of 384,000 kilometers. Use these facts to determine the mass of the Earth. You may neglect the mass of the Moon and assume M Earth + M Moon M Earth. (The Moon's mass is about 1/80 of Earth's.) 2. Jupiter's moon Io orbits Jupiter every 42.5 hours at an average distance of 422,000 kilometers from the center of Jupiter. Calculate the mass of Jupiter. (Io's mass is very small compared to Jupiter's.) 3. Calculate the orbital period of the Space Shuttle in an orbit 300 kilometers above the Earth's surface. 4. Pluto's moon Charon orbits Pluto every 6.4 days with a semimajor axis of 19,700 kilometers. Calculate the combined mass of Pluto and Charon. Compare this combined mass to the mass of the Earth. 16. Weights on Other Worlds. Calculate the acceleration of gravity on the surface of each of the following worlds. How much would you weigh, in pounds, on each of these worlds? 1. Mars (mass = 0.11M Earth, radius = 0.53R Earth). 2. Venus (mass = 0.82M Earth, radius = 0.95R Earth). 3. Jupiter (mass = 317.8M Earth, radius = 11.2R Earth). Bonus: Given that Jupiter has no solid surface, how could you weigh yourself on Jupiter? 4. Jupiter's moon Europa (mass = 0.008M Earth, radius = 0.25R Earth). 5. Mars's moon Phobos (mass = 1.1 1016 kg, radius = 12 km). 17. Calculate the escape velocity from each of the following. (Masses and radii are listed in problem 16.) 1. The surface of Mars. 2. The surface of Phobos. 3. The cloud tops of Jupiter. 4. Our solar system, starting from the Earth's orbit. (Hint: Most of the mass of our solar system is in the Sun; M Sun = 2.0 1030 kg.) 5. Our solar system, starting from Saturn's orbit. Web Projects Find useful links for Web projects on the text Web site. 1. Players in the Copernican Revolution. A number of interesting personalities played important roles in the Copernican revolution besides Copernicus, Tycho, Kepler, and Galileo. Research one or more of these people and write a short biography of their scientific lives and their contributions to the Copernican revolution. Among the people you might consider: Nicholas of Cusa (1401–1464), who argued for a Sun-centered solar system and believed that other stars might be circled by their own planets; Leonardo da Vinci (1452–1519), who made many contributions to science, engineering, and art and also believed the Earth not to be the center of the universe; Rheticus (1514–1574), a student of Copernicus who persuaded him to publish his work; William Gilbert (1540–1603), who studied the Earth's magnetism and influenced the thinking of Kepler; Giordano Bruno (1548–1600), who was burned at the stake for his beliefs in the Copernican system and the atomism of Democritus; and Francis Bacon (1561–1626), whose writings contributed to the acceptance of experimental methods in science. 2. Tide Tables. Find a tide table or tide chart for a beach town that you'd like to visit. Briefly explain how to read the table or chart, and discuss any differences between the actual tidal pattern and the idealized tidal pattern described in this chapter. 3. Space Elevator. Read more about space elevators (see problem 12) and how they might make it easier and cheaper to get to Earth orbit or beyond. Write a short report about the feasibility of building a space elevator, and briefly discuss the pros and cons of such a project. Chapter 6 Review Questions 1. What is the difference between energy and power, and what units do we use to measure each? Even without opening your eyes, it's clear that light is a form of energy, called radiative energy. Outside on a hot, sunny day, you can feel the radiative energy of sunlight being converted to thermal energy as it strikes your skin. On an economic level, electric companies charge you for the energy needed by your light bulbs (and other appliances). The rate at which a light bulb uses energy (converts electrical energy to light and heat) is usually printed on it—for example "100 watts." A watt is a unit of power, which describes the rate of energy use; 1 watt of power means that 1 joule of energy is being used each second: energy is Broadly speaking, energy is what can make matter move. The three basic types of energy are kinetic, potential, and radiative. power is The rate of energy usage, usually measured in watts (1 watt = 1 joule/s). for every second that you leave a 100-watt light bulb turned on, you will have to pay the utility company for 100 joules of energy. Interestingly, the power requirement of an average human—about 10 million joules per day—is about the same as that of a 100-watt light bulb. 2. What do we mean when we speak of a spectrum produced by a prism or diffraction grating? spectrum (of light) See electromagnetic spectrum. diffraction grating is A finely etched surface that can split light into a spectrum. Another basic property of light is what our eyes perceive as color. You've probably seen a prism split light into a spectrum (plural, spectra), or rainbow of colors. You can also produce a spectrum with a diffraction grating—a piece of plastic or glass etched with many closely spaced lines. The colors in a spectrum are pure forms of the basic colors red, orange, yellow, green, blue, and violet. The wide variety of all possible colors comes from mixtures of these basic colors in varying proportions; white is simply what we see when the basic colors are mixed in roughly equal proportions. Your television takes advantage of this fact to simulate a huge range of colors by combining only three specific colors of red, green, and blue light. 3. Describe each of the four basic ways that light can interact with matter: emission, absorption, transmission, and reflection. How is scattering related to reflection? emission is (of light) The process by which matter emits energy in the form of light. absorption is (of light) The process by which matter absorbs radiative energy. transmission is (of light) The process in which light passes through matter without being absorbed. reflection is (of light) The process by which matter changes the direction of light. Energy carried by light can interact with matter in four general ways: Emission: When you turn on a lamp, electric current flowing through the filament of the light bulb heats it to a point at which it emits visible light. Absorption: If you place your hand near a lit light bulb, your hand absorbs some of the light, and this absorbed energy makes your hand warmer. Transmission: Some forms of matter, such as glass or air, transmit light; that is, they allow light to pass through them. Reflection: A mirror reflects light in a very specific way, similar to the way a rubber ball bounces off a hard surface, so that the direction of a reflected beam of light depends on the direction of the incident (incoming) beam of light. Sometimes, reflection is more random, so that an incident beam of light is scattered in many different directions. The screen in a movie theater, for example, scatters a narrow beam of light from the projector into an array of beams that reach every member of the audience 4. What does it mean for a material to be transparent? To be opaque? What is opacity? transparent (material) Describes a material that transmits light. opaque (material) Describes a material that absorbs light. Materials that transmit light are said to be transparent, and materials that absorb light are called opaque. Many materials are neither perfectly transparent nor perfectly opaque, and the technical term that describes how much light they transmit and absorb is opacity. opacity A measure of how much light a material absorbs compared to how much it transmits; materials with higher opacity absorb more light. 5. How does a particle differ from a wave? Define each of the following terms as it applies to waves: wavelength, frequency, cycles per second, hertz, speed. Newton guessed that light, with all its colors, is made up of countless tiny particles. However, later experiments by other scientists demonstrated that light behaves like waves. Marbles, baseballs, and individual atoms are all examples of particles. A particle of matter can sit still or it can move from one place to another. imagine tossing a pebble into a pond. The ripples moving out from the place where the pebble lands are waves, consisting of peaks where the water is higher than average and troughs where the water is lower than average. wavelength The distance between adjacent peaks (or troughs) of a wave. frequency Describes the rate at which peaks of a wave pass by a point; measured in units of 1/s, often called cycles per second or hertz. cycles per second Units of frequency for a wave; describes the number of peaks (or troughs) of a wave that pass by a given point each second. Equivalent to hertz. hertz (Hz) The standard unit of frequency for light waves; equivalent to units of 1/s. speed The rate at which an object moves. Its units are distance divided by time, such as m/s or km/hr. The wavelength, frequency, and speed of a wave are related by a simple formula, which we can understand with the help of an example. Suppose a wave has a wavelength of 1 centimeter and a frequency of 2 hertz. The wavelength tells us that each time a peak passes by, the wave peak has traveled 1 centimeter. The frequency tells us that two peaks pass by each second. Thus, the speed of the wave must be 2 centimeters per second. If you try a few more similar examples, you'll find that the general rule is wavelength X frequency = speed 6. What is a photon? In what way is a photon like a particle? In what way is it like a wave? photon An individual particle of light, characterized by a wavelength and a frequency. light behaves as both a particle and a wave. Like particles, light comes in individual "pieces," called photons, that can hit a wall one at a time. Like ripples on a pond, light can make (charged) particles bob up and down. We will discuss the implications of this "wave–particle duality". Here we need only discuss how we measure the wave and particle properties of light. 7. Briefly describe the concept of a field, and use it to explain why we say that light is an electromagnetic wave. field is An abstract concept used to describe how a particle would interact with a force. For example, the idea of a gravitational field describes how a particle would react to the local strength of gravity, and the idea of an electromagnetic field describes how a charged particle would respond to forces from other charged particles. light, it is electric and magnetic fields that vibrate. The concept of a field is a bit abstract. Fields associated with forces, such as electric and magnetic fields, describe how these forces affect a particle placed at any point in space. For example, we say that the Earth has a gravitational field because if you place an object above the Earth's surface, the force of gravity pulls the object to the ground. That is, any object placed in a gravitational field feels the force of gravity. In a similar way, a charged particle (such as an electron) placed in an electric field or a magnetic field feels electric or magnetic forces. Light is an electromagnetic wave—a wave in which electric and magnetic fields vibrate. Like a leaf on a rippling pond, an electron will bob up and down when an electromagnetic wave passes by. If you could set up a row of electrons, they would wriggle like a snake. 8. Explain why light with a shorter wavelength must have a higher frequency, and vice versa. A row of electrons would wriggle up and down as light passes by, showing that light carries a vibrating electric field. It also carries a magnetic field (not shown) that vibrates perpendicular to the direction of the electric field vibrations. Characteristics of light waves. Because all light travels at the same speed, light of longer wavelength must have lower frequency. The wavelength is the distance between adjacent peaks of the electric or magnetic field, and the frequency is the number of peaks that pass by any point each second (Figure 6.4b). All light travels at the same speed (in a vacuum)—about 300,000 kilometers per second, or 3 X 108 m/s—regardless of its wavelength or frequency. Therefore, light with a shorter wavelength must have a higher frequency. 9. Describe the electromagnetic spectrum. In terms of frequency, wavelength, and energy, distinguish among radio, infrared, visible light, ultraviolet, X rays, and gamma rays. electromagnetic spectrum is The complete spectrum of light, including radio waves, infrared, visible light, ultraviolet light, X rays, and gamma rays. frequency Describes the rate at which peaks of a wave pass by a point; measured in units of 1/s, often called cycles per second or hertz. wavelength The distance between adjacent peaks (or troughs) of a wave. energy Broadly speaking, energy is what can make matter move. The three basic types of energy are kinetic, potential, and radiative. radio waves is Light with very long wavelengths (and low frequencies)—longer than those of infrared light. infrared light is Light with wavelengths that fall in the portion of the electromagnetic spectrum between radio waves and visible light. visible light is The light our eyes can see, ranging in wavelength from about 400 to 700 nm. ultraviolet light is Light with wavelengths that fall in the portion of the electromagnetic spectrum between visible light and X rays. X rays Light with wavelengths that fall in the portion of the electromagnetic spectrum between ultraviolet light and gamma rays. gamma rays Light with very short wavelengths (and hence high frequencies)—shorter than those of X rays. The visible light that we see with our eyes has wavelengths ranging from about 400 nm at the blue end of the rainbow to about 700 nm at the red end. Light with wavelengths somewhat longer than red light is called infrared, because it lies beyond the red end of the rainbow. Light with very long wavelengths is called radio (or radio waves)— radio is a form of light, not a form of sound. At the other end of the spectrum, light with wavelengths somewhat shorter than blue light is called ultraviolet, because it lies beyond the blue (or violet) end of the rainbow. Light with even shorter wavelengths is called X rays, and the shortest-wavelength light is called gamma rays. Note that visible light is an extremely small part of the entire electromagnetic spectrum: The reddest red that our eyes can see has only about twice the wavelength of the bluest blue, but the radio waves from your favorite radio station. 10. Explain how transitions between energy levels can cause atoms to emit or absorb photons. Whenever matter and light interact, matter leaves its fingerprints. Examining the color of an object is a crude way of studying the clues left by the matter it contains. For example, a red shirt absorbs all visible photons except those in the red part of the spectrum, so we know that it must contain a dye with these special light-absorbing characteristics. If we take light and disperse it into a spectrum, we can see the spectral fingerprints in more detail. 11. Explain how spectral lines can be used to determine the composition and temperature of their source. A schematic spectrum obtained from the light of a distant object. The "rainbow" at bottom shows how the light would appear when viewed through a prism or diffraction grating. The graph shows the corresponding intensity of the light at each wavelength. Note that the intensity is high where the rainbow is bright and low where it is dim (such as in places where the rainbow shows dark lines). gases can absorb light; for example, ozone in the Earth's atmosphere absorbs ultraviolet light from space, preventing it from reaching the ground. Gases can also emit light, which is what makes neon lights and interstellar clouds glow so beautifully. Photons emitted by various energy level transitions in hydrogen. (b ) The visible emission line spectrum from heated hydrogen gas. These lines come from transitions in which electrons fall from higher energy levels to level 2. (c ) If we pass white light through a cloud of cool hydrogen gas, we get this absorption line spectrum. These lines come from transitions in which electrons jump from energy level 2 to higher levels. 12. What is thermal radiation? Describe the two laws of thermal radiation. Explain how the effects of both laws can be seen in Figure 6.12. thermal radiation The spectrum of radiation produced by an opaque object that depends only on the object's temperature; sometimes called blackbody radiation. the radiation coming from an opaque object depends only on its temperature and is called thermal radiation (sometimes called blackbody radiation). Two simple rules describe how a thermal radiation spectrum depends on the temperature of the emitting object: 1. Hotter objects emit more total radiation per unit surface area. The radiated energy is proportional to the fourth power of the temperature expressed in Kelvin (not in Celsius or Fahrenheit). For example, a 600 K object has twice the temperature of a 300 K object and therefore radiates 24 = 16 times as much total energy per unit surface area. 2. Hotter objects emit photons with a higher average energy, which means a shorter average wavelength. Figure 6.12 (click image to enlarge) Graphs of idealized thermal radiation spectra. Note that, per unit surface area, hotter objects emit more radiation at every wavelength, demonstrating rule 1 for thermal radiation. The peaks of the spectra occur at shorter wavelengths (higher energies) for hotter objects, demonstrating rule 2 for thermal radiation. 13. Summarize the circumstances under which objects produce thermal, emission line, or absorption line spectra as shown in Figure 6.13. Any opaque object produces thermal radiation over a broad range of wavelengths. If the object is hot enough to produce visible light, as is the case with the filament of a light bulb, we see a smooth, continuous rainbow when we disperse the light through a prism or a diffraction grating (Figure 6.13a). On a graph of intensity versus wavelength, the rainbow becomes the characteristic hump of a thermal radiation spectrum. When thermal radiation passes through a thin cloud of gas, the cloud leaves fingerprints that may be either absorption lines or emission lines, depending on its temperature. If the background source of thermal radiation is hotter than the cloud, the balance between emission and absorption in the cloud's spectral lines tips toward absorption. We then see absorption lines cutting into the thermal spectrum. This is the case when the light from the hot light bulb passes through a cool gas cloud (Figure 6.13b). On the graph of intensity versus wavelength, these absorption lines create dips in the thermal radiation spectrum; the width and depth of each dip depend on how much light is absorbed by the chemical responsible for the line. If the background source is colder than the cloud or if there is no background source at all, the spectrum is dominated by bright emission lines produced by the cloud's atoms and molecules (Figure 6.13c). These lines create narrow peaks on a graph of intensity versus wavelength. the hump of thermal emission shows that this object has a surface temperature of about 225 K, well below the freezing point of water. The absorption bands in the infrared come mainly from carbon dioxide, which tells us that the object has a carbon dioxide atmosphere. The emission lines in the ultraviolet come from hot gas in a high, thin layer of the object's atmosphere. The reflected light looks like the Sun's 5,800 K thermal radiation except that the blue light is missing, so the object must be reflecting sunlight and must look red in color. Perhaps by now you have guessed that this figure represents the spectrum of the planet Mars 14. Study Figure 6.14 carefully, and explain each feature in the spectrum. emission lines hot upper atmosphere. Object absorbs blue light from the sun. object reflects red sunlight rust colored surface. CO 2 absorption bands carbon dioxide atmosphere. Thermal emission peak in infrared indicates surface temperature about 225 K. ultraviolet, blue, green, red, infrared 15. Describe the Doppler effect for light. Explain why light from objects moving toward us shows a blueshift, while light from objects moving away from us shows a redshift. What can we say about an object with a large Doppler shift, compared to an object with a small Doppler shift? The volume of information about temperature and composition that light contains is truly amazing, but we can learn even more once we identify the various lines in a spectrum. Among the most important pieces of information contained in light is information about motion. In particular, we can determine the radial motion (toward or away from us) of a distant object from changes in its spectrum caused by the Doppler effect. The Doppler effect causes similar shifts in the wavelengths of light. If an object is moving toward us, then its entire spectrum is shifted to shorter wavelengths. Because shorter wavelengths are bluer when we are dealing with visible light, the Doppler shift of an object coming toward us is called a blueshift. If an object is moving away from us, its light is shifted to longer wavelengths; we call this a redshift because longer wavelengths are redder when we are dealing with visible light. Note that the terms blueshift and redshift are used even when we are not dealing with visible light. Spectral lines provide the reference points we use to identify and measure Doppler shifts (Figure 6.16). For example, suppose we recognize the pattern of hydrogen lines in the spectrum of a distant object. 16. Describe how the Doppler effect allows us to determine the rotation rates of distant stars. The Doppler effect not only tells us how fast a distant object is moving toward or away from us but also can reveal information about motion within the object. For example, suppose we look at spectral lines of a planet or star that happens to be rotating. As the object rotates, light from the part of the object rotating toward us will be blueshifted, light from the part rotating away from us will be redshifted, and light from the center of the object won't be shifted at all. The net effect, if we look at the whole object at once, is to make each spectral line appear wider than it would if the object were not rotating. The faster the object is rotating, the broader in wavelength the spectral lines become. we can determine the rotation rate of distant objects by measuring the width of their spectral lines. As we will see later, this is only a small part of the information revealed through the Doppler effect on the spectra of celestial objects. For example, suppose we recognize the pattern of hydrogen lines in the spectrum of a distant object. We know the rest wavelengths of the hydrogen lines—that is, their wavelengths in stationary clouds of hydrogen gas—from laboratory experiments in which a tube of hydrogen gas is heated so the wavelengths of the spectral lines can be measured. If the hydrogen lines from the object appear at longer wavelengths, then we know that they are redshifted and the object is moving away from us; the larger the shift, the faster the object is moving. If the lines appear at shorter wavelengths, then we know that they are blueshifted and the object is moving toward us. Note that the Doppler shift tells us only the component of an object's velocity that is directly toward or away from us (that is, the radial component); it does not give us any information about the component of velocity across our line of sight. Doppler effect (shift) The effect that shifts the wavelengths of spectral features in objects that are moving toward or away from the observer. Discussion Questions 1. The Changing Limitations of Science. In 1835, French philosopher Auguste Comte stated that the composition of stars could never be known by science. Although spectral lines had been seen in the Sun's spectrum by that time, not until the mid-1800s did scientists recognize that spectral lines give clear information about chemical composition (primarily through the work of Foucault and Kirchhoff). Why might our present knowledge have seemed unattainable in 1835? Discuss how new discoveries can change the apparent limitations of science. Today, other questions seem beyond the reach of science, such as the question of how life began on Earth. Do you think such questions will ever be answerable by science? Defend your opinion. 2. Your Microwave Oven. Microwaves is a name sometimes given to light near the long-wavelength end of the infrared portion of the spectrum. A microwave oven emits microwaves that happen to have just the right wavelength needed to cause energy level jumps in water molecules. Use this fact to explain how a microwave oven cooks your food. Why doesn't a microwave oven make a plastic or ceramic dish get hot? Problems Sensible Statements? For problems 1–4, decide whether the statement is sensible and explain why it is or is not. 1. If you could view a spectrum of light reflecting off a blue sweatshirt, you'd find the entire rainbow of color. 2. Because of their higher frequency, X rays must travel through space faster than radio waves. 3. If the Sun's surface became much hotter (while the Sun's size remained the same), the Sun would emit more ultraviolet light but less visible light than it currently emits. 4. If a distant galaxy has a substantial redshift (as viewed from our galaxy), then anyone living in that galaxy would see a substantial redshift in a spectrum of the Milky Way Galaxy. 5. Spectral Summary. Clearly explain how studying an object's spectrum can allow us to determine each of the following properties of the object. 1. The object's surface chemical composition. 2. The object's surface temperature. 3. Whether the object is a thin cloud of gas or something more substantial. 4. Whether the object has a hot upper atmosphere. 5. The speed at which the object is moving toward or away from us. 6. The object's rotation rate. 6. Planetary Spectrum. Suppose you take a spectrum of light coming from a planet that looks blue to the eye. Do you expect to see any visible light in the planet's spectrum? Is the visible light emitted by the planet, reflected by the planet, or both? Which (if any) portions of the visible spectrum do you expect to find "missing" in the planet's spectrum? Explain your answers clearly. 7. Hotter Sun. Suppose the surface temperature of the Sun were about 12,000 K, rather than 6,000 K. 1. How much more thermal radiation would the Sun emit? 2. How would the thermal radiation spectrum of the Sun be 3. Do you think it would still be possible to have life on Earth? Explain. 8. The Doppler Effect. In hydrogen, the transition from level 2 to level 1 has a rest wavelength of 121.6 nm. Suppose you see this line at a wavelength of 120.5 nm in Star A, at 121.2 nm in Star B, at 121.9 nm in Star C, and at 122.9 nm in Star D. Which stars are coming toward us? Which are moving away? Which star is moving fastest relative to us (either toward or away)? Explain your answers without doing any calculations. 9. The Expanding Universe. Recall from Chapter 1 that we know the universe is expanding because (1) all galaxies outside our Local Group are moving away from us and (2) more distant galaxies are moving faster. Explain how Doppler shift measurements allow us to know these two facts. 10. Human Wattage. A typical adult uses about 2,500 Calories of energy each day. 1. Using the fact that 1 Calorie is about 4,000 joules, convert the typical adult energy usage to units of joules per day. 2. Use your answer from part (a) to calculate a typical adult's average power requirement, in watts. Compare this to that of a light bulb. 11. Wavelength, Frequency, and Energy. 1. What is the frequency of a visible light photon with wavelength 550 nm? 2. What is the wavelength of a radio photon from an AM radio station that broadcasts at 1,120 kilohertz? What is its energy? 3. What is the energy (in joules) of an ultraviolet photon with wavelength 120 nm? What is its frequency? 4. What is the wavelength of an X-ray photon with energy 10 keV (10,000 eV)? What is its frequency? (Hint: Recall that 1 eV = 1.60 10–19 joule.) 12. How Many Photons? Suppose that all the energy from a 100-watt light bulb came in the form of photons with wavelength 600 nm. (This is not quite realistic; see problem 15.) 1. Calculate the energy of a single photon with wavelength 600 nm. 2. How many 600-nm photons must be emitted each second to account for all the light from this 100-watt light bulb? Based on your answer, explain why we don't notice the particle nature of light in our everyday lives. 13. Taking the Sun's Temperature. The Sun radiates a total power of about 4 X 1026 watts into space. The Sun's radius is about 7 X 108 meters. 1. Calculate the average power radiated by each square meter of the Sun's surface. (Hint: The formula for the surface area of a sphere is A = 4pr 2.) 2. Using your answer from part (a) and the Stefan–Boltzmann law (see Mathematical Insight 6.2), calculate the average surface temperature of the Sun. (Note: The temperature calculated this way is called the Sun's effective temperature.) 14. Doppler Calculations. Calculate the speeds of each of the stars described in problem 8. Be sure to state whether each star is moving toward or away from us. 15. Understanding Light Bulbs. A standard (incandescent) light bulb uses a hot tungsten coil to produce a thermal radiation spectrum. The temperature of this coil is typically about 3,000 K. 1. What is the wavelength of maximum intensity for a standard light bulb? Compare this to the 500-nm wavelength of maximum intensity for the Sun. Also explain why standard light bulbs must emit a substantial portion of their radiation as invisible, infrared light. 2. Overall, do you expect the light from a standard bulb to be the same as, redder than, or bluer than light from the Sun? Why? Use your answer to explain why professional photographers use a different type of film for indoor photography than for outdoor photography. 3. Fluorescent light bulbs primarily produce emission line spectra rather than thermal radiation spectra. Explain why, if the emission lines are in the visible part of the spectrum, a fluorescent bulb can emit more light than a standard bulb of the same wattage. 4. Today, compact fluorescent light bulbs are designed to produce so many emission lines in the visible part of the spectrum that their light looks very similar to the light of standard bulbs. However, they are much more energy-efficient: A 15-watt compact fluorescent bulb typically emits as much visible light as a standard 75-watt bulb. Although compact fluorescent bulbs generally cost more than standard bulbs, is it possible that they could save you money? Besides initial cost and energy efficiency, what other factors must be considered? Chapter 7 Review Questions 1. Briefly describe how the eye collects light. How is a camera lens similar to the eye? The eye is more complex than any human-made instrument, but its basic components are a lens, a pupil, and a retina. The retina contains light-sensitive cells (called cones and rods) that, when triggered by light, send signals to the brain via the optic nerve. The lens of an eye acts much like a simple glass lens. Light rays that enter the lens farther from the center are bent more, and rays that pass directly through the center are not bent at all. In this way, parallel rays of light, such as the light from a distant star, converge to a point called the focus. If you have perfect vision, the focus of your lens is on your retina. That is why distant stars appear as points of light to our eyes or on photographs. the image formed by a lens is upside down. It is flipped right side up by your brain, where the true miracle of vision occurs. The pupil controls the amount of light that enters the eye by adjusting the size of its opening. The pupil dilates (opens wider) in low light levels, allowing your eye to gather as many photons as possible. It constricts in bright light, so that your eye is not overloaded with light. 2. What is the focus of a lens? What is the focal plane? The place where the image appears in focus is called the focal plane of the lens. Again, in a healthy eye, the focal plane is on your retina. (The retina actually is curved, rather than a flat plane, but we will ignore this detail.) Note that the image formed by a lens is upside down. It is flipped right side up by your brain, where the true miracle of vision occurs. focal plane is The place where an image created by a lens or mirror is in focus. 3. What is angular resolution? Suppose you look at two stars with an angular resolution smaller than that of your eye. What will you see? angular resolution (of a telescope) The smallest angular separation that two pointlike objects can have and still be seen as distinct points of light (rather than as a single point of light). The human eye has an angular resolution of about 1 arcminute (1/60°), meaning that two stars will appear distinct if they lie farther than 1 arcminute apart in the sky. Two stars separated by less than 1 arcminute therefore appear as a single point of light. Most stars are actually members of binary or multiple-star systems, but, because they are so far away, the angular separation of the individual stars is far below the angular resolution of our eyes. 4. Briefly describe how a camera collects and records light. How do we control the exposure time with a camera? The basic operation of a camera is quite similar to that of an eye. The camera lens plays the role of the lens of the eye, and film plays the role of the retina. The camera is "in focus" when the film lies in the focal plane of the lens. Fancier cameras even have an adjustable circular opening, called the camera's aperture, that controls the amount of light entering the camera just as the pupil controls the amount of light entering the eye. A camera works much like an eye. When the shutter is open, light passes through the lens to form an image on the film or electronic detector. (b ) Basic components of a camera. 5. What is a CCD? Briefly describe the advantages of using CCDs over using photographic film. CCD (charge coupled device) A type of electronic light detector that has largely replaced photographic film in astronomical research. charge-coupled devices, or CCDs, that can accurately record 90% or more of the photons that strike them. A CCD is a chip of silicon carefully engineered to be extraordinarily sensitive to photons (Figure 7.6). The chip is physically divided into a grid of squares called picture elements, or pixels for short. 6. Briefly distinguish between a refracting telescope and a reflecting telescope. refracting telescope A telescope that uses lenses to focus light. reflecting telescope A telescope that uses mirrors to focus light. Telescopes come in two basic designs: refracting and reflecting. A refracting telescope operates much like an eye, using transparent glass lenses to focus the light from distant objects. A reflecting telescope uses a precisely curved primary mirror to gather and focus light. Note that the mirror focuses light at the prime focus, which lies in front of the mirror. if we place a camera at the prime focus, it blocks some of the light entering the telescope. This does not create a serious problem as long as the camera is small compared to the primary mirror. If the telescope is large enough, a "cage" in which an astronomer can work can be suspended over the prme focus. 7. Define and distinguish between a telescope's light-collecting area and its angular resolution. Why are these properties the two most important properties of a telescope? light-collecting area (of a telescope) The area of the primary mirror or lens that collects light in a telescope. angular resolution (of a telescope) The smallest angular separation that two pointlike objects can have and still be seen as distinct points of light (rather than as a single point of light). The power of any telescope, whether refracting or reflecting, is characterized by two fundamental properties: its light-collecting area, which describes the telescope's size in terms of how much light it can collect, and its angular resolution, which tells us how much detail we can see in the telescope's images. Light-Collecting Area The "size" of a telescope is usually described by the diameter of its primary mirror (or lens). For example, a "5-meter telescope" is a telescope with a primary mirror measuring 5 meters in diameter. The light-collecting area is proportional to the square of the mirror diameter. (More specifically, for a round mirror surface, we can use the formula for the area of a circle: area = p X (radius)2.) a 2-meter telescope has 22 = 4 times the light-collecting area of a 1-meter telescope. most astronomical research involves reflecting telescopes, mainly for two practical reasons. First, because light passes through the lens of a refracting telescope, lenses must be made from clear, high-quality glass with precision-shaped surfaces on both sides. In contrast, only the reflecting surface of a mirror must be precisely shaped, and the quality of the underlying glass is not a factor. Second, large glass lenses are extremely heavy and can be held in place only by their edges, making it difficult to stabilize refracting telescopes, in which lenses are positioned at the top. The primary mirror of a reflecting telescope is mounted at the bottom, where its weight is a far less serious problem. 8. What is the diffraction limit of a telescope, and how does it depend on the telescope's size and the particular wavelength of light being observed? diffraction limit The angular resolution that a telescope could achieve if it were limited only by the interference of light waves; it is smaller better angular resolution for larger telescopes. The angular resolution that a telescope could achieve if it were limited only by the interference of light waves is called its diffraction limit. (Diffraction is a technical term for the specific effects of interference that limit telescope resolution.) It depends on both the diameter of the primary mirror and the wavelength of the light being observed. Larger telescopes have smaller diffraction limits for any particular wavelength of light. However, achieving a particular angular resolution requires a larger telescope for longer-wavelength light. That is why, for example, a radio telescope must be far larger than an optical telescope to achieve the same angular resolution. The wavelength of light and the diameter of the telescope must be in the same units. Example 1: What is the diffraction limit of the 2.4-m Hubble Space Telescope for visible light with a wavelength of 500 nm? Solution: For light with a wavelength of 500 nm (500 X 10–9 m), the diffraction limit of the Hubble Space Telescope is approximately: When you realize that each Keck telescope has more than a million times the light-collecting area of the human eye, it is no wonder that modern telescopes have so dramatically enhanced our ability to observe the universe. 9. Define and differentiate between the three basic categories of astronomical observation: imaging, spectroscopy, and timing. imaging (in astronomical research) The process of obtaining pictures of astronomical objects. spectroscopy (in astronomical research) The process of obtaining spectra from astronomical objects. timing (in astronomical research) The process of tracking how the light intensity from an astronomical object varies with time. Imaging yields pictures of astronomical objects. At its most basic, an imaging instrument is simply a camera. Astronomers sometimes place filters in front of the camera that allow only particular colors or wavelengths of light to pass through. Most of the richly hued images in this and other astronomy books are made by combining images recorded through different filters. Spectroscopy involves spreading light into a spectrum. Instruments called spectrographs use diffraction gratings (or other devices) to disperse light into spectra, which are then recorded with a detector such as a CCD. Timing tracks how an object's brightness varies with time. For a slowly varying object, a timing experiment may be as simple as comparing a set of images or spectra obtained on different nights. For more rapidly varying sources, specially designed instruments essentially make rapid multiple exposures, in some cases recording the arrival time of every individual photon. 10. What is a false-color image? Why are false-color images useful? false-color image An image displayed in colors that are not the true, visible-light colors of an object. The brightest regions are yellow, while the violet and black represent regions that emit few, if any, X rays. All images recorded in nonvisible light must necessarily use some kind of color or gray-scale coding. Because the colors in these images do not represent what our eyes actually see, they are often called false-color images. 11. What do we mean by spectral resolution? Explain why high spectral resolution is desirable but more difficult to achieve than lower spectral resolution. spectral resolution Describes the degree of detail that can be seen in a spectrum; the higher the spectral resolution, the more detail we can see. a spectrum can reveal a wealth of information about an object, including its chemical composition, temperature, and rotation rate. However, just as the amount of information we can glean from an image depends on the angular resolution, the information we can glean from a spectrum depends on the spectral resolution: The higher the spectral resolution, the more detail we can see. Higher spectral resolution means we can see more details in the spectrum. Both (a ) and (b ) show spectra of the same object for the same wavelength band, but the higher spectral resolution in (b ) enables us to see individual spectral lines that appear merged together in (a ). (The spectrum shows interstellar absorption lines.) 12. Explain how light pollution and atmospheric turbulence affect astronomical observations made from the Earth's surface. light pollution Human-made light that hinders astronomical observations. A telescope on the ground does not look directly into space but rather looks through the Earth's sometimes murky atmosphere. In fact, the Earth's atmosphere creates several problems for astronomical observations. The most obvious problem is weather-an optical telescope is useless under cloudy skies. Another problem is that our atmosphere scatters the bright lights of cities, creating what astronomers call light pollution, which can obscure the view even for the best telescopes. For example, the 2.5-meter telescope at Mount Wilson, the world's largest when it was built in 1917, would still be very useful today if it weren't located so close to the lights of what was once the small town of Los Angeles. Similar but less serious light pollution hinders many other telescopes, including the Mount Palomar telescopes near San Diego and the telescopes of the National Optical Astronomy Observatory on Kitt Peak near Tucson. Fortunately, many communities are working to reduce light pollution. Placing reflective covers on the tops of streetlights directs more light toward the ground, rather than toward the sky. A somewhat less obvious problem is the fact that the atmosphere distorts light. The ever-changing motion, or turbulence, of air in the atmosphere bends light in constantly shifting patterns. This turbulence causes the familiar twinkling of stars and blurs astronomical images. turbulence Rapid and random motion. 13. What is adaptive optics? What problems caused by the Earth's atmosphere can it solve? adaptive optics A technique in which telescope mirrors flex rapidly to compensate for the bending of starlight caused by atmospheric turbulence. Perhaps the most amazing new technology is adaptive optics, which can eliminate most atmospheric distortion. Atmospheric turbulence causes a stellar image to dance around in the focal plane of a telescope. Adaptive optics essentially make the telescope's mirrors do an opposite dance, canceling out the atmospheric distortions 14. Study Figure 7.21 in detail, and describe how deeply each portion of the electromagnetic spectrum penetrates the Earth's atmosphere. In figure 7.21 gamma ray medium long lines x-ray short lines ultraviolet visible short lines infrared medium long lines radio long black lines. 500 km 100 km 10 km 15. Briefly describe the advantages of putting telescopes in space. Are there any disadvantages? Explain. no light pollution be able to see in clearer detail. Unfortunately, the atmosphere poses a major problem that no Earth-bound technology can overcome: It prevents most forms of light from reaching the ground at all. astronomers study light across the entire spectrum. With the exception of telescopes for radio, some infrared, and visible-light observations, most of these telescopes are in space. Indeed, while the Hubble Space Telescope is the only major visible-light observatory in space (it is also used for infrared and ultraviolet observations), many less famous observatories are in Earth orbit for the purpose of making observations in nonvisible wavelengths. 16. Why is it useful to study light from across the spectrum? Briefly describe the characteristics of telescopes used to observe different portions of the spectrum. If we studied only visible light, we'd be missing much of the picture. Planets are relatively cool and emit primarily infrared light. The hot upper layers of stars like the Sun emit ultraviolet and X-ray light. Many objects emit radio waves, including some of the most exotic objects in the cosmos-quasars, which may contain black holes buried in their centers. Some violent events even produce gamma rays that travel through space to the Earth. Indeed, most objects emit light over a broad range of wavelengths. Only radio waves, visible light, parts of the infrared spectrum, and the longest wavelengths of ultraviolet light reach the ground. Observing other wavelengths requires placing telescopes in space (or, in a few cases, very high in the atmosphere on airplanes or balloons). astronomers study light across the entire spectrum. With the exception of telescopes for radio, some infrared, and visible-light observations, most of these telescopes are in space. Indeed, while the Hubble Space Telescope is the only major visible-light observatory in space (it is also used for infrared and ultraviolet observations), many less famous observatories are in Earth orbit for the purpose of making observations in nonvisible wavelengths. Table 7.2 lists some of the most important existing and planned telescopes in space. 17. Briefly explain the purpose of using two or more telescopes together through interferometry. interferometry A telescopic technique in which two or more telescopes are used in tandem to produce much better angular resolution than the telescopes could achieve individually. 18. Describe each of the four main categories of spacecraft and their uses. most robotic spacecraft fall into four main categories: 1. Earth-orbiters. Simply being in space is enough to overcome the observational problems presented by Earth's atmosphere, so most space-based astronomical observatories orbit the Earth. Earth orbit is also the obvious place for spacecraft that study the Earth itself. 2. Flybys. Close-up study of other planets requires sending spacecraft to them. Flybys follow unbound orbits past their destinations; that is, they fly past a world just once and then continue on their way. For example, Voyager 2's orbit allowed it to make flybys of Jupiter, Saturn, Uranus, and Neptune (Figure 7.27). 3. Orbiters (of other worlds). A flyby can study a planet or moon close up-but only once. For more detailed or longer-term studies, we need a spacecraft that goes into orbit around another world. 4. Probes and landers. The most "up close and personal" study of other worlds comes from spacecraft that send probes into their atmospheres or landers to their surfaces. 19. Briefly explain the trade-offs between orbital considerations and cost involved in planning a spacecraft mission. How were costs reduced in the Mars Pathfinder mission, the Mars Global Surveyor mission, and the Cassini mission? Because spacecraft require very high speeds to leave the Earth, spacecraft must be launched atop large rockets. The heavier the spacecraft, the larger and more expensive the rocket required. The most obvious way to reduce the weight and launch cost of a spacecraft is to make it smaller. Just as powerful computers today are smaller than ever, new technologies are reducing the size of many scientific instruments. Once a spacecraft is on its way, it requires no more fuel unless it needs to change its orbit Two 1997 Mars missions used imaginative techniques to reduce the amount of fuel they needed to carry. The Pathfinder lander used parachutes to slow its descent through the thin Martian atmosphere. Before hitting the surface at about 50 km/hr, it deployed air bags around itself for protection The Mars Global Surveyor, an orbiter, saved on weight by carrying only enough fuel to change its flyby trajectory to a highly eccentric orbit around Mars. To settle into a smaller and more circular orbit, it skimmed the Martian atmosphere at the low point of each elliptical orbit. Atmospheric drag slowed the spacecraft, removing its unwanted orbital energy. Discussion Questions 1. Science and Technology Funding. Technological innovation clearly drives scientific discovery in astronomy, but the reverse is also true. For example, Newton's discoveries were made in part to explain the motions of the planets, but they have had far-reaching effects on our civilization. Congress often must make decisions between funding programs with purely scientific purposes ("basic research") and programs designed to develop new technologies. If you were a member of Congress, how would you try to allocate spending between basic research and technology? Why? 2. A Lunar Observatory. Do the potential benefits of building an astronomical observatory on the Moon justify its costs at the present time? If it were up to you, would you recommend that Congress begin funding such an observatory? Defend your opinions. Problems Sensible Statements? For problems 1-8, decide whether the statement is sensible and explain why it is or is not. 1. The image was blurry because the photographic film was not placed at the focal plane. 2. By using a CCD, I can photograph the Andromeda Galaxy with a shorter exposure time than I would need with photographic film. 3. Thanks to adaptive optics, the telescope on Mount Wilson can now make ultraviolet images of the cosmos. 4. New technologies will soon allow astronomers to use X-ray telescopes on the Earth's surface. 5. Thanks to interferometry, a properly spaced set of 10-meter radio telescopes can achieve the angular resolution of a single, 100-kilometer radio telescope. 6. Thanks to interferometry, a properly spaced set of 10-meter radio telescopes can achieve the light-collecting area of a single, 100-kilometer radio telescope. 7. Scientists are planning a flyby of Uranus in order to do long-term monitoring of the planet's weather. 8. An observatory on the Moon's surface could have telescopes monitoring light from all regions of the electromagnetic spectrum. 9. Angular Resolution. 1. Briefly describe why smaller is better when it comes to angular resolution. 2. Suppose that two stars are separated in the sky by 0.1 arcsecond. What will you see if you look at them with a telescope that has an angular resolution of 0.01 arcsecond? What will you see if you look at them with a telescope that has an angular resolution of 0.5 arcsecond? 10. Light-Collecting Area. 1. How much greater is the light-collecting area of one of the 10-meter Keck telescopes than that of the 5-meter Hale telescope? 2. Suppose astronomers built a 100-meter telescope. How much greater would its light-collecting area be than that of the 10-meter Keck telescope? 11. Project: Twinkling Stars. Using a star chart, identify 5 to 10 bright stars that should be visible in the early evening. On a clear night, observe each of these stars for a few minutes. Note the date and time, and for each star record the following information: approximate altitude and direction in your sky, brightness compared to other stars, color, how much the star twinkles compared to other stars. Study your record. Can you draw any conclusions about how brightness and position in your sky affect twinkling? Explain. 12. Angular Separation Calculations. 1. Two light bulbs are separated by 0.2 meter and you look at them from a distance of 2 kilometers. What is the angular separation of the lights? Can your eyes resolve them? Explain. 2. The diameter of a dime is about 1.8 centimeters. What is its angular diameter if you view it from across a 100-meter-long football field? 13. Calculating the Sun's Size. The angular diameter of the Sun is about the same as that of the Moon (0.5°). Use this fact and the Sun's average distance of about 150 million km to estimate the diameter of the Sun. Compare your result to the Sun's actual diameter of 1.392 million km. 14. Viewing a Dime with the HST. The Hubble Space Telescope (HST) has an angular resolution of about 0.05 arcsecond. How far away would you have to place a dime (diameter = 1.8 cm) for its angular diameter to be 0.05 arcsecond? (Hint: Start by converting an angular diameter of 0.05 arcsecond into degrees.) 15. Close Binary System. Suppose that two stars in a binary star system are separated by a distance of 100 million km and are located at a distance of 100 light-years from Earth. What is the angular separation of the two stars? Give your answer in both degrees and arcseconds. Can the Hubble Space Telescope resolve the two stars? 16. Diffraction Limit of the Eye. Calculate the diffraction limit of the human eye, assuming a lens size of 0.8 cm, for visible light of 500-nm wavelength. How does this compare to the diffraction limit of a 10-meter telescope? 17. The Size of Radio Telescopes. What is the diffraction limit of a 100-meter radio telescope observing radio waves with a wavelength of 21 cm? Compare this to the diffraction limit of the 2.4-meter Hubble Space Telescope for visible light. Use your results to explain why radio telescopes must be much larger than optical telescopes to be useful. 18. Hubble's Field of View. Large telescopes often have small fields of view. For example, the Hubble Space Telescope's (HST) "wide field" camera has a field of view that is roughly square and about 0.04° on a side. 1. Calculate the angular area of the HST's field of view in square degrees. 2. The angular area of the entire sky is about 41,250 square degrees. How many pictures would the HST have to take with its wide field camera to obtain a complete picture of the entire sky? 3. Assuming that it requires an average of 1 hour to take each picture, how long would it take to acquire the number of pictures you calculated in part (b)? Use your answer to explain why astronomers would like to have more than one large telescope in space. Web Projects Find useful links for Web projects on the text Web site. 1. Planetary Mission. Choose a current mission to a planet and find as much information as you can about the mission. Write a two- to three-page summary of the mission, including discussion of its purpose, design, and cost. 2. Major Observatories. Take a virtual tour of one of the world's major astronomical observatories. Write a short report on why the observatory is useful to astronomy. 3. Earth-Observing Satellites. Research one or more satellites that are designed to study the Earth. Briefly explain the purpose of each satellite and why it is able to collect data from space that would be more difficult to collect on the ground. Chapter 8 Review Questions 1. What is comparative planetology? What is its basic premise? What are its primary goals? comparative planetology is The study of the solar system by examining and understanding the similarities and differences among worlds. the differences between these worlds must be attributable to physical processes that we can study and understand by comparing the worlds to one another. This approach is called comparative planetology; the term planetology is used broadly to include moons, asteroids, and comets as well as planets. The idea is that we can learn more about the Earth, or any other world, by studying it in the context of other objects in our solar system—rather like learning about 2. Briefly summarize the observed patterns of motion in our solar system. All orbits except Mercury and Pluto are nearly circular. Most moons orbit in the same direction as the planets orbit and rotate: counterclockwise when seen from above Earth's North Pole. b Side view of the solar system. Arrows indicate the orientation of the rotation axes of the planets and their orbital motion. All planets orbit the Sun in the same direction—counterclockwise as seen from high above the Earth's North Pole. All planetary orbits lie nearly in the same plane. Almost all planets travel on nearly circular orbits, and the spacing between planetary orbits increases with distance from the Sun according to a fairly regular trend. The most notable exception to this trend is an extra-wide gap between Mars and Jupiter that is populated with asteroids. Most planets rotate in the same direction in which they orbit—counterclockwise as seen from above the Earth's North Pole—with fairly small axis tilts (i.e., less than about 25°). Almost all moons orbit their planet in the same direction as the planet's rotation and near the planet's equatorial plane. The Sun rotates in the same direction in which the planets orbit. 3. Summarize the differences between terrestrial planets and jovian planets. Why is the Moon grouped with the terrestrial planets? Where does Pluto fit in? terrestrial planets are Rocky planets similar in overall composition to Earth. jovian planets are Giant gaseous planets similar in overall composition to Jupiter. Pluto is left out in the cold, both literally and figuratively. On one hand, it is small and solid like the terrestrial planets. On the other hand, Pluto is far from the Sun, cold, and made of low-density ices. Pluto also has an unusual orbit, more eccentric than the orbit of any other planet and substantially inclined to the plane in which the other planets orbit the Sun. For a long time, scientists considered Pluto to be a lone misfit. However, some scientists now classify Pluto with other icy bodies in the outer solar system: comets 4. What are asteroids? Where are they found? What are comets, and how do those of the Oort cloud and the Kuiper belt differ in terms of their orbits? asteroid is A relatively small and rocky object that orbits a star; asteroids are sometimes called minor planets because they are similar to planets but smaller. asteroid belt The region of our solar system between the orbits of Mars and Jupiter in which asteroids are heavily concentrated. 5. Summarize the four challenges that any theory of the solar system must explain. Solar System formation dust and gas. The third challenge for any theory of solar system formation is to explain the existence and general properties of the large numbers of asteroids and comets. 6. What is the nebular theory? How does it get its name? What do we mean by the solar nebula? nebular theory The detailed theory that describes how our solar system formed from a cloud of interstellar gas and dust. solar nebula The piece of interstellar cloud from which our own solar system formed. 7. Describe the processes that led the solar nebula to collapse into a spinning disk. Also describe the evidence supporting the idea that our solar system had a protosun and a protoplanetary disk early in its history. First, the temperature of the solar nebula increased as it collapsed. Such heating represents energy conservation in action [Section 4.2]. As the cloud shrank, its gravitational potential energy was converted to the kinetic energy of individual gas particles falling inward. These particles crashed into one another, converting the kinetic energy of their inward fall into the random motions of thermal energy. Some of this energy was radiated away as thermal radiation. The solar nebula became hottest near its center, where much of the mass collected to form the protosun. The protosun eventually became so hot that nuclear fusion ignited in its core—at which point our Sun became a full-fledged star. Second, like an ice skater pulling in her arms as she spins, the solar nebula rotated faster and faster as it shrank in radius. This increase in rotation rate represents the conservation of angular momentum in action [Section 5.2]. The rotation helped ensure that not all of the material in the solar nebula collapsed onto the protosun: The greater the angular momentum of a rotating cloud, the more spread out it will be. Third, the solar nebula flattened into a disk—the protoplanetary disk from which the planets eventually formed. This flattening is a natural consequence of collisions between particles, which explains why flat disks are so common in the universe (e.g., the disks of spiral galaxies like the Milky Way, ring systems around planets, and accretion disks around neutron stars or black holes Figure 8.6 This sequence of paintings shows the collapse of an interstellar cloud. In our solar nebula, the hot, dense central bulge became the Sun, and the planets formed in the disk. a The original cloud is large and diffuse, and its rotation is almost imperceptibly slow.b The cloud heats up and spins faster as it contracts. c The result is a spinning, flattened disk, with mass concentrated near the center. 8. Distinguish among metals, rocks, hydrogen compounds, and light gases. What were their relative abundances in the solar nebula? The churning and mixing of the gas in the solar nebula ensured that its composition was about the same throughout: roughly 98% hydrogen and helium, and 2% heavier elements such as carbon, nitrogen, oxygen, silicon, and iron. Metals include iron, nickel, aluminum, and other materials that are familiar on Earth but less common on the surface than ordinary rock. Most metals condense into solid form at temperatures between 1,000 K and 1,600 K. Metals made up less than 0.2% of the solar nebula's mass. Rocks are materials common on the surface of the Earth, primarily silicon-based minerals (silicates). Rocks are solid at temperatures and pressures found on Earth but typically melt or vaporize at temperatures of 500–1,300 K depending on their type. Rocky materials made up about 0.4% of the nebula by mass. Hydrogen compounds are molecules such as methane (CH4), ammonia (NH3), and water (H2O) that solidify into ices below about 150 K. These compounds were significantly more abundant than rocks and metals, making up 1.4% of the nebula's mass. Light gases (hydrogen and helium) never condense under solar nebula conditions. These gases made up the remaining 98% of the nebula's mass. The order of condensation temperatures is easy to remember: It's the same as the order of densities. 9. Explain how temperature differences in the solar nebula led to the condensation of different materials at different distances from the protosun. What do we mean by the frost line in the solar nebula? The vast majority of the material in the solar nebula was gaseous: High temperatures kept virtually all the ingredients of the solar nebula vaporized near the protosun. Farther out the nebula was still primarily gaseous because hydrogen and helium are gases at nearly all temperatures. But the 2% of material consisting of heavier elements could form solid seeds where temperatures were low enough. The formation of solid or liquid particles from a cloud of gas is called condensation. Pressures in the solar nebula were so low that liquid droplets rarely formed, but solid particles could condense in the same way that snowflakes condense from water vapor in our atmosphere. We refer to such solid particles as condensates. The different kinds of planets and satellites formed out of the different kinds of condensates present at different locations in the solar nebula. frost line is The boundary in the solar nebula beyond which ices could condense; only metals and rocks could condense within the frost line. Only beyond the frost line, which lay between the present-day orbits of Mars and Jupiter, were temperatures low enough (150 K @ –123°C) for hydrogen compounds to condense into ices. (Water ice did not form at the familiar 0°C because the pressures in the nebula were 10,000 times lower than on Earth.) 10. What is accretion? What are planetesimals? Explain the role of electrostatic forces in getting accretion started and the role of gravity in accelerating accretion as planetesimals grow larger. accretion The process by which small objects gather together to make larger objects. planetesimals The building blocks of planets, formed by accretion in the solar nebula. gravity One of the four fundamental forces; it is the force that dominates on large scales. the flakes were far too small to attract one another by gravity, but they were able to stick together through electrostatic forces—the same "static electricity" that makes hair stick to a comb. the flakes grew slowly into larger particles. As the particles grew in mass, gravity began to aid the process of their sticking together, accelerating their growth. This process of growing by colliding and sticking is called accretion. The growing objects formed by accretion are called planetesimals, which essentially means "pieces of planets." Small planetesimals probably came in a variety of shapes, such as we see in many small asteroids today. Larger planetesimals (i.e., those several hundred kilometers across) became spherical because the force of gravity was strong enough to overcome the strength of rock and pull everything toward the center. 11. Briefly explain why accretion was able to produce much larger planetesimals in the outer solar system than in the inner solar system. the flakes grew slowly into larger particles. As the particles grew in mass, gravity began to aid the process of their sticking together, accelerating their growth. This process of growing by colliding and sticking is called accretion. The growing objects formed by accretion are called planetesimals, which essentially means "pieces of planets." Larger planetesimals (i.e., those several hundred kilometers across) became spherical because the force of gravity was strong enough to overcome the strength of rock and pull everything toward the center. The growth of planetesimals was rapid at first: As planetesimals grew larger, they had both more surface area with which to collide and more gravity to attract other planetesimals. Some probably grew to hundreds of kilometers in size in only a few million years. 12. Describe the process of nebular capture that allowed the jovian planets to grow to large sizes. How does this process explain the satellite systems of jovian planets? Accretion proceeded rapidly in the outer solar system, because the presence of ices meant much more material in solid form. Some of the icy planetesimals of the outer solar system quickly grew to sizes many times larger than the Earth. At these large sizes, their gravity was strong enough to capture the far more abundant hydrogen and helium gas from the surrounding nebula. As they accumulated substantial amounts of gas, the gravity of these growing planets grew larger still—allowing them to capture even more gas. The process by which icy planetesimals act as seeds for capturing far larger amounts of hydrogen and helium gas, called nebular capture, led directly to the formation of the jovian worlds (Figure 8.14). It explains their huge sizes and the large abundance of hydrogen and helium reflected in their low average densities. nebular capture is The process by which icy planetesimals capture hydrogen and helium gas to form jovian planets. 13. What is the solar wind? How did its strength in the past differ from its strength today? What role did it play in ending the growth of the planets? solar wind is A stream of charged particles ejected from the Sun. Although the solar wind is fairly weak today, we have evidence that it was much stronger when the Sun was young—strong enough to have swept huge quantities of gas out of our solar system. The clearing of the gas interrupted the cooling process in the nebula. Had the cooling continued longer, ices might have condensed in the inner solar system. Instead, the solar wind swept the still-vaporized hydrogen compounds away from the inner solar system, along with the remaining hydrogen and helium throughout the solar system. When the gas cleared, the compositions of objects in the early solar system were essentially set. 14. Why does the Sun's slow rotation rate seem, at least at first, to contradict the nebular theory? Explain how the process of magnetic braking accounts for this apparent contradiction. the nebular theory also makes one prediction that at first seems to contradict our observations: Conservation of angular momentum in the collapsing solar nebula means that the young Sun should have been rotating very fast, but the Sun actually rotates quite slowly, with each full rotation taking about a month. Fortunately, this apparent contradiction between theory and observation has a simple resolution. Angular momentum cannot simply disappear, but it is possible to transfer angular momentum from one object to another—and then get rid of the second object. A spinning skater can slow her spin by grabbing her partner and then pushing him away. Beginning in the 1950s, scientists realized that the young Sun's rapid rotation would have generated a magnetic field far stronger than that of the Sun today. magnetic braking The process by which a star's rotation slows as its magnetic field transfers its angular momentum to the surrounding nebula. 15. Why do we think that asteroids and comets are leftover planetesimals? Briefly describe how gravitational encounters affected their orbits. Origin of Asteroids and Comets The strong wind from the young Sun cleared excess gas from the solar nebula, but many planetesimals remained scattered between the newly formed planets. These "leftovers" became comets and asteroids. Like the planetesimals that formed the planets, they formed from condensation and accretion in the solar nebula. Their compositions followed the pattern determined by condensation: planetesimals of rock and metal in the inner solar system, and icy planetesimals in the outer solar system. Leftover planetesimals originally must have had nearly circular orbits in the same plane as the orbits of the planets. But gravitational encounters with the newly formed planets soon made their orbits more random. When small planetesimals passed near a large planet, the planet was hardly affected, but the planetesimals were flung off at high speed in random directions. The strong gravity of the jovian planets, in particular, tugged and nudged the orbits of leftover planetesimals, even at great distances. 16. What was the early bombardment? How can we use impact crators to estimate the age of a planetary surface? The Early Bombardment: A Rain of Rock and Ice The collision of a leftover planetesimal with a planet is called an impact, and the responsible planetesimal is called the impactor. On planets with solid surfaces, impacts leave the scars we call impact craters. Impacts were extremely common in the young solar system; in fact, impacts were part of the accretion process in the late stages of planetary formation. The vast majority of impacts occurred in the first few hundred million years of our solar system's history. The heavy bombardment of planetary surfaces in the early solar system would have resembled a rain of rock and ice from space meteorites Although thousands of asteroids remain in the asteroid belt, their combined mass is less than 1/1,000 of Earth's mass. Jupiter's gravity continues to nudge these asteroids, changing their orbits and sometimes leading to violent, shattering collisions. Debris from these collisions often crashes to Earth in the form of meteorites. one way of estimating the age of a planetary surface (the time since the surface last changed in a substantial way) is to count the number of craters: If there are many craters, the surface must still look much as it did when the early bombardment ended, about 4 billion years ago. The early rain of rock and ice did more than just scar planetary surfaces. It also brought the materials from which atmospheres, oceans, and polar caps eventually formed. 17. What clues suggest that a moon was captured instead of forming with its planet? How do we think such captures occurred? Give a few examples of moons thought to have been captured. some moons have unusual orbits—orbits in the "wrong" direction (opposite the rotation of their planet) or with large inclinations to the planet's equator. These unusual moons are probably leftover planetesimals that were captured into orbit around a planet. a moon orbiting Jupiter unless it somehow loses orbital energy. Captures probably occurred when the capturing planet had a very extended atmosphere or, in the case of the jovian planets, its own miniature solar nebula. Passing planetesimals could be slowed by friction with the gas, just as artificial satellites are slowed by drag with the Earth's atmosphere. If friction reduced a planetesimal's orbital energy enough, it could have become an orbiting moon. 18. Describe the process by which a giant impact may have led to the formation of our Moon. What other oddities of our solar system might be explained by giant impacts? Our Moon is much too large to have been captured by Earth. Today, such a giant impact is the leading hypothesis for explaining the origin of our Moon. The Moon's composition is similar to that of the Earth's outer layers, exactly what we would predict for the kind of collision. the impact of a Mars-size object with Earth, as may have occurred soon after Earth's formation. The ejected material comes mostly from the outer rocky layers and accretes to form the Moon, which is poor in metal. 19. Summarize how the nebular theory meets the four challenges laid out in this chapter. Describe a few of the remaining unanswered questions. the unusual properties of specific planets—properties that defy the general trends expected by the nebular theory—may be the results of giant impacts. Mercury may have lost much of its outer, rocky layer in a giant impact, leaving it with a huge metallic core. A giant impact might even have contributed to the slow, backward rotation of Venus, which may have had a "normal" rotation until the arrival of the giant impactor. Giant impacts probably also were responsible for the axis tilts of many planets (including Earth) and for tipping Uranus on its side. Pluto's moon Charon may have formed in a giant-impact process similar to the one that formed our Moon. 20. Briefly describe the process of radioactive dating and how we use it to establish the age of our solar system. Why can't we determine the age of our solar system by dating Earth rocks? What kinds of rocks can we use? radioactive dating. The process of determining the age of a rock (i.e., the time since it solidified) by comparing the present amount of a radioactive substance to the amount of its decay product. 21. What evidence suggests that a nearby stellar explosion may have triggered the collapse of the solar nebula? In fact, xenon-129 is a decay product of iodine-129. But iodine-129 has a half-life of just 17 million years, so this iodine must have traveled from the star in which it was produced to our solar nebula fairly quickly. (If the supernova had occurred a billion years earlier, the iodine would have decayed entirely into xenon, which would not have condensed or accreted.) This suggests that a nearby star exploded only a few million years (or less) before our solar system formed. The shock wave emanating from the exploding star may even have triggered the collapse of the solar nebula by giving gravity a little extra push. Once gravity got started, the rest of the collapse was inevitable. the presence of these elements in meteorites and on Earth underscores the fact that our solar system is made from the remnants of past generations of stars. The discovery of daughter elements of short-lived radioactive elements has further implications. The rare isotope xenon-129 is found in some meteorites. Xenon is gaseous even at extremely low temperatures, so it could not have condensed and become trapped in planetesimals forming in the solar nebula. solar nebula The piece of interstellar cloud from which our own solar system formed. 22. Describe how we can detect extrasolar planets today, and summarize the current evidence concerning planets in other solar systems. The discovery of extrasolar planets presents us with opportunities to test our theory of solar system formation. Can our existing theory explain other planetary systems, or will we have to go back to the drawing board? the discoveries have presented at least one significant challenge. The new challenge arises from the fact that most of the recently discovered planets are quite different from those of our solar system. Many have highly elliptical orbits rather than the nearly circular orbits of planets in our solar system, and most of the planets are more massive than Jupiter. Most intriguing is the fact that many of these large planets lie quite close to their stars—a very different situation from that in our solar system, where the large planets are found in the outer solar system. Moreover, as we discussed in Section 8.4, our theory has a good explanation for why large planets should form only in the outer solar system: That is the only place where the solar nebula was cool enough for ices to condense and grow into the large seeds needed for jovian planets. The existence of dozens of systems with large, close-in planets seems to contradict our theory. 23. What have we learned about solar system formation from discoveries of extrasolar planets? the gas in a forming solar system can exert drag on young jovian planets, tending to make them migrate closer to their stars. if a star's wind does not sweep the remaining nebular gas into space soon enough, the jovian planets may end up close to their stars—which could explain the large, close-in planets we've detected. In some cases, the planets may even end up being consumed by their parent stars! If this idea proves correct, the layout of our solar system suggests that the solar wind blew out the remaining gas of the solar nebula relatively early compared to other star systems. high-resolution interferometers that will enable us to obtain images and spectra of planets in other solar systems. Then, at last, we will know whether solar systems like ours—and planets like Earth—are rare or common. Discussion Questions 1. Theory and Observation. Discuss the interplay between theory and observation that has led to our modern theory of the formation of the solar system. What role does technology play in allowing us to test this theory? 2. Random Events in Solar System History. According to our theory of solar system formation, numerous random events, such as giant impacts, had important consequences for the way our solar system turned out. Can you think of other random events that might have caused the planets to form very differently? If there had been a different set of random events, what important properties of our solar system would have turned out the same and what ones might be different? Discuss. 3. Lucky to Be Here? In considering the overall process of solar system formation, do you think it was very likely for a planet like Earth to have formed? Could random events in the early history of the solar system have prevented us from even being here today? Defend your opinion. Do your opinions on these questions have any implications for your belief in the possibility of Earth-like planets around other stars? Problems Surprising Discoveries? For problems 1–8, suppose we found a solar system with the property described. (These are not real discoveries.) In light of our theory of solar system formation, decide whether the discovery should be considered reasonable or surprising. Explain. 1. A solar system has five terrestrial planets in its inner solar system and three jovian planets in its outer solar system. 2. A solar system has four large jovian planets in its inner solar system and seven small planets made of rock and metal in its outer solar system. 3. A solar system has ten planets that all orbit the star in approximately the same plane. However, five planets orbit in one direction (e.g., counterclockwise), while the other five orbit in the opposite direction (e.g., clockwise). 4. A solar system has 12 planets that all orbit the star in the same direction and in nearly the same plane. The 15 largest moons in this solar system orbit their planets in nearly the same direction and plane as well. However, several smaller moons have highly inclined orbits around their planets. 5. A solar system has six terrestrial planets and four jovian planets. Each of the six terrestrial planets has at least five moons, while the jovian planets have no moons at all. 6. A solar system has four Earth-size terrestrial planets. Each of the four planets has a single moon nearly identical in size to Earth's Moon. 7. A solar system has many rocky asteroids and many icy comets. However, most of the comets orbit the star in a belt much like the asteroid belt of our solar system, while the asteroids inhabit regions much like the Kuiper belt and Oort cloud of our solar system. 8. A solar system has several planets similar in composition to our jovian planets but similar in mass to our terrestrial planets. 9. Two Classes of Planets. Explain in terms a friend or roommate would understand why the jovian planets are lower in density than the terrestrial planets even though they all formed from the same cloud. 10. A Cold Solar Nebula. Suppose the entire solar nebula had cooled to 50 K before the solar wind cleared it away. How would the composition and sizes of the terrestrial planets be different from what we see today? Explain your answer in a few sentences. 11. No Nebular Capture. Suppose the solar wind had cleared away the solar nebula before the process of nebular capture was completed in the outer solar system. How would the jovian planets be different? Would they still have satellites? Explain your answer in a few sentences. 12. Angular Momentum. Suppose our solar nebula had begun with much more angular momentum than it did. Do you think planets could still have formed? Why or why not? What if the solar nebula had started with zero angular momentum? Explain your answers in one or two paragraphs. 13. Jupiter's Action. Suppose that, for some reason, the planet Jupiter had never formed. How do you think the distribution of asteroids and comets in our solar system would be different? How would these differences have affected Earth? Explain your answer in a few sentences. 14. Satellite Systems as Mini–Solar Systems. The nebula surrounding the forming jovian planets was hotter near its center, so satellites forming from the nebula could be built from different types of condensates, just as the planets were. Would satellite densities increase or decrease with increasing distance from the planet? According to Appendix C, which jovian planet satellite system best matches this prediction? Explain your answers in a few sentences. 15. Dating Lunar Rocks. Suppose you are analyzing Moon rocks that contain small amounts of uranium-238, which decays into lead with a half-life of 4.5 billion years. 1. In one rock from the lunar highlands, you determine that 55% of the original uranium-238 remains; the other 45% has decayed into lead. How old is the rock? 2. In a rock from the lunar maria, you find that 63% of its original uranium-238 remains; the other 37% has decayed into lead. Is this rock older or younger than the highlands rock? By how much? (The significance of these ages will become clear in the next chapter.) 16. Radioactive Dating with Carbon-14. The half-life of carbon-14 is about 5,700 years. 1. You find a piece of cloth painted with organic dyes. By analyzing the dye in the cloth, you find that only 77% of the carbon-14 originally in the dye remains. When was the cloth painted? 2. A well-preserved piece of wood found at an archaeological site has 6.2% of the carbon-14 that it must have had when it was alive. Estimate when the wood was cut. 3. Is carbon-14 useful for establishing the age of the Earth? Why or why not? 17. Unusual Meteorites. Some unusual meteorites thought to be chips from Mars [Section 12.3] contain small amounts of the radioactive element thorium-232 and its decay product lead-208. The half-life for this decay process is 14 billion years. A detailed analysis shows that 94% of the original thorium remains. How old are these meteorites? Compare your answer to the age of the solar system and comment briefly. 18. 51 Pegasi. The star 51 Pegasi has about the same mass as our Sun, and the planet discovered around it has an orbital period of 4.23 days. The mass of the planet is estimated to be 0.6 times the mass of Jupiter. 1. Use Kepler's third law to find the planet's average distance (semimajor axis) from its star. (Hint: Because the mass of 51 Pegasi is about the same as the mass of our Sun, you can use Kepler's third law in its original form, p 2 = a 3 [see Chapter 5]; be sure to convert the period into years.) 2. Briefly explain why, according to our theory of solar system formation, it is surprising to find a planet the size of the 51 Pegasi planet orbiting at this distance. 3. Hypothesize as to how the 51 Pegasi planet might have come to exist. Explain your hypothesis in a few sentences. 19. Transiting Planets. The star HD209548 is about the same size as our Sun, and the planet discovered around it blocks 1.7% of the star's area when it passes in front of the star. (Appendix E contains useful data for this problem.) 1. How large a planet is required to block the observed fraction of the star's area? Give your answer in kilometers. (Hint: Remember that the brightness drop tells us that the planet blocked 1.7% of the star's visible area.) 2. The mass of the planet is estimated to be 0.6 times the mass of Jupiter. What is the density of the planet? 3. Compare the density of this planet to that of planets in our solar system, and comment on whether this density makes the planet terrestrial or jovian in nature. Web Projects Find useful links for Web projects on the text Web site. 1. New Planets. Find up-to-date information about discoveries of planets in other solar systems. Create a personal "Web journal," complete with pictures from the Web, describing at least three recent discoveries of new planets. For each case, write one or two paragraphs in your journal describing the method used in the discovery, comparing the discovered planet to the planets of our own solar system, and summarizing whether the discovery poses any new challenges to our theory of solar system formation. 2. Missions to Search for Planets. Learn about one proposed space mission to search for planets around other stars, such as Kepler, SIM, or Terrestrial Planet Finder. Write a short report about the plans for the mission and its current status. Chapter 9 Review Questions 1. Briefly explain how the terrestrial planets ended up spherical in shape. Would you also expect small asteroids to be spherical? Why or why not? The rocky terrestrial worlds became spherical because of rock's ability to flow. Even when rock is solid, the strength of gravity in a moderately large world (over about 500 km in diameter) can overcome the strength of solid rock and make the world spherical in less than a billion years. Planets are all approximately spherical and quite smooth relative to their size. For example, compared to the Earth's radius of 6,378 km, the tallest mountains could be represented by grains of sand on a typical globe. rocks as the very definition of strength, but rocks are not always as solid as they may seem. Most rocks are a hodgepodge of different minerals, each characterized by its chemical composition. 2. What is viscosity? Give examples of substances with low viscosity and substances with high viscosity. viscosity Describes the thickness of a liquid in terms of how rapidly it flows; low-viscosity liquids flow quickly (water), while high-viscosity liquids flow slowly molasses. 3. How does differentiation occur, and under what circumstances? Explain how differentiation led to the core–mantle–crust structure of the terrestrial worlds. differentiation is The process in which gravity separates materials according to density, with high-density materials sinking and low-density materials rising. 4. What is a lithosphere? What determines the strength and thickness of a planet's lithosphere? lithosphere is The relatively rigid outer layer of a planet; generally encompasses the crust and the uppermost portion of the mantle. The terms core, mantle, and crust are defined by the composition within each layer. But characterizing the layers by rock strength rather than composition turns out to be more useful for understanding geological activity. From this point of view, we speak of an outer layer of relatively rigid rock called the lithosphere (lithos means "stone" in Greek). The lithosphere generally encompasses the crust and the uppermost portion of the mantle. Beneath the lithosphere, the higher temperatures allow rock to deform and flow much more easily. 5. Describe and distinguish among the three major processes by which planetary interiors get hot: accretion, differentiation, and radioactivity. the smaller worlds have thicker lithospheres, indicating that they have cooler interiors. The cores and mantles also differ in their relative sizes: Because cores are made from metals and mantles are made from rock, their relative sizes depend on the proportions of metal and rock in a planet. These proportions were determined primarily by condensation in the solar nebula, but they may also have been affected by giant impacts [Section 8.5]. Planetary cores may be partially or completely molten, depending on the particular combination of internal temperature and pressure. You may be wondering how we know what the interiors of the terrestrial worlds look like. After all, even on Earth our deepest drill shafts barely prick the lithosphere. Fortunately, several techniques allow us to study planetary interiors without actually having to drill into them. First, we can measure a planet's size from telescopic or spacecraft images, and its mass by applying Newton's version of Kepler's third law to the orbital properties of a natural or artificial satellite. 6. Describe and distinguish among the three major processes by which planetary interiors transfer heat to planetary surfaces: conduction, convection, and eruption. How does the heat escape from the planet's surface into space? Accretion was the earliest major source of internal heat for the terrestrial worlds. The many violent impacts that occurred during the latter stages of accretion deposited so much energy that planet-wide melting occurred. Imagine the entire Earth engulfed in molten rock! This melting enabled the process of differentiation, in which the densest materials (metals) settled to the planet's core, while lighter rocks rose to the surface. Both accretion and differentiation yield heat by converting gravitational potential energy into thermal energy. An object that hits an accreting world starts with a lot of gravitational potential energy when it is far away. This gravitational potential energy is converted to kinetic energy as gravity makes the object accelerate toward the planet's surface. Upon impact, the kinetic energy is converted to sound and heat, adding to the thermal energy of the planet. Differentiation converts gravitational potential energy to thermal energy just like a brick falling to the bottom of a swimming pool. The brick loses gravitational potential energy as it falls, and this energy ultimately appears as thermal energy in the water. the Sun contributes very little to a planet's internal temperature. In fact, the Sun's only role is in helping to determine the starting point for the interior temperature structure: A terrestrial world is coolest at its surface and gets warmer as you go into its interior. The three most important sources of internal heat are accretion, differentiation, and radioactivity. the Earth's surface receives more than 10,000 times as much energy from the Sun as from its own interior. In general, the energy a world receives from sunlight depends on its distance from the Sun. This energy, along with properties of the planet's atmosphere, The third internal heat source is the decay of radioactive elements such as uranium, potassium, thorium, and others. When radioactive nuclei decay, subatomic particles fly off at high speeds, colliding with neighboring atoms and heating them. 7. What is the primary factor in determining how long a planetary interior remains hot? Why? accretion and differentiation deposited heat in planetary interiors billions of years ago, but radioactivity continues to heat the terrestrial planets to this very day. the radioactive elements decay (billions of years from now), Earth's deep interior will become quite cool even though the pressure will be the same as it is today. The temperatures inside Earth and the other planets can remain high only if there is an internal source of heat, such as accretion, differentiation, or radioactivity. A planet's hot interior also convects, but much more slowly. The rising hot material transfers heat from deep in the planetary interior toward the surface. When the material fully cools, it begins to descend back down until the heating from below heats it enough to make it rise upward again. Convection is an ongoing process, and each small region of rising and falling material is called a convection cell. The third major process by which heat can escape a planet's interior is volcanic eruption. An eruption directly transfers heat outward by depositing hot lava on the surface. Regardless of whether heat reaches the surface through the slow leakage of convection and conduction or through the sudden burst of an eruption, this heat eventually radiates away into space. 8. What is a magnetic field? Contrast the magnetic fields of terrestrial planets. magnetic field Describes the region surrounding a magnet in which it can affect other magnets or charged particles in its vicinity. magnetic field lines Lines that represent how the needles on a series of compasses would point if they were laid out in a magnetic field. 9. Briefly describe the four major geological processes: impact cratering, volcanism, tectonics, and erosion. impact cratering is The excavation of bowl-shaped depressions (impact craters) by asteroids or comets striking a planet's surface. volcanism is The eruption of molten rock, or lava, from a planet's interior onto its surface. tectonics is The disruption of a planet's surface by internal stresses. erosion is The wearing down or building up of geological features by wind, water, ice, and other phenomena of planetary weather. geological processes is The four basic geological processes are impact cratering, volcanism, tectonics, and erosion. 10. Describe and distinguish between what we call formation properties and geological controlling factors in the context of planetary geology. Summarize in your own words the relationships shown in Figure 9.10. formation properties (of planets) In this book, for the purpose of understanding geological processes, planets are defined to be born with four formation properties: size (mass and radius), distance from the Sun, composition, and rotation rate. geological controlling factors In this book, for the purpose of understanding geological processes, geology is considered to be influenced primarily by four geological controlling factors: surface gravity, internal temperature, surface temperature, and the presence (and extent) of an atmosphere. Arrows between the geological controlling factors show how they affect one another. Both surface gravity and surface temperature have arrows pointing to atmosphere, because a planet's ability to hold atmospheric gases depends on both how fast the gas molecules move The atmosphere, in turn, points back to surface temperature because a thick atmosphere can make a planet's surface warmer than it would be otherwise (through the greenhouse effect. 11. Briefly describe how impacts affect planetary surfaces, and explain how we can estimate the geological age of a planetary surface from its number of impact craters. Impact cratering occurs when a leftover planetesimal (such as a comet or an asteroid) crashes into the surface of a terrestrial world. Impacts can have devastating effects on planetary surfaces, which we can see both from the impact craters left behind and from laboratory experiments that reproduce the impact process (Figure 9.11). Impactors typically hit planets at speeds between 30,000 and 250,000 km/hr (10–70 km/s) and pack enough energy to vaporize solid rock and excavate a crater.example, a 1-kilometer-wide impactor creates a crater about 10 kilometers wide and 1–2 kilometers deep. Debris from the blast, called ejecta, shoots high into the atmosphere and then rains down over a large area. If the impact is large enough, some of the atmosphere may be blasted away into space, and some of the rocky ejecta may completely escape from the planet. Sandy grains circle young star. 12. What created the "soil" on the lunar surface? Explain why the footprints of the astronauts on the Moon will last a long time, but not forever. The most common impactors are sand-size particles called micrometeorites when they impact a surface. Such tiny particles burn up as meteors in the atmospheres of Venus, Earth, and Mars. But on worlds that lack significant atmospheres, such as Mercury and the Moon, the countless impacts of micrometeorites gradually pulverize the surface rock to create a layer of powdery "soil." impacts still occur today, the vast majority of craters formed during the "rain of rock and ice" that ended around 3.8 billion years ago. Radioactive dating of moon rocks shows that the maria are 3–3.5 billion years old, but they have only 3% as many craters as the lunar highlands. 13. Explain how differences in lava viscosity lead to volcanic plains, shield volcanoes, or stratovolcanoes. when lavas erupt, materials such as water may form gas bubbles that increase the viscosity. (You can understand why bubbles increase viscosity by thinking about how much higher a "mountain" you can build with bubble-bath foam than you can with soapy water.) The runniest basalt lavas flow far and flatten out before solidifying, creating vast volcanic plains such as the lunar maria (Figure 9.17a). Somewhat more viscous basalt lavas solidify before they can completely spread out, resulting in shield volcanoes (so-named because they are shield-shaped). Shield volcanoes can be very tall, but they are not very steep; most have slopes of only 5°–10° The mountains of the Hawaiian Islands are shield volcanoes; measured from the ocean floor to their summits, the Hawaiian mountains are the tallest (and widest) on Earth. Tall, steep stratovolcanoes such as Mount St. Helens are made from much more viscous lavas that can't flow very far before solidifying 14. Describe several types of internal stress that can drive tectonic activity. Under what conditions does a lithosphere break into plates and show plate tectonics? volcanism. The main point to keep in mind is that internal temperature exerts the greatest control over volcanism: A hotter interior means that lava lies closer to the surface and can erupt more easily. The formation property of composition is also very important, because it determines the melting temperatures and viscosities of lavas that erupt and therefore what types of volcanoes form. Volcanism is connected to other geological processes in several ways beyond the simple fact that lava flows can cover up or fill in previous geological features. Tectonics and volcanism often go together: Tectonic stresses can force lava to the surface or cut off eruptions. Another connection reveals far-reaching effects: Volcanism affects erosion indirectly, because volcanoes are the primary source of gases in the current terrestrial planet atmospheres. tectonics the internal forces and stresses that act on the lithosphere to create surface features. Several types of internal stress can drive tectonic activity. On planets with internal convection, the strongest type of stress often comes from the circulation of the convection cells themselves. The tops of convection cells can drag against the lithosphere, sometimes forcing sections of the lithosphere together or apart. On Earth, these forces have broken the lithosphere into plates that move over, under, and around each other in what we call plate tectonics. 15. What are volatiles, and how are they important to erosion? Briefly explain why Mercury and the Moon have virtually no erosion. volatiles Refers to substances, such as water, carbon dioxide, and methane, that are usually found as gases, liquids, or surface ices on the terrestrial worlds. erosion, which encompasses a variety of processes connected by a single theme: the breakdown and transport of rocks by volatiles. The term volatile means "evaporates easily" and refers to substances—such as water, carbon dioxide, and methane—that are usually found as gases, liquids, or surface ices on the terrestrial worlds. Wind, rain, rivers, flash floods, and glaciers are just a few examples of processes that contribute to erosion on Earth. Erosion not only breaks down existing geological features (wearing down mountains and forming gullies, riverbeds, and deep valleys), but also builds new ones (such as sand dunes, river deltas, and lakebed deposits). If enough material is deposited over time, the layers can compact to form sedimentary rocks. Virtually no erosion takes place on worlds without a significant atmosphere, such as Mercury and the Moon. But planets with atmospheres can have significant erosional activity. Larger planets are better able to generate atmospheres by releasing gases trapped in their interiors; their stronger gravity also tends to prevent their atmospheres from escaping to space [Section 10.5]. In general, a thick atmosphere is more capable of driving erosion than a thin atmosphere, but a planet's rotation rate is also important. Slowly rotating planets like Venus have correspondingly slow winds and therefore weak or nonexistent wind erosion. Surface temperature also matters: Erosion isn't very effective if most of the volatiles stay frozen on the surface, but it can be very powerful when volatiles are able to evaporate and then recondense as rain or snow. Figure 9.21 summarizes the connections between erosion and other geological processes and properties. Virtually no erosion takes place on worlds without a significant atmosphere, such as Mercury and the Moon. But planets with atmospheres can have significant erosional activity. Larger planets are better able to generate atmospheres by releasing gases trapped in their interiors; their stronger gravity also tends to prevent their atmospheres from escaping to space [Section 10.5]. In general, a thick atmosphere is more capable of driving erosion than a thin atmosphere, but a planet's rotation rate is also important. Slowly rotating planets like Venus have correspondingly slow winds and therefore weak or nonexistent wind erosion. Surface temperature also matters: Erosion isn't very effective if most of the volatiles stay frozen on the surface, but it can be very powerful when volatiles are able to evaporate and then recondense as rain or snow. 16. Briefly summarize the geological history of the Moon. How and when did the maria form? Why is the Moon geologically "dead" today? Moon formed early in the history of our solar system when a giant impact blasted away some of Earth's rocky outer layers. The impact did not dredge up metallic core material, which explains why the Moon has a lower metal content than Earth and a smaller metal core. lunar rocks contain a much smaller proportion of volatiles (such as water) than Earth rocks, presumably because heat from the giant impact evaporated the volatiles and allowed them to escape into space before the Moon formed from the debris. Lunar samples confirm that the highlands are composed of low-density rocks. As the bombardment tailed off, around 3.8 billion years ago, a few larger impactors struck the surface and formed impact basins. Almost all the geological features of the Moon were formed by impacts and volcanism, although a few small-scale tectonic stresses wrinkled the surface as the lava of the maria cooled and contracted (Figure 9.22c). The Moon has virtually no erosion because of the lack of atmosphere, but the continual rain of micrometeorites has rounded crater rims. The heyday of lunar volcanism is long gone—3 billion years gone. Over time, the Moon's small size allowed its interior to cool, thickening the lithosphere. Today, the Moon's lithosphere probably extends to a depth of 1,000 km, making it far too thick to allow further volcanic or tectonic activity. The Moon has probably been in this geologically "dead" state for 3 billion years. 17. Briefly summarize the geological history of Mercury. What is the Caloris Basin? How did Mercury get its many huge cliffs? Based on its relatively high density, Mercury must be about 61% iron by mass, with a core that extends to perhaps 75% of its radius. Mercury's high metal content is due to its formation close to the Sun, possibly enhanced by a giant impact that blasted away its outer, rocky layers [Section 8.6]. Mercury has craters almost everywhere, indicating an ancient surface. A huge impact basin, called the Caloris Basin (Figure 9.23a), covers a large portion of one hemisphere. Like the large lunar basins, the Caloris Basin has few craters within it, indicating that it must have been formed toward the end of the solar system's early period of heavy bombardment. Despite the superficial similarity between their cratered surfaces, Mercury and the Moon also exhibit significant differences. Mercury has noticeably fewer craters than the lunar highlands (compare Figure 9.12a to Figure 9.23b). Smooth patches between many of the craters tell us that volcanic lava once flowed, covering up small craters. Mercury has no vast maria but has smaller lava plains almost everywhere, suggesting that Mercury had at least as much volcanism as the Moon. Tectonic processes played a more significant role on Mercury than on the Moon, as evidenced by tremendous cliffs. The cliff shown in Figure 9.24a is several hundred kilometers long and up to 3 kilometers high in places; the central crater apparently crumpled during the cliff's formation. This cliff, and many others on Mercury, probably formed when tectonic forces compressed the crust (Figure 9.24b). However, nowhere on Mercury do we find evidence of extension (stretching) to match this crustal compression. 18. Briefly discuss the superficial similarities between Mars and Earth that led many people in the early 1900s to believe that Mars must harbor life. What were the canali that some astronomers reported on Mars? Do they really exist? Early telescopic observations of Mars revealed several uncanny resemblances to Earth. A Martian day is just over 24 hours, and the Martian rotation axis is tilted about the same amount as Earth's. Mars also has polar caps, which we now know to be composed primarily of frozen carbon dioxide, with smaller amounts of water ice. Telescopic observations also showed seasonal variations in surface coloration over the course of the Martian year (about 1.9 Earth years). All these discoveries led to the perception that Mars and Earth were at least cousins, if not twins. By the early 1900s, many astronomers—as well as the public—envisioned Mars as nearly Earth-like, possessing water, vegetation that changed with the seasons, and possibly intelligent life. linear features across the surface of Mars through his telescope. He named these features canali, the Italian word for "channels." channels contained water or was merely continuing the tradition, started with the Moon, of naming dark features after bodies of water. 19. Briefly describe major geological features on Mars and their possible origins. the canali were canals being used by intelligent Martians to route water around their planet. He suggested that Mars was falling victim to unfavorable climate changes and that water was a precious resource that had to be managed carefully. canali turned out to be nothing more than dark dust deposits redistributed by seasonal winds. Several other spacecraft studied Mars in the 1960s and 1970s, culminating with the impressive Viking missions in 1976. Each of the two Viking spacecraft deployed an orbiter that mapped the Martian surface from above and landers that returned surface images and regular weather reports for almost 5 years. More than 20 years passed before the next successful missions to Mars, the Mars Pathfinder mission and Mars Global Surveyor mission in 1997. Martian Geology The Viking and Mars Global Surveyor images show a much wider variety of geological features than seen on the Moon or Mercury. Some areas of the southern hemisphere are heavily cratered (Figure 9.26a), while the northern hemisphere is covered by huge volcanoes surrounded by extensive volcanic plains. Volcanism was expected on Mars—40% larger than Mercury, it should have retained a hot interior much longer. But no one knows why volcanism affected the northern hemisphere so much more than the southern hemisphere, or why the northern hemisphere on average is lower in altitude than the southern hemisphere. 20. Describe the evidence for past water flow on Mars, including catastrophic floods and rainfall. Is it possible that water still flows on Mars today? Explain. Frozen polar ice caps Underground ice may be the key to one of the biggest floods in the history of the solar system. Figure 9.27b shows a landscape hundreds of kilometers across that was apparently scoured by rushing water. Geologists theorize that heat from a volcano melted great quantities of underground ice, unleashing a catastrophic flood that created winding channels and large sandbars along its way. In some places, erosion has even acted below the surface, where underground water and ice have broken up or dissolved the rocks. When the water and ice disappeared, a wide variety of odd pits and troughs were left behind. This process may have contributed to the formation of parts of Valles Marineris. Mars shows unmistakable evidence of widespread erosion. The latest results point to the action of liquid water. a This Viking photo (from orbit) shows ancient riverbeds that were probably created billions of years ago. b This photo shows winding channels and sandbars that were probably created by catastrophic floods. 21. Briefly describe the evidence for volcanic and tectonic activity on Venus. Does Venus have plate tectonics? Does it show signs of significant erosion? Venusian Impacts and Volcanism Most of Venus is covered by relatively smooth, rolling plains with few mountain ranges. The surface has some impact craters (Figure 9.28a), but very few compared to the Moon or even Mars. Venus lacks very small craters, because small impactors burn up in its dense atmosphere. But large craters are also rare, indicating that they must be erased by other geological processes. Volcanism is clearly at work on Venus, as evidenced by an abundance of volcanoes and lava flows. Some are shield volcanoes, indicating familiar basaltic eruptions (Figure 9.28b). Some volcanoes have steeper sides, probably indicating eruptions of a higher-viscosity lava (Figure 9.28c). The surface of Venus is covered with abundant lava flows and tectonic features, along with a few large impact craters. Because these images were taken by the Magellan spacecraft radar, dark and light areas correspond to how well radio waves are reflected, not visible light. The most remarkable features on Venus are tectonic in origin. Its crust is quite contorted; in some regions, the surface appears to be fractured in a regular pattern (Figure 9.28d; see also 9.19). Many of the tectonic features are associated with volcanic features, suggesting a strong linkage between volcanism and tectonics on Venus. One striking example of this linkage is a type of roughly circular feature called a corona (Latin for "crown") that probably resulted from a hot, rising plume in the mantle (Figure 9.28e). The plume pushed up on the crust, forming rings of tectonic stretch marks on the surface. The plume also forced lava to the surface, dotting the area with volcanoes. 22. Briefly explain how Earth's geology fits the general patterns we should expect based on study of other terrestrial worlds. Convincing evidence for plate tectonics might include deep trenches and linear mountain ranges like those we see on Earth, but Magellan found no such evidence on Venus. The apparent lack of plate tectonics suggests that Venus's lithosphere is quite different from Earth's. Some geologists theorize that Venus's lithosphere is thicker and stronger, preventing its surface from fracturing into plates. Another possibility is that plate tectonics happens only occasionally on Venus. The uniform but low abundance of craters suggests that most of the surface formed around a billion years ago. Plate tectonics is one candidate for the process that wiped out older surface features and created a fresh surface at that time. For the last billion years, only volcanism, a bit of impact cratering, and small-scale tectonics have occurred. We've toured our neighboring terrestrial worlds and found a clear relationship between size and volcanic and tectonic activity. Thus, it should come as no surprise that Earth, the largest of the terrestrial worlds, has a high level of ongoing volcanism and tectonics. We've already discussed some of the volcanic and tectonic features on Earth, and we'll explore others in Chapter 13, where we'll also see how plate tectonics has affected Earth's climate and hence its biology. Figure 9.29 summarizes the trends among the terrestrial worlds for volcanism and tectonics. It shows one of the key rules in planetary geology: Larger planets stay volcanically and tectonically active much longer than smaller planets. The situation for erosion is somewhat more complex. Earth has far more erosion than any other terrestrial world, but the most similar erosion is found on Mars, whose surface is sculpted by flowing water despite its small size. To understand erosion, we must look more closely at planetary atmospheres—the topic of our next chapter. Discussion Questions 1. Making Models. In this chapter, we developed a relatively simple conceptual model to describe the complex interactions that govern planetary geology. Use a similar approach to make a model for a complex problem of interest to you. The problem need not be astronomical; for example, you might consider global warming, changes in the stock market, or ways that class size could be reduced at your college or university. Your model need not use flowcharts, but it should include (1) some phenomenon you wish to understand, (2) the processes that affect it, and (3) the various factors those processes depend on. 2. Geological Connections. Consider the four geological processes: impact cratering, volcanism, tectonics, and erosion. Which two do you think are most closely connected to each other? Explain your answer, giving several ways in which the processes are connected. 3. Testing the Model. Our theories of planetary geology seem to explain the terrestrial worlds fairly well, but do they work elsewhere in the solar system? 1. According to the model based on the terrestrial worlds, which of the four geological processes would you predict to be most important on Jupiter's moon Io (1,815-km radius) and Uranus's moon Miranda (243-km radius)? 2. Based on the photos of these moons (Figure 11.17 and Figure 11.25), are your predictions correct? 3. In a strictly logical sense, what would you conclude about our model of planetary geology based on your answer to part (b)? Explain. Problems Surprising Discoveries? For problems 1–4, suppose a spacecraft were to make the observations described. (These are not real discoveries.) In light of your understanding of planetary geology, decide whether the discovery should be considered reasonable or surprising. Explain your answer, tracing your logic back to the planet's formation properties. Explain. 1. The next mission to Mercury photographs part of the surface never seen before and detects vast fields of sand dunes. 2. A radar mapper in orbit around Venus detects a new volcano larger than any other on Venus but not seen by the Magellan spacecraft. 3. A Venus radar mapper discovers extensive regions of layered sedimentary rocks similar to those found on Earth and Mars. 4. Clear-cutting in the Amazon rain forest exposes vast regions of ancient terrain that is as heavily cratered as the lunar highlands. 5. Earth vs. Moon. Why is the Moon heavily cratered, but not Earth? Explain in a paragraph or two, relating your answer to their planetary formation properties. 6. Erosion. Consider erosion on Mercury, Venus, the Moon, and Mars. Which of these four worlds shows the greatest erosion? Why? Write a paragraph for each world explaining why the other three worlds do not have significant erosion and relating erosional activity to the four planetary formation properties. 7. Miniature Mars. Suppose Mars had turned out to be significantly smaller than its current size—say, the size of our Moon. How would this have affected the number of geological features due to each of the four major geological processes (impact cratering, volcanism, tectonics, and erosion)? Do you think Mars would still be a good candidate for harboring extraterrestrial life? Why or why not? Summarize your answers in two or three paragraphs. 8. Mystery Planet. It's the year 2098, and you are designing a robotic mission to a newly discovered planet around a star that is nearly identical to our Sun. The planet is as large in radius as Venus, rotates with the same daily period as Mars, and lies 1.2 AU from its star. Your spacecraft will orbit but not land. 1. Some of your colleagues believe that the planet has no metallic core. How could you support or refute their hypothesis? (Hint: Remember that metal is dense and electrically conducting.) 2. Other colleagues believe that the planet formed with few if any radioactive elements. How could images of the surface support or refute their hypothesis? 3. Others suspect it has no atmosphere, but the instruments designed to study the planet's atmosphere fail due to a software error. How could you use the spacecraft's photos of geological features to determine whether a significant atmosphere is (or was) present on this planet? 9. Dating Planetary Surfaces. We have discussed two basic techniques for determining the age of a planetary surface: studying the abundance of impact craters, and radioactive dating of surface rocks [Section 8.6]. 1. Which technique seems more reliable? Why? 2. Which technique is easier to use for planets besides Earth? Why? 10. Impact Energies. A relatively small impact crater 10 km in radius could be made by a comet 1 km in radius traveling at 30 km/s. 1. Assume the comet has a density of 1 g/cm3 (1,000 kg/m3), and calculate its total kinetic energy. Hints: First find the volume of the comet in m3, then find its mass by multiplying its volume by its density, and finally calculate its kinetic energy. You'll need the following formulas; if you use mass in kg and velocity in m/s, the answer for kinetic energy will have units of joules:volume of sphere = (radius)3 kinetic energy = mass (velocity)2 2. Convert your answer from part (a) to megatons of TNT, the unit used for nuclear bombs. Comment on the degree of devastation that the impact of such a comet could cause if it struck a populated region on Earth. (Hint: One megaton of TNT releases 4.2 1015 joules of energy.) 11. Project: Geological Properties of Silly Putty. 1. Roll room-temperature Silly Putty into a ball and measure its diameter. Place the ball on a table and gently place one end of a heavy book on it. After 5 seconds, measure the height of the squashed ball. 2. Warm the Silly Putty in hot water and repeat the experiment in part (a). Then chill the Silly Putty in ice water and repeat. How did the different temperatures affect the rate of squashing? 3. Did heating and cooling have a small or large effect on the rate of squashing? How does this experiment relate to planetary geology? 12. Project: Planetary Cooling in a Freezer. To simulate the cooling of planetary bodies of different sizes, use a freezer and two small plastic containers of similar shape but different size. Fill them with cold water and place them in the freezer. Checking every hour or so, record the time and your estimate of the thickness of the "lithosphere" (the frozen layer) in the two tubs. 1. On a graph, plot the lithospheric thickness versus time for each tub. In which tub does the lithosphere thicken faster? 2. How long does it take each tub to freeze completely? What is the ratio of the two freezing times? 3. Describe in a few sentences the relevance of your experiment to planetary geology. 13. Amateur Astronomy: Observing the Moon. Any amateur telescope is adequate to identify geological features on the Moon. The light highlands and dark maria should be evident, and the shading of topography will be seen in the region near the terminator (the line between night and day). Try to observe near first- or third-quarter phase. Sketch the Moon at low magnification, and then zoom in on a region of interest, noting its location on your sketch. Sketch your field of view, label its features, and identify the geological process that created them. Look for craters, volcanic plains, and tectonic features. Estimate the horizontal size of the features by comparing them to the size of the whole Moon (radius = 1,738 km). Web Projects Find useful links for Web projects on the text Web site. 1. Current Mars Exploration. Find the latest results from current Mars missions and briefly explain how the latest results have changed or improved our understanding of Mars. 2. Future Planetary Missions. Learn about at least one upcoming mission designed to study a terrestrial world. Write a short summary of the mission and what it is designed to accomplish. Chapter 10 Review Questions 1. What is an atmosphere? List a few of the most common atmospheric gases. Where does an atmosphere end? the atmospheres of solid bodies—terrestrial worlds, jovian moons with atmospheres, and Pluto—are relatively thin layers of gas that contain only a minuscule fraction of a world's mass. carbon dioxide and molecular oxygen. Earth atmosphere contains molecular oxygen. Venus atmosphere contains carbon dioxide and does not contain any of the molecular oxygen (O2) on which we depend. The atmosphere of Mars is also made mostly of carbon dioxide, but much less of it than on Venus. The result is very thin air with a pressure so low that your body tissues would bulge painfully if you stood on the surface without wearing a full space suit. In fact, the pressure and temperature are both so low that liquid water would rapidly disappear, some evaporating and some freezing into ice. Earth's atmosphere of nitrogen and oxygen is the only one under which human life is possible, at least without the creation of an artificial environment. An atmosphere is a layer of gases that surrounds a world. The air that makes up any atmosphere is a mixture of many different gases that may consist either of individual atoms or of molecules. At the relatively low temperatures found throughout most planetary atmospheres, most atoms in gases combine to form molecules. For example, the air that we breathe consists of molecular nitrogen (N2) and oxygen (O2), Two perspectives on Earth's atmosphere. a Most of Earth's atmosphere is confined to a layer less than 100 km thick. b The atmosphere does not end suddenly; some gas is present even at altitudes of hundreds of kilometers, causing the glow visible around the tail of the Space Shuttle as it orbits. 2. Explain the microscopic origin of gas pressure. What is 1 bar of pressure? gas pressure Describes the force (per unit area) pushing on any object due to surrounding gas. bar The standard unit of pressure, approximately equal to the Earth's atmospheric pressure at sea level. molecule in the air around you will suffer a million collisions in the time it takes to read this paragraph. All these collisions in a gas create the gas pressure. An easy way to understand 3. Briefly describe the three factors that would determine planetary temperatures in the absence of greenhouse gases. How do the "no greenhouse" temperatures of the terrestrial planets compare to their actual temperatures? Why? an atmosphere can greatly affect a planet's temperature through the greenhouse effect, which we'll discuss in detail shortly. But first we need to look at how sunlight would heat a planet without an atmosphere—or at least without any of the gases that contribute to the greenhouse effect. In that case, the surface temperature of any planet would be determined by only three basic properties: 1. How far is the planet from the Sun? The closer it is to the Sun, the more energy the planet receives from sunlight on each square meter of its surface. 2. How much sunlight does the surface absorb, and how much does it reflect? The darker the surface, the more light it absorbs and the less it reflects. The term albedo describes the fraction of sunlight reflected by the planet. A higher albedo means more reflection and less absorption: albedo = 0 means no reflection at all (a perfectly black surface); albedo = 1 means all light is reflected (a perfectly white surface). Clouds, snow, and ice have albedos of 0.7 or more, meaning that they reflect 70% or more of the light that hits them. Rocks have low albedos, usually between 0.1 and 0.25. 4. What types of gases absorb infrared light? Ultraviolet light? X rays? Explain how these interactions between light and matter lead to the generic atmospheric structure profile shown in Figure 10.5. Some gases absorb infrared light, which causes the gas molecules to begin "wiggling" (i.e., vibrating and rotating). These added random motions mean the gases are warmer. Molecules that are particularly good at absorbing infrared light—such as carbon dioxide, methane, and water vapor—are called greenhouse gases. 5. Briefly explain why the sky is blue in the daytime and why sunrises and sunsets are red. our atmosphere scatters light. The scattering of light by the atmosphere also explains why the sky is blue. It turns out that molecules scatter blue light (higher frequencies) much more effectively than red light (lower frequencies). At sunset (or sunrise), the sunlight must pass through a greater amount of atmosphere on its way to you. most of the blue light is scattered away from you altogether (making someone else's sky blue), leaving only red light to color your sunset. 6. Give a few examples of greenhouse gases. Briefly describe how the greenhouse effect makes a planetary surface warmer than it would be otherwise. greenhouse gases are Gases, such as carbon dioxide, water vapor, and methane, that are particularly good absorbers of infrared light but are transparent to visible light. greenhouse effect are The process by which greenhouse gases in an atmosphere make a planet's surface temperature warmer than it would be in the absence of an atmosphere. The more greenhouse gases present, the greater the degree of greenhouse warming. 7. What is convection? Briefly explain why it occurs in the troposphere but not in the stratosphere. convection is The energy transport process in which warm material expands and rises, while cooler material contracts and falls. Air is denser at lower altitudes, so the greenhouse effect primarily affects temperatures in the troposphere. Above the troposphere, there is so little air that greenhouse gases cannot effectively trap infrared radiation. The fact that the greenhouse effect makes air warmer near the ground drives convection. in the troposphere. The warm air near the ground expands and rises, while cooler air near the top of the troposphere contracts and falls. The descending cooler air gets heated, and the cycle repeats. we need to consider only the effects of sunlight in investigating atmospheric structure above the troposphere. As we move upward through the stratosphere, the primary source of atmospheric heating is absorption of ultraviolet light from the Sun. This heating tends to be stronger at higher altitudes because the ultraviolet light gets absorbed before it reaches lower altitudes. As a result, the stratosphere gets warmer with increasing altitude—the opposite of the situation in the troposphere. Convection therefore cannot occur in the stratosphere: Heat cannot rise if the air is even hotter higher up. (Convection lessens even in the upper troposphere, where temperature changes slowly with altitude. 8. Briefly explain why a planet can have a stratosphere only if it has ultraviolet-absorbing molecules in its atmosphere. What molecule plays this role on Earth? a planet can have a stratosphere only if its atmosphere contains molecules that are particularly good at absorbing ultraviolet photons. Ozone plays this role on Earth. In fact, Earth is the only terrestrial planet with such an ultraviolet-absorbing layer and the only terrestrial planet with a stratosphere—at least in our solar system. 9. Explain how X-ray absorption in the thermosphere creates an ionosphere and how the ionosphere affects radio communications. all gases are good X-ray absorbers, because X rays have sufficient energy to ionize almost any atom and more than enough to dissociate almost any molecule. Solar X rays are absorbed by the first gases they encounter as they enter the atmosphere. This X-ray absorption strongly heats the upper atmosphere in the daytime, usually to much higher temperatures than those on the surface. That is why this upper region of the atmosphere is called the thermosphere. Despite its high temperatures, the gas in the thermosphere would not feel hot to your skin because its density and pressure are so low. The thermosphere contains a small but important fraction of its gas as charged ions and free electrons—the result of ionization. The layer within the thermosphere that contains most of these ions is called the ionosphere. The ionosphere is very important for radio communications on Earth. Most radio broadcasts are completely reflected back to Earth's surface by the ionosphere, almost as though the Earth were wrapped in aluminum foil. Without this reflection by the ionosphere, radio communication would work only between locations in sight of each other. 10. Briefly describe the actual atmospheric structure of each of the five terrestrial worlds; contrast these structures with the generic structure in Figure 10.5. The atmospheres of the Moon and Mercury have so little gas that they essentially possess only the top layer, the exosphere. Venus, Earth, and Mars have denser atmospheres and are more comparable (Figure 10.9). The similarities and differences among these three planetary atmospheres make sense in light of our study of the generic atmosphere. All three have a warm troposphere at the bottom, created by the greenhouse effect, and a warm thermosphere at the top, where solar X rays are absorbed. The greatest difference is the extra "bump" of Earth's stratosphere, where ultraviolet light is absorbed. Without the warming in our unique layer of stratospheric ozone, Earth's middle altitudes would be almost as cold as those on Mars. Although the structures of the tropospheres are similar on Venus, Earth, and Mars, the tropospheric temperatures on the three planets are dramatically different. On Venus, the thick CO2 atmosphere causes a greenhouse effect that raises the surface temperature about 500 K above what it would be without greenhouse gases. The thin CO2 atmosphere of Mars creates only a weak greenhouse effect, making its surface temperature only 5 K warmer than its "no greenhouse" temperature. Earth has a moderate greenhouse effect that increases its temperature about 40 K, making it comfortable for life. The greenhouse effect on Earth is almost entirely due to gases that make up less than 2% of our atmosphere: mainly carbon dioxide, water vapor, and methane. The major constituents of Earth's atmosphere, N2 and O2, have no effect on infrared light and do not contribute to the greenhouse effect. (Molecules with only two atoms—and especially molecules with two of the same kind of atom—are poor infrared absorbers because they have very few ways to vibrate and rotate.) If they did contribute to the greenhouse effect, Earth might be too warm for life. 11. What is a magnetosphere? What are charged particle belts? Briefly describe how the solar wind affects magnetospheres and how auroras are produced. magnetosphere is The region surrounding a planet in which charged particles are trapped by the planet's magnetic field. charged particle belts are Zones in which ions and electrons accumulate and encircle a planet. solar wind is A stream of charged particles ejected from the Sun. aurora are Dancing lights in the sky caused by charged particles entering our atmosphere; called the aurora borealis in the Northern Hemisphere and the aurora australis in the Southern Hemisphere. 12. Briefly distinguish between weather and climate. weather Describes the ever-varying combination of winds, clouds, temperature, and pressure in a planet's troposphere. climate Describes the long-term average of weather. This ever-varying combination of winds, clouds, temperature, and pressure is what we call weather. Local weather can vary dramatically from one day to the next, or even from hour to hour. 13. Explain why Earth and Mars have seasons but Venus does not. How do seasons on Mars differ from seasons on Earth? Why does atmospheric pressure on Mars change during the seasons, while atmospheric pressure on Earth remains steady year-round? In general, a planet has seasons only if it has a significant axis tilt, so that over the course of its orbit around the Sun first one hemisphere and then the other receives more direct sunlight. Otherwise, both hemispheres receive the same amount of sunlight year-round. For example, Venus has no seasons because its axis is nearly perpendicular to the ecliptic. Mars has seasonal changes like Earth because its 25° axis tilt is comparable to Earth's 23½° tilt. when one Martian hemisphere is in summer, the other is in winter, and vice versa. However, Martian seasons last almost twice as long as Earth seasons because a Martian year is almost twice as long as an Earth year. A planet's changing distance from the Sun can affect the severity of seasons. Earth's nearly circular orbit makes this effect unimportant. But Mars has a more elliptical orbit that puts it significantly closer to the Sun during southern hemisphere summer, making it warmer than summer in the northern hemisphere, and farther from the Sun during southern hemisphere winter, making it colder than winter in the northern hemisphere. 14. What do we mean by global wind patterns? Briefly explain why terrestrial planets tend to have huge circulation cells carrying warm air toward the poles and cool air toward the equator. global wind patterns are Wind patterns that remain fixed on a global scale, determined by the combination of surface heating and the planet's rotation. Winds are flows of air caused by pressure differences between different regions of a planet. On a local scale, winds vary as much as the weather, blowing in different directions and with different strengths at different times. But certain wind patterns are fixed on a global scale, creating what we call global wind patterns (or global circulation). The first major factor affecting global wind patterns is atmospheric heating. In general, the equatorial regions of a planet receive more heat from the Sun than do polar regions. The excess heat makes the atmosphere expand above the equator, and air spills northward and southward at high altitudes (Figure 10.12). By itself, this process creates two huge circulation cells resembling convection cells but much larger. Dust also settles onto the polar caps, making alternating layers of darker dust and brighter frost (Figure 10.16c). The dust storms leave Mars with a perpetually dusty sky, giving it a pale pink color. 15. What is the origin of the Coriolis effect? How does it affect global wind patterns? If your merry-go-round rotates counterclockwise, the ball therefore deviates to the right instead of heading straight inward. The deviation caused by the merry-go-round's rotation is called the Coriolis effect. It also works in reverse: If you roll the ball outward from the center, the ball lags behind the faster-moving outer regions, again deviating to the right. If your merry-go-round instead rotates clockwise, the deviations are to the left. Coriolis effect Causes air or objects moving on a rotating planet to deviate from straight-line trajectories. 16. Briefly describe how clouds form and how they affect planetary weather. What causes rain? Clouds are also important to planetary geology because they are a prerequisite for rain, a major cause of erosion. Despite these significant effects, clouds on most planets form from very minor ingredients of the atmosphere Clouds form when one of the gases in the air condenses into liquid or solid form, a process usually resulting from convection (Figure 10.17). On Earth, evaporation of surface water (or sublimation of ice and snow) releases water vapor into the atmosphere. Convection carries the water vapor to high, cold regions of the troposphere, where it condenses into droplets or flakes of ice. clouds on Earth consist of countless tiny water droplets or ice flakes, a fact you can feel if you walk through a cloud on a mountaintop. The droplets or flakes grow within the clouds until they become so large that the upward convection currents can't hold them aloft. They then begin to fall toward the surface as rain, snow, or hail. 17. Briefly describe the four factors that can lead to long-term climate change and the effects of each factor. long-term climate change can occur. For example, the Earth has been in and out of ice ages throughout its history. What can change the climate of an entire planet? At least four factors can cause climate change. First, the Sun slowly grows in brightness as it ages [Section 14.3]. The Sun was about 30% fainter when the solar system first formed than it is today. Planets therefore may have been cooler early in the history of the solar system, or perhaps greenhouse gases were more abundant. Second, changes in the tilt of a planet's axis can cause climate change. The axis tilt may slowly change over thousands or millions of years because of small gravitational tugs from moons, other planets, or the Sun. Although average planetary temperature may not be affected by the axis tilt, temperatures in different regions may change a great deal. A smaller axis tilt means year-round reduced sunlight in polar regions. Temperatures therefore drop in the polar regions, and perhaps even in mid-latitudes, causing ice ages. Earth and Mars probably both experience ice ages for this reason, and several of the icy satellites of the outer solar system undergo analogous cycles. A third influence on climate change is changes in a planet's albedo. If a planet reflects more sunlight, it absorbs less—which can lead to planet-wide cooling. Ice ages may lead to further planetary cooling because the extra ice covering can increase the planet's albedo. Microscopic dust particles, or aerosols, released by volcanic eruptions can have the same effect. If the dust particles are blasted all the way into the stratosphere, they will remain suspended there for years, reflecting sunlight back to space. Human activity may be changing Earth's albedo. Smog particles can act like volcanic dust, reflecting sunlight before it reaches the ground. Deforestation can also increase Earth's albedo by removing sunlight-absorbing plants. But some human activity decreases albedo, such as paving a road with blacktop. Clearly, the overall human effect on Earth's albedo is not easy to gauge. The fourth major cause of climate change is varying atmospheric conditions, particularly the abundance of greenhouse gases. If the abundance of greenhouse gases increases, the planet generally will warm. If the planet warms enough, increased evaporation and sublimation may add substantial amounts of gases to the planet's atmosphere, leading to an increase in atmospheric pressure. Conversely, if the abundance of greenhouse gases decreases, the planet generally will cool, and atmospheric pressure may decrease as gases freeze. We'll apply all four of these concepts to the planets in the next section to understand their evolving climates. 18. Briefly describe the three processes that can add gas to a planetary atmosphere and the five processes by which a planetary atmosphere can lose gas. Terrestrial atmospheres can get their gas from three different processes: outgassing, evaporation/sublimation, and bombardment. The most important process is outgassing, the release of gases from the planetary interior by volcanic eruptions. Evaporation/sublimation is considered the second most important way in which gases are supplied to an atmosphere. Even though the gases first entered the atmosphere through outgassing, sublimation and evaporation can resupply gases that the atmosphere had lost. Sublimation is most important on relatively cold bodies where ices form. It adds gas to the Martian atmosphere with the changing Martian seasons, as the warmer southern summer releases vast amounts of carbon dioxide from the south polar cap. Bombardment can make only a thin atmosphere (a denser atmosphere would protect the surface from the bombarding particles), but it is the primary source of the atmospheres of the Moon and Mercury. The atmosphere may be composed both of vaporized surface materials and of any gas released by the material doing the bombardment. an atmosphere can lose gas in several ways: thermal escape, bombardment, atmospheric cratering, condensation, and chemical reactions. 19. Why do Mercury and the Moon have only thin exospheres? Why may there be ice in some polar craters on these worlds? The extremely thin atmospheres of the Moon and Mercury are the easiest to explain (Figure 10.24). Volcanic outgassing ceased long ago on these small worlds, and any early atmosphere was lost. Both Mercury and the Moon may have some ice in craters near their poles, but it remains perpetually frozen. exosphere is The hot, outer layer of an atmosphere, where the atmosphere fades away to space. 20. Briefly describe the atmospheric history of Mars. Mars is only 40% larger in radius than Mercury, but its surface tells of a much more fascinating and complex atmospheric history. Pictures show clear evidence that water once flowed on the Martian surface. The abundant geological signs of water erosion on Mars present a major enigma to our understanding of the planet. The evidence includes not only obvious features such as dried-up streambeds (see Figure 9.27a), but also subtler features such as eroded crater rims and floors. Further evidence comes from the study of meteorites believed to have come to Earth from Mars [Section 12.3]. These Martian meteorites contain types of minerals (clays and carbonates) that can form only in the presence of liquid water. Some planetary geologists even believe they have found evidence in Mars images for ancient oceans and glaciers on Mars, although these conclusions are controversial (Figure 9.27). Mars must have had a much stronger greenhouse effect and much higher atmospheric pressure. Computer simulations show that these requirements can be met by a carbon dioxide atmosphere about 400 times denser having greater pressure than the current Martian atmosphere—or about twice as thick as Earth's atmosphere. The idea that Mars had a much denser atmosphere in the past is reasonable. Mars has plenty of ancient volcanoes, and calculations show that these volcanoes could have supplied all of the carbon dioxide needed to warm the planet. Even CO2 ice clouds could have helped hold heat in the Martian troposphere. 21. Why should we expect Venus and Earth to have had very similar early atmospheres? How did the two planetary atmospheres become so different? Venus presents a stark contrast to Mars. Its thick carbon dioxide atmosphere creates an extreme greenhouse effect that bakes the surface to unbearable temperatures. Venus's larger size allowed it to retain more interior heat than Mars, leading to greater volcanic activity. The associated outgassing produced the vast quantities of carbon dioxide in Venus's atmosphere, as well as the much smaller amounts of nitrogen and sulfur dioxide. But the outgassing presents a quandary when we consider water. We expect similar gases to come out of volcanoes on Earth and Venus, since both planets have similar overall compositions. Water vapor is the most common gas from volcanic outgassing on Earth, but Venus is incredibly dry, with only minuscule amounts of water vapor in its atmosphere and not a drop on the surface. Did Venus once have huge amounts of water? If so, what happened to it? The leading theory suggests that Venus did indeed outgas plenty of water. But Venus's proximity to the Sun kept surface temperatures too high for oceans to form as they did on Earth. Outgassed water vapor accumulated in the atmosphere along with carbon dioxide and other gases. Because both water and carbon dioxide are strong greenhouse gases, Venus rapidly grew warmer still. Before the water disappeared, the surface temperature may have been double its current high value. Solar ultraviolet photons broke water molecules apart, and the high temperature allowed rapid escape of hydrogen (just as on Mars). Venus is covered with clouds because its high surface temperature drives strong convection and circulation (Figure 10.18). In contrast to Earth's water clouds, the clouds of Venus are made of sulfuric acid (H2SO4) dissolved in water droplets. These droplets form high in Venus's troposphere, where temperatures are 400 K cooler than on the surface. The droplets grow in the clouds until they form a sulfuric acid rain that falls toward the surface. But the droplets evaporate completely long before they reach the ground. Discussion Questions 1. Charting Atmospheric Evolution. How would you develop "planetary flowcharts" for the atmospheric source and loss processes analogous to those developed for geological processes in Chapter 9? Develop two charts, one for a source process and one for a loss process. Be sure your flowchart includes all the relevant connections described in this chapter. 2. Mars: Past and Future. Summarize the evolution of the Martian atmosphere since planetary formation, emphasizing the important source and loss processes. What is your prediction for the future of the Martian atmosphere? Problems Plausible Claims? For problems 1–7, suppose you heard someone make the given claim. Decide whether the claim seems plausible. Explain. 1. If the Earth's atmosphere did not contain molecular nitrogen, X rays from the Sun would reach the surface. 2. When Mars had a thicker atmosphere in the past, it probably also had a stratosphere. 3. If the Earth rotated faster, storms would probably be more common and more severe. 4. Mars would not have seasons if it had a circular rather than an elliptical orbit around the Sun. 5. If the solar wind were much stronger, Mercury might develop a carbon dioxide atmosphere. 6. The Earth's oceans probably formed at a time when no greenhouse effect operated on Earth. 7. Mars once may have been warmer, but because it is farther from the Sun than is Earth, it's not possible that it could ever have been warmer than the Earth. 8. Cool Venus. Table 10.2 shows that Venus's temperature in the absence of the greenhouse effect is lower than Earth's, even though it is closer to the Sun. 1. Explain this unexpected result in a sentence or two. 2. Now suppose that Venus had neither clouds nor greenhouse gases. What do you think would happen to the temperature of Venus? Why? 3. How are clouds and volcanoes linked on Venus? What change in volcanism might result in the disappearance of clouds? Explain. 9. Atmospheric Structure. Study Figure 10.5, which shows the atmospheric structure for a generic terrestrial planet. For each of the following cases, make a sketch similar to Figure 10.5 showing how the atmospheric structure would be different and explain the differences in words. 1. Suppose the planet had no greenhouse gases. 2. Suppose the Sun emitted no solar ultraviolet light. 3. Suppose the Sun had a higher output of X rays. 10. Inversions. Consider a local inversion, in which the air is colder near the surface than higher up in the troposphere. 1. Explain why convection is suppressed in an inversion. 2. Cities that experience frequent inversions, such as Los Angeles and Denver, often have more serious problems with air pollution than other cities of similar size. Explain how an inversion can trap pollutants, keeping them close to the city in which they are generated. 11. Coastal Winds. During the daytime, heat from the Sun tends to make the air temperature warmer over land near the coast than over the water offshore. But at night, when land cools off faster than the sea, the temperatures tend to be cooler over land than over the sea. Use these facts to predict the directions in which winds generally blow during the day and at night in coastal regions; for example, do the winds blow out to sea or in toward the land? (Hint: How are these conditions similar to those that cause planetary circulation cells?) Explain your reasoning in a few sentences. Diagrams may help. 12. A Swiftly Rotating Venus. Suppose Venus had rotated as rapidly as Earth throughout its history. Briefly explain how and why you would expect it to be different in terms of each of the following: geological processes, atmospheric circulation, magnetic field, and atmospheric evolution. Write a few sentences about each. 13. Sources and Losses. Choose one atmospheric source process and one atmospheric loss process. Describe for each the ways in which the process is related to the four planetary formation properties discussed in Chapter 9. (For example, how is the creation of atmospheric gas by bombardment related to a planet's size, distance from the Sun, composition, and rotation rate?) (Hint: A process may not depend on all four formation properties.) 14. Project: Atmospheric Science in the Kitchen. 1. Find an empty plastic bottle, such as a water bottle with a screwtop that makes a good seal. Warm the air inside by filling the bottle partway with hot water, and then shaking and emptying the bottle. Seal the bottle and place it in the refrigerator or freezer. What happens after 15 minutes or so? Explain why this happens, imagining that you could see the individual air molecules. 2. You may have noticed that loose ice cubes in the freezer gradually shrink away to nothing or that frost sometimes builds up in old freezers. What are the technical terms used in this chapter for these phenomena? On what terrestrial planet do these same processes play a major role in controlling the atmosphere? 15. Habitable Planet Around 51 Peg? A recently discovered planet orbits the star 51 Pegasi at a distance of only 0.051 AU. The star is approximately as bright as our Sun. The planet has a mass 0.6 times that of Jupiter, but no one knows if it is more similar to our jovian or to our terrestrial planets (if either). 1. Suppose it is a terrestrial-type planet with an albedo of 0.15 (i.e., without clouds). Calculate its no greenhouse temperature, assuming it rotates fast enough to have the same temperatures on its dayside and its nightside. How does this temperature compare to that of Earth? 2. Repeat part (a), but this time assume that the planet is covered in very reflective clouds, giving it an albedo of 0.8. 3. Based on your answers to parts (a) and (b), do you think it is likely that the conditions on this planet are conducive to life? Explain your answer in one or two paragraphs. 16. Escape from Venus. 1. Calculate the escape velocity from Venus's exosphere (about 200 km above Venus's surface). (Hint: See Mathematical Insight 5.3.) 2. Calculate and compare the thermal speeds of hydrogen and deuterium atoms at the exospheric temperature of 350 K. The mass of a hydrogen atom is 1.67 10–27 kg, and the mass of a deuterium atom is about twice the mass of a hydrogen atom. 3. Comment in a few sentences on the relevance of the calculations in parts (a) and (b) to atmospheric evolution on Venus. Web Projects Find useful links for Web projects on the text Web site. 1. Spacecraft Study of Atmospheres. Learn about a current or planned mission to study the atmosphere of one of the terrestrial worlds. Write a one- to two-page essay describing the mission and what it may teach us about terrestrial planet atmospheres. 2. Martian Weather. Find the latest weather report for Mars from spacecraft and other satellites. What season is it in the northern hemisphere? When was the most recent dust storm? What surface temperature was most recently reported from Mars's surface, and where was the lander located? Summarize your findings by writing a 1-minute script for a television news update on Martian weather. 3. Terraforming Mars. Some people have proposed that we might someday terraform Mars, making it more Earth-like so that we might live there more easily. Research some proposals for terraforming Mars. Do you think the proposals could work? Do you think it would be a good idea to terraform Mars? Write a one- to two-page essay summarizing your findings and defending your opinions. Chapter 11 Review Questions 1. Briefly describe the past and present space exploration of the jovian worlds. Summarize what we've learned about the jovian planets in terms of composition, rotation rate, and shape. Jupiter is the third-brightest object that appears regularly in our night skies, after the Moon and Venus. Saturn is fainter and slowermoving. Once distances were established, scientists could calculate the truly immense sizes of the jovian planets from their angular sizes as measured through telescopes. Knowing the distance scale also allowed calculating jovian planet masses by applying Newton's version of Kepler's third law to observed orbital characteristics of jovian moons. Together, the measurements of size and mass revealed the low densities of the jovian planets, proving that these worlds are very different from the Earth. The slow pace of discovery about the jovian planets gave way to revolutionary advances with the era of spacecraft exploration. The first spacecraft to the outer planets, Pioneer 10 and Pioneer 11, flew past Jupiter and Saturn in the early 1970s. The Voyager missions followed less than a decade later. Voyager 2 continued on a "grand tour" of the jovian planets, flying past Uranus in 1986 and Neptune in 1989. The results were spectacular. Exploration of the jovian planet systems continued with the Galileo spacecraft, which went into orbit around Jupiter in 1995. Still ahead is the Cassini mission, scheduled for arrival at Saturn in 2004. Jupiter, Saturn, Uranus, and Neptune are so different from the terrestrial planets. The most obvious difference between the jovian and terrestrial planets is size. Earth's mass in comparison to that of Jupiter is like the mass of a squirrel in comparison to that of a full-grown person. By volume, Earth in comparison to Jupiter is like a pea in a cup of soup. volume is proportional to the cube of the radius. Jupiter's radius is 11.2 times Earth's, its volume is 11.23 = 1,405 times Earth's. The overall composition of the jovian planets—particularly Jupiter and Saturn—is more similar to that of the Sun than to any of the terrestrial worlds. Their primary chemical constituents are the light gases hydrogen and helium, although their atmospheres also contain many hydrogen compounds and their cores consist of a mixture of rocks, metals, and hydrogen compounds. Although these cores are small in proportion to the jovian planet volumes, each is still more massive than any terrestrial planet. Moreover, the pressures and temperatures near the cores are so extreme that the "surfaces" of the cores do not resemble terrestrial surfaces at all. In a sense, the general structures of the jovian planets are opposite those of the terrestrial planets: Whereas the terrestrial planets have thin atmospheres around rocky bodies, the jovian planets have proportionally small, rocky cores surrounded by massive layers of gas. The jovian planets may be Sun-like in composition, but their masses are far too low to provide the interior temperatures and densities needed for nuclear fusion. Calculations show that nuclear fusion is possible only with a mass at least 80 times that of Jupiter. The jovian planets have undoubtedly lost internal heat during the more than 4 billion years since their formation and must have been much warmer in the distant past. This heat may have "puffed up" their atmospheres, making them larger and brighter in the past. If so, Jupiter would have been even more prominent in Earth's sky billions of years ago than it is today. The jovian planets rotate much more rapidly than any of the terrestrial worlds, but precisely defining their rotation rates can be difficult because they are not solid. We can measure a terrestrial rotation period simply by watching the apparent movement of a mountain or crater as a planet rotates, but on jovian planets we can observe only the movements of clouds. Cloud movements can be deceptive, because their apparent speeds may be affected by winds as well as by planetary rotation. Nevertheless, observations of clouds at different latitudes suggest that the jovian planets rotate faster near their equators than near their poles. The Sun also exhibits this type of differential rotation. We can measure the rotation rates of the jovian interiors by tracking emissions from charged particles trapped in their magnetospheres. This technique allows us to observe the rotation period of a magnetosphere, which should be the same as the rotation period deep in the interior, where the magnetic fields are generated. These measurements show that the jovian "days" range from only about 10 hours on Jupiter and Saturn to 16–17 hours on Uranus and Neptune. 2. Describe the interior structure of Jupiter. Contrast Jupiter's interior structure with the structures of the other jovian planets. Why is Jupiter denser than Saturn? Why is Neptune denser than Saturn? Gaseous Hydrogen 1 bar 125 K. Liquid Hydrogen 500,000 bars 2,000 K. Metallic Hydrogen 2,000,000 bars 5,000 K. rocks, metals, and hydrogen compounds. The overall composition of the jovian planets—particularly Jupiter and Saturn—is more similar to that of the Sun than to any of the terrestrial worlds. Their primary chemical constituents are the light gases hydrogen and helium, although their atmospheres also contain many hydrogen compounds and their cores consist of a mixture of rocks, metals, and hydrogen compounds. Although these cores are small in proportion to the jovian planet volumes, each is still more massive than any terrestrial planet. Moreover, the pressures and temperatures near the cores are so extreme that the "surfaces" of the cores do not resemble terrestrial surfaces at all. In a sense, the general structures of the jovian planets are opposite those of the terrestrial planets: The balance tips most strongly toward flattening on Saturn, with its rapid 10-hour rotation period and its relatively weak surface gravity. Saturn is about 10% wider at its equator than at its poles. In addition to altering a planet's appearance, the equatorial bulge itself exerts an extra gravitational pull that helps keep satellites and rings aligned with the equator, Jupiter's interior structure, labeled with the pressure, temperature, and density at various depths. Earth's interior structure is shown to scale for comparison. Note that Jupiter's core is only slightly larger than Earth but is about 10 times more massive. Saturn's core makes up a larger fraction of its mass than Jupiter's core. 3. How do we think Jupiter generates its internal heat? How do other jovian planets generate internal heat? Jupiter is still slowly contracting, as if it has not quite finished forming from a jovian nebula. This gravitational contraction is so gradual that we cannot measure it directly, but it converts gravitational potential energy to thermal energy, keeping Jupiter hot inside. Building a planet of hydrogen and helium. internal heat sources can have a strong effect on the behavior of planets, so it is natural to ask if Jupiter and the other jovian planets are also affected by internal heat sources. Jupiter has a tremendous amount of internal heat—so much that it emits almost twice as much energy as it receives from the Sun. The metallic and electrically conducting nature of this interior hydrogen is important in generating Jupiter's strong magnetic field. 125 K (–148°C), the density to be a low 0.0002 g/cm3, and the atmospheric pressure to be about 1 bar. The pillow analogy suggests that a hydrogen/helium planet less massive than Saturn should have an even lower density. Because Uranus and Neptune have significantly higher densities than Saturn, we conclude that they cannot have the same hydrogen/helium composition. Instead, they must have a much larger fraction of higher-density material, such as hydrogen compounds and rocks, and a smaller fraction of "plain" hydrogen and helium. 4. Describe the composition and temperature structure of Jupiter's atmosphere and contrast it with Earth's. Compare the temperature structures of the other jovian planets to that of Jupiter. Jupiter's core at a depth of 60,000 km, about 10,000 km from the center. The core is a mix of hydrogen compounds, rocks, and metals, but these materials bear little resemblance to familiar solids or liquids because of the extreme 20,000-K temperature and 100-million-bar pressure. The similar cores also mean that the interior structures of the jovian planets differ mainly in the hydrogen/helium layers that surround the cores (Figure 11.5). Saturn is large enough for interior densities, temperatures, and pressures to be high enough to force gaseous hydrogen into liquid and then metallic form, just as in Jupiter. But these conditions occur relatively deeper in Saturn than in Jupiter, because of its smaller size. Pressures within Uranus and Neptune are not high enough to form liquid or metallic hydrogen. However, their cores of rock, metal, and hydrogen compounds may be liquid, making for very odd "oceans" buried deep inside them. Like Jupiter, Saturn emits nearly twice as much energy as it receives from the Sun. Saturn's mass is too small for it to be generating all its excess heat by contracting like Jupiter. Instead, its lower temperatures probably allow helium to condense and "rain down" from higher regions in the interior. The gradual rain of these relatively dense helium droplets resembles the process of differentiation that once occurred in terrestrial planet interiors. Voyager observations confirmed that Saturn's atmosphere is somewhat depleted of helium (compared to Jupiter's atmosphere), just as we would expect if helium has been raining down into Saturn's interior for billions of years. Neither Uranus nor Neptune has conditions that allow helium rain to form, and most of their original heat from accretion should have escaped long ago. This explains why Uranus emits virtually no excess internal energy. Neptune is much more mysterious: Like Jupiter and Saturn, it emits nearly twice as much energy as it receives from the Sun. The only reasonable explanation for Neptune's internal heat source is that the planet is somehow still contracting, rather like Jupiter, thereby converting gravitational potential energy into thermal energy. But no one knows why a planet of Neptune's size would still be contracting more than 4 billion years after its formation. 5. Why does Jupiter have several distinct layers of clouds? Jupiter has at least three distinct cloud layers because different atmospheric gases condense at different temperatures and at different altitudes. Jupiter's atmosphere is almost entirely hydrogen and helium (about 75% hydrogen and 24% helium by mass), but it also contains trace amounts of many other hydrogen compounds. Because oxygen, carbon, and nitrogen are the most common elements besides hydrogen and helium, the most common hydrogen compounds are methane (CH4), ammonia (NH3), and water (H2O). Spectroscopy reveals the presence of more complex compounds, including acetylene (C2H2), ethane (C2H6), propane (C3H8), and larger molecules that can act like haze particles. 6. How are the circulation cells on Jupiter similar to and different from those on Earth? What are belts and zones? circulation cells (also called Hadley cells) Large-scale cells (similar to convection cells) in a planet's atmosphere that transport heat between the equator and the poles. zones (on a jovian planet) Bright bands of rising air that encircle a jovian planet at a particular set of latitudes. belts (on a jovian planet) Dark bands of sinking air that encircle a jovian planet at a particular set of latitudes. Jupiter also has planet-wide circulation cells similar to those on Earth, where solar heat causes equatorial air to expand and spill northward and southward toward the poles. However, whereas Earth's rotation splits its circulation cells into just three separate cells in each hemisphere, Jupiter's much more rapid rotation creates a strong Coriolis effect that causes its circulation cells to split into many huge bands encircling the entire planet at fixed latitudes. The bands of rising air are called zones, and they appear white because of the ammonia clouds that form as the air rises to high, cool altitudes. Within the zones, ammonia "snowflakes" rain downward against the rising convective motions. The adjacent belts of falling air are depleted in the cloud-forming ingredients and do not contain any white ammonia clouds. They appear dark because we can see down to the red or tan ammonium-hydrosulfide clouds that form at lower altitudes. 7. What is the Great Red Spot? Is it the same type of storm as a hurricane on Earth? Explain. Great Red Spot is A large, high-pressure storm on Jupiter. The Great Red Spot is huge—more than twice as wide as the Earth. Could it be a tremendous low-pressure storm like a hurricane on Earth? Not quite. Hurricane winds circulate around low-pressure regions and therefore circulate clockwise in the southern hemisphere [Section 10.4]. The winds in the Great Red Spot circulate counterclockwise, indicating that it is a high-pressure storm, possibly kept spinning by the influence of nearby belts and zones. Other, smaller storms are always brewing in Jupiter's atmosphere—small only in comparison to the Great Red Spot. Brown ovals are low-pressure storms with their cloud tops deeper in Jupiter's atmosphere, and white ovals are high-pressure storms topped with ammonia clouds. No one knows what drives Jupiter's storms, why Jupiter has only one Great Red Spot, or why the Great Red Spot lasts so much longer than storms on Earth. Storms on Earth lose their strength when they pass over land, so perhaps Jupiter's biggest storms last for centuries because there is no solid surface below to sap their energy. 8. Describe the possible origins of Jupiter's vibrant colors. Contrast these with the origins of the colors of the other jovian planets. The most striking difference among the jovian atmospheres is their colors. Starting with Jupiter's distinct red colors, the jovian planets turn to Saturn's more subdued yellows, to Uranus's faint blue-green tinge, and finally to Neptune's pronounced blue hue. What's responsible for this regular progression of colors? The primary constituents in all the jovian atmospheres (hydrogen and helium) are colorless, so the planetary colors must come from trace gases or chemical reactions that create colored compounds. In fact, we can understand the color differences by comparing the atmospheric structures and compositions of the four planets. All four are quite similar, except for the effects of the lower temperatures and lower gravities on the more distant planets. Saturn's reds and tans almost certainly come from the same compounds that produce these colors on Jupiter—whatever those compounds may be. As on Jupiter, these compounds are probably created by chemical reactions beneath the cloud layers and carried upward by convection. However, because of Saturn's lower temperatures, its cloud layers lie deeper in its atmosphere than Jupiter's. As a result, a thicker layer of tan "smog" overlies the clouds, washing out Saturn's colors. 9. Does Jupiter have seasons? Why or why not? Do other jovian planets have seasons? Explain. Seasonal changes play a relatively small role on most jovian planets. We might expect seasons on Saturn and Neptune because they have axis tilts similar to that of Earth, and some seasonal weather changes have been observed. But their internal heat sources maintain similar temperatures all over, just as Jupiter's internal heat keeps its polar and equatorial temperatures about the same. The greatest surprise in the weather patterns on the jovian planets is the weather on Uranus, the planet tipped on its side. When the Voyager spacecraft flew past in 1986, it was midsummer in Uranus's northern hemisphere, with the summer pole pointed almost directly at the Sun. Photographs revealed virtually no clouds, belts, or zones, which scientists attributed to the lack of a significant internal heat source on Uranus. But recently the Hubble Space Telescope has detected storms ranging on the planet bright spots. The seasons are changing, and the winter hemisphere is seeing sunlight for the first time in decades. Jupiter's weather phenomena (clouds, belts, zones, and other storms) are by far the strongest and most active. Saturn also possesses belts and zones (in more subdued colors), along with some small storms and an occasional large storm, but it lacks any weather feature as prominent as Jupiter's Saturn's winds are even stronger than Jupiter's.) Neptune's atmosphere is also banded and has a high-pressure storm, called the Great Dark Spot, that acts much like Jupiter's Great Red Spot. 10. Why does Jupiter have auroras? Contrast Jupiter's magnetosphere with those of the Earth and the other jovian planets. 11. What is the Io torus? Why doesn't Saturn, Uranus, or Neptune have a similar "torus"? Jupiter's magnetosphere, with Io embedded deep within. An orange glow around Io represents its escaping atmosphere, and the red donut represents the Io torus—the charged particle belt formed by Io. The blue lines show Jupiter's strong magnetic field. On Io, the bombardment leads to the continuous escape of the atmospheric gases released by volcanic outgassing. As a result, Io loses atmospheric gases faster than any other object in the solar system. The escaping gases (sulfur, oxygen, and a hint of sodium) are ionized and feed a donut-shaped charged particle belt, called the Io torus, that approximately traces Io's orbit. 12. Briefly describe some of the general characteristics of the jovian moons. these moons (particularly those farther from their planets) also have unusual orbits, with significant eccentricities, large orbital tilts, or orbits that go backward relative to the planet's rotation. Such orbits are signs that the moons are captured asteroids rather than moons that formed from the "miniature solar nebulae" that surrounded each jovian planet. Jupiter's icy moons. Nearly 90 known moons (satellites) orbit the jovian planets. Figure 11.15 shows the larger ones, and Appendix C lists fundamental data for the known moons. It's worth taking a few minutes to study the figure and the appendix, looking for patterns, before you read on. 13. How is the ice geology of the jovian moons similar to the rock geology of the terrestrial planets? How is it different? These moons are planetlike in almost all ways. They are approximately spherical, each has a solid surface with its own unique geology, and some possess atmospheres, hot interiors, and even magnetic fields. A few are planetlike in size as well. The two largest moons—Jupiter's moon Ganymede and Saturn's moon Titan—are larger than the planet Mercury. Four others are larger than Pluto: Jupiter's moons Io, Europa, and Callisto, and Neptune's moon Triton. Because they were so far from the Sun, temperatures in these nebulae were quite cool and were rich with ice crystals of various hydrogen compounds (mostly water, but also small amounts of ammonia and methane). As a result, the jovian planet satellites contain much higher proportions of ice relative to rock than do the terrestrial planets. We even find distinctions among the jovian satellite systems: Jupiter's satellites have the highest proportion of rock, while the satellites of more distant planets contain higher proportions of the more volatile methane and ammonia ices. 14. Describe the volcanoes of Io and the mechanism of tidal heating that generates Io's internal heat. Despite Io's unusual colors and frost-covered surface, planetary scientists found volcanic eruptions remarkably similar to those of basalt volcanoes on Earth (Figure 11.17b). When the flowing lava comes in contact with frost, the resulting "steam" jets off at high speed to make the plume. The process is similar to lava flowing into the ocean on Earth, but Io's relative lack of atmosphere and low gravity let the plumes reach great altitude (Figure 11.17c). Not all of Io's volcanoes erupt so violently. Lava flows out of some vents, and sulfur gas expelled from the volcano coats the surface in red patches (Figure 11.17d). tidal heating A source of internal heating created by tidal friction. It is particularly important for satellites with eccentric orbits such as Io and Europa. Tidal forces lock Io in synchronous rotation so that it keeps the same face toward Jupiter. But Io's orbit is slightly elliptical, so its orbital speed and distance from Jupiter vary. As a result, the strength and even the direction of the tidal force change very slightly over its orbit: Io is continuously flexed by Jupiter (Figure 11.18a). The flexing of Io's rocky crust and interior releases heat, just as flexing warms. moons have so much more geological activity than similar-size (or larger) planets. 15. What are orbital resonances? Explain how the resonance between Io, Europa, and Ganymede makes their orbits slightly elliptical. orbital resonance Describes any situation in which one object's orbital period is a simple ratio of another object's period, such as 1/2, 1/4, or 5/3. In such cases, the two objects periodically line up with each other, and the extra gravitational attractions at these times can affect the objects' orbits. Gravitational nudges between Io, Europa, and Ganymede maintain orbital resonances between them (Figure 11.18b). During the time in which Ganymede completes one orbit of Jupiter, Europa completes exactly two orbits and Io completes exactly four orbits. The satellites therefore line up periodically, and the gravitational tugs these satellites exert on one another add up over time. The satellites are always tugged in exactly the same direction, and the satellite orbits become very slightly elliptical as a result. 16. Describe the evidence suggesting that Europa may have a subsurface ocean of liquid water. Europa Europa's bizarre, fractured crust is proof enough that tidal heating has taken hold there (Figure 11.19a). The icy surface is nearly devoid of impact craters and may be only a few million years old. Jumbled icebergs (Figure 11.19b) suggest that an ocean of liquid water lies just a few kilometers below the surface, extending down to perhaps 100 km deep. The icy shell overlying the ocean is repeatedly flexed by tidal forces, resulting in a global network of cracks. Close-up images of the cracks taken by the Galileo orbiter show that most have a remarkable double-ridged pattern, perhaps the result of debris piling up around a crack that is repeatedly opened and closed by tidal flexing 17. Describe the general surface characteristics of Ganymede and Callisto. What do these characteristics tell us about internal heating on these worlds? Ganymede Photographs of Ganymede tell the story of an interesting geological history. Parts of the surface have many impact craters, indicating that these regions are billions of years old (Figure 11.21a). But other areas show unusual "grooved terrain" unlike anything we've seen in terrestrial geology (Figure 11.21b,c). The grooves may form either from tectonic stresses or from water erupting along a crack in the surface; because ice expands when it solidifies (unlike rock), the grooves may form as the surface refreezes. A freezing surface patch on Ganymede therefore pushes outward, perhaps creating the grooves and ridges seen on its surface. Ganymede also shows some evidence of tectonics similar to plate tectonics on Earth: The precise nature of Ganymede's internal heating remains mysterious, although it certainly is some combination of tidal heating and radioactive decay. Surprisingly, Ganymede has its own magnetic field—perhaps indicating a molten, convecting core. It may even harbor a liquid-water layer below the ice, but evidence for such an ocean is still quite tentative. Callisto The outermost Galilean satellite, Callisto, looks most like what scientists first expected for outer solar system satellites: a heavily cratered iceball (Figure 11.22a). The bright patches on its surface are the result of cratering: Large impactors dug up cleaner ice from deep down and spread it over the surface. The odd rings in the upper left of Callisto's image also came from impacts: The largest impactors shattered the icy sphere in a way that produced concentric rings around the impact site. 18. Describe the atmosphere of Titan. What evidence suggests that Titan may have oceans of liquid ethane? Titan's hazy and cloudy atmosphere hides its surface (Figure 11.23a). The atmosphere is about 90% nitrogen, making it the only world besides Earth where nitrogen is the dominant atmospheric constituent. However, on Earth the rest of the atmosphere is mostly oxygen, while the rest of Titan's atmosphere consists of argon, methane, and other hydrogen compounds, including ethane (C2H6). Titan is composed mostly of ices, including methane and ammonia ice. Some of this ice sublimed long ago to form an atmosphere on Titan. Over billions of years, solar ultraviolet light broke apart the ammonia molecules (NH3) into hydrogen and nitrogen. The light hydrogen escaped from the atmosphere (through thermal escape [Section 10.5]), but the heavier nitrogen molecules remained and accumulated. Methane is no longer present in large quantities, so some process must have removed it from the atmosphere. The most likely process is chemical reactions, triggered by solar ultraviolet light, that transform methane into ethane. If this idea is correct, atmospheric ethane may form clouds and rain on Titan, perhaps creating oceans of liquid ethane on the surface (Figure 11.23b). 19. Describe a few general features of Saturn's medium-size moons. Why is it surprising to find evidence of geological activity on some of these moons, and how do we explain it? Saturn's medium-size moons (Rhea, Iapetus, Dione, Tethys, Enceladus, and Mimas) show evidence of substantial geological activity (Figure 11.24). While all show some cratered surfaces, Enceladus has grooved terrain similar to Ganymede's, and the others show evidence of flows of "ice lava." But these satellites are considerably smaller than Ganymede: Enceladus is barely 500 kilometers across—small enough to fit inside the borders of Colorado. The answer probably lies with "ice geology," in which icy combinations of water, ammonia, and methane can melt, deform, and flow at remarkably low temperatures. 20. Describe a few general features of Uranus's medium-size moons. Why is the geological activity on Ariel and Titania puzzling? How do we explain the odd appearance of Miranda? Uranus is orbited by 5 medium-size moons (Figure 11.15) and 10 smaller moons discovered by Voyager. Astronomers have recently discovered 6 more moons, including several that orbit the planet backward. The medium-size moons pose several puzzles. For example, Ariel and Umbriel are virtual twins in size, yet Ariel shows evidence of volcanism and tectonics, while the heavily cratered surface of Umbriel suggests a lack of geological activity. Titania and Oberon also are twins in size, but Titania appears to have had much more geological activity than Oberon. No one knows why these two pairs of similar-size moons should vary so greatly in geological activity. Miranda, the smallest of Uranus's medium-size moons (radius = 235 km), is the most surprising (Figure 11.25). Prior to the Voyager flyby, scientists expected Miranda to be a cratered iceball like Saturn's similar-size moon Mimas (see Figure 11.24). Instead, Voyager images of Miranda show tremendous tectonic features and relatively few craters. Why should Miranda be so much more geologically active than Mimas? Our best guess is an episode of tidal heating from a temporary orbital resonance with another satellite of Uranus billions of years ago. 21. How do we know that Triton is not a typical large jovian satellite? Describe Triton's general characteristics and give possible ideas of where Triton came from. Triton and Nereid) were known to exist before the Voyager visit. Triton is the only large moon in the Neptune system, and only one other moon (Proteus) even makes it into our "medium-size" category. Triton may appear to be a typical satellite, but it is not. Its orbit is retrograde (it travels in a direction opposite to Neptune's rotation) and highly inclined to Neptune's equator. These are telltale signs of a captured satellite. But Triton is not small and potato-shaped like most captured asteroids. Instead it is large, spherical, and icy. In fact, it is larger than the planet Pluto. As such, Triton presents many challenges to our understanding of satellite capture. Nonetheless, it is almost certain that Triton once orbited the Sun instead of orbiting Neptune. A quick study of the Triton photos in Figure 11.26 reveals a surface unlike any other in the solar system, and one that poses many unanswered questions. Are the flat surfaces like the lunar maria? Are the wrinkly ridges (nicknamed "cantaloupe terrain") tectonic in nature? Are the bright polar caps similar to those on Mars? Why is Triton's surface composition (a mixture of ices of nitrogen, methane, carbon dioxide, and carbon monoxide) unlike that of any other satellite? Clearly, Triton is more than a cratered iceball. The undisturbed craters suggest that major geological activity has subsided, but Triton appears to have undergone some sort of icy volcanism in the past. Such geological activity is astonishing in light of Triton's extremely low (40 K) surface temperature, but it probably involved low-melting-point mixtures of water, methane, and ammonia ices. 22. Describe the appearance and structure of Saturn's rings. Why are the rings so thin? Where do the rings lie in relation to Saturn's Roche tidal zone? You can see Saturn's rings through a backyard telescope, but learning about their nature requires higher resolution. Even through large telescopes on Earth, the rings appear to be continuous, concentric sheets of material separated by gaps (Figure 11.27a). Spacecraft images reveal these "sheets" to be made of many more individual rings, each broken up into even smaller concentric ringlets, and different regions of a ring to range from transparent to opaque (Figure 11.27b). But even these appearances are somewhat deceiving. If we could wander into the rings, we'd see that they are made of countless individual particles orbiting Saturn together, each obeying Kepler's laws and occasionally colliding with nearby particles (Figure 11.27c). The particles range in size from large boulders to dust grains—far too small to be photographed, even when spacecraft like Voyager or Cassini pass nearby. Saturn's rings lie in a thin plane directly above the planet's bulging equator, so they share Saturn's 27° axis tilt. Over the course of Saturn's year, the rings present a changing appearance to the Earth and Sun, appearing wide open at Saturn's solstices and edge-on at its equinoxes. An important clue is that the rings lie close to the planet in a region where tidal forces are very influential. Within two to three planetary radii (of any planet), the tidal forces tugging an object apart become comparable to the gravitational forces holding it together. This region is called the Roche tidal zone. Only relatively small objects held together by nongravitational forces (such as the electrostatic forces that hold solid rock—or spacecraft or human beings—together) can survive within the Roche tidal zone. there are two basic scenarios for the origin of the rings. One possibility is that a wandering moon strayed too close to Saturn and was torn apart. A more likely scenario is that tidal forces prevented the material in Saturn's rings from accreting into a single large moon, instead forming many smaller moons. 23. Briefly describe how gap moons and orbital resonances can lead to gaps within ring systems. Rings and gaps are caused by particles bunching up at some orbital distances and being forced out at others. This bunching happens when gravity nudges the orbits of ring particles in some particular way. One source of nudging is tiny moons—called gap moons—located within the rings themselves. The gravity of a gap moon tugs gently on nearby particles, effectively nudging them farther away to other orbits.(*footnote) This clears a gap in the rings around the moon's orbit. Voyager spacecraft photographed a few gap moons, and there may be thousands more that are too small to see in the Voyager images. 24. Contrast the rings of the other jovian planets with Saturn's rings. The ring systems of Jupiter, Uranus, and Neptune are so much fainter than Saturn's ring system that it took almost four centuries longer to discover them. Ring particles in these three systems are far less numerous, generally smaller, and much darker. Saturn's rings were the only ones known until 1977, when the rings of Uranus were discovered during observations of a stellar occultation—a star passing behind Uranus as seen from the Earth. During the occultation, the star "blinked" on and off nine times before it disappeared behind Uranus, and nine more times as it emerged. Scientists concluded that these nine "blinks" were caused by nine thin rings encircling Uranus. Similar observations of stars passing behind Neptune gave more confounding results: Rings appeared to be present some of the time, but not at other times. 25. Describe two possible scenarios for the origin of planetary rings. What makes us think that ring systems must be continually replenished? ring particles may not last very long. Ring particles orbiting Saturn bump into one another every few hours, and even with low-velocity collisions the particles are chipped away over time. Basketball-size ring particles around Saturn are ground away to dust in a few million years. Other processes dismantle rings around the other jovian planets. The thermosphere of Uranus extends into its Roche tidal zone, so atmospheric drag slowly causes ring particles to spiral into the planet. Dust orbiting Jupiter is slightly slowed by the flood of solar photons passing by, and the particles we now see in Jupiter's ring will fall into the planet in only a few million years. In summary, particles in the four ring systems cannot last as long as the 4.6-billion-year age of our solar system. If ring particles are rapidly disappearing, some source of new particles must keep the rings supplied. The most likely source is collisions. As ring particles are ground away by collisions, small moons (perhaps the gap moons) occasionally collide and create more ring particles. Meteorites may also strike these moons, with the impacts releasing even more ring particles. We now believe that the "miniature solar nebulae" that surrounded the jovian planets formed many small satellites and that the gradual dismantling of these satellites creates the dramatic ring systems we see today. The appearance of any particular ring system probably changes dramatically over millions and billions of years. The spectacle of Saturn's brilliant rings may be a special treat of our epoch, one that could not have been seen a billion years ago and that may not last long on the time scale of our solar system. Discussion Questions 1. A Miniature Solar System? In what ways is the Jupiter system similar to a miniature solar system? In what ways is it different? 2. Jovian Mission. We can study terrestrial planets up close by landing on them, but jovian planets have no surfaces to land on. Suppose you are in charge of planning a long-term mission to "float" in the atmosphere of a jovian planet. Describe the technology you will use and how you will ensure survival for any people assigned to this mission. 3. Extrasolar Planets. Many of the newly discovered planets orbiting other stars are more massive than Jupiter and much closer to their stars. Assuming that they are in fact jovian (as opposed to terrestrial or something else), how would you expect these new planets to differ from the jovian planets of our solar system? How would any magnetospheres, satellites, or rings be different? Explain. Problems Surprising Discoveries? For problems 1–8, suppose someone claimed to make the discovery described. (These are not real discoveries.) Decide whether the discovery should be considered reasonable or surprising. More than one right answer may be possible, so explain your answer clearly. 1. Saturn's core is pockmarked with impact craters and dotted with volcanoes erupting basaltic lava. 2. Neptune's deep blue color is not due to methane, as previously thought, but instead is due to its surface being covered with an ocean of liquid water. 3. A jovian planet in another star system has a moon as big as Mars. 4. An extrasolar planet is discovered that is made primarily of hydrogen and helium; it has approximately the same mass as Jupiter but is 10 times larger than Jupiter in radius. 5. A new small moon is discovered to be orbiting Jupiter. It is smaller than any other of Jupiter's moons and orbits slightly farther from Jupiter than any of the other moons, but it has several large, active volcanoes. 6. A new moon is discovered to be orbiting Neptune. The moon orbits in Neptune's equatorial plane and in the same direction in which Neptune rotates, but it is made almost entirely of metals such as iron and nickel. 7. An icy, medium-size moon is discovered to be orbiting a jovian planet in a star system that is only a few hundred million years old. The moon shows evidence of active tectonics. 8. A jovian planet is discovered in a star system that is much older than our solar system. The planet has no moons at all, but it has a system of rings as spectacular as the rings of Saturn. 9. The Importance of Rotation. Suppose the material that formed Jupiter came together without any rotation, so that no "jovian nebula" formed and the planet today wasn't spinning. How else would the jovian system be different? Think of as many effects as you can, and explain each in a sentence. 10. The Great Red Spot. Based on the infrared and visible-wavelength images in Figure 11.7, is Jupiter's Great Red Spot warmer or cooler than nearby clouds? Does this mean it is higher or lower in altitude than the nearby clouds? (Hint: Use what you know about the belts and zones as you study these images.) 11. Comparing Jovian Planets. You can do comparative planetology armed only with telescopes and an understanding of gravity. 1. The satellite Amalthea orbits Jupiter at just about the same distance in kilometers at which Mimas orbits Saturn. Yet Mimas takes almost twice as long to orbit. What can you deduce from this difference, qualitatively? 2. Jupiter and Saturn are not very different in radius. When you combine this information with your answer to part (a), what can you conclude? 12. Minor Ingredients Matter. Suppose the jovian planet atmospheres were composed 100% of hydrogen and helium rather than 98% of hydrogen and helium. How would the atmospheres be different in terms of color and weather? Explain. 13. Disappearing Satellite. Io loses about a ton (~1,000 kg) of sulfur dioxide per second to Jupiter's magnetosphere. 1. At this rate, what fraction of its mass would Io lose in 5 billion years? 2. Suppose sulfur dioxide currently makes up 1% of Io's mass. When will Io run out of this gas at the current loss rate? 14. Ring Particle Collisions. Each ring particle in the densest part of Saturn's rings collides with another about every 5 hours. If a ring particle survived for the age of the solar system, how many collisions would it undergo? Do you consider it likely that the ring particles we see in Saturn's rings today have been there since the formation of the solar system? Explain the ramifications of your answer for understanding the origin of the jovian planet rings. 15. Project: Jupiter's Moons. Using binoculars or a small telescope, view the moons of Jupiter. Make a sketch of what you see, or take a photograph. Repeat your observations several times (nightly, if possible) over a period of a couple of weeks. Can you determine which moon is which? Can you measure their orbital periods? Can you determine their approximate distances from Jupiter? Explain. 16. Project: Saturn and Its Rings. Using binoculars or a small telescope, view the rings of Saturn. Make a sketch of what you see, or take a photograph. What season is it in Saturn's northern hemisphere? How far above Saturn's atmosphere do the rings extend? Can you identify any gaps in the rings? Describe any other features you notice. Web Projects Find useful links for Web projects on the text Web site. 1. Galileo and Cassini Missions. Find the latest news on the Galileo and Cassini missions. 1. Print out (or describe) an image from the Galileo mission of interest to you, and interpret it using the techniques developed in this chapter. 2. In a few sentences, describe the main scientific goals of the Cassini mission. What is the current health of the spacecraft, and how is the mission progressing? 2. Oceans of Europa. The possibility of subsurface oceans on Europa holds great scientific interest and may even mean that life could exist on Europa. Find some of the latest research concerning Europa and learn about proposed missions to Europa. Write a one- to two-page summary of what you learn. Chapter 12 Review Questions 1. Briefly explain why comets, asteroids, and meteorites are so useful in terms of helping us understand the formation and development of our solar system. Asteroids and comets are also important for a very different reason: They are remnants from the birth of our solar system and therefore provide an important testing ground for our theories of how our solar system came to be. comets, asteroids, and meteorites carry the history of our solar system encoded in their compositions, locations, and numbers. the "scraps" left over from the formation of our solar system allow us to understand how the planets and larger moons came to exist. the leftovers from the process of accretion in the early solar system fall into three fairly distinct groups, distinguished by their physical and orbital properties: asteroids, Kuiper belt comets, and Oort cloud comets. Asteroids are rocky or metallic in composition, and most orbit the Sun between the orbits of Mars and Jupiter. In contrast, comets are mostly icy in composition and spend most of their time well outside the orbits of the planets. This compositional difference is directly related to where the objects formed: Asteroids formed inside the frost line of the solar nebula, and comets formed outside. dust, ice. Asteroid: a rocky leftover planetesimal orbiting the Sun. Comet: an icy leftover planetesimal orbiting the Sun—regardless of its size or whether or not it has a tail. Meteor: a flash of light in the sky caused by a particle entering the atmosphere, whether the particle comes from an asteroid or a comet. Meteorite: any piece of rock that fell to the ground from space, whether from an asteroid, a comet, or even another planet. 2. What is the asteroid belt, and where is it located? How does the total mass of all the asteroids compare to the mass of a terrestrial world? asteroid belt is The region of our solar system between the orbits of Mars and Jupiter in which asteroids are heavily concentrated. The main asteroid belt lies between 2.2 and 3.3 AU from the Sun, though some interesting asteroids lie outside the belt. Asteroid orbits are distinctly elliptical and can be inclined relative to the ecliptic by as much as 20°–30°, but all orbit the Sun in the same direction as the planets. Science fiction movies often show the asteroid belt as a crowded and hazardous place, but the average distance between asteroids is millions of kilometers. 3. Briefly describe how orbital resonances with Jupiter have affected the asteroid belt. orbital resonance occurs whenever one object's orbital period is a simple ratio of another object's period, such as ½, ¼, or 5/3. In such cases, the two objects periodically line up with each other, and the extra gravitational attractions at these times can affect the objects' orbits. Consider, for example, the orbital resonances between Saturn's moons and particles in its rings: The moons are much larger than the ring particles and therefore force the ring particles out of resonant orbits, clearing gaps in the rings [Section 11.6]. In the asteroid belt, similar orbital resonances occur between asteroids and Jupiter, the most massive planet by far. For example, any asteroid in an orbit that takes 6 years to circle the Sun—half of Jupiter's 12-year orbital period—would receive the same gravitational nudge from Jupiter every 12 years and would soon be pushed out of this orbit. The same is true for asteroids with orbital periods of 4 years ( 1/3 of Jupiter's period) and 3 years (¼ of Jupiter's period). 4. How do we detect asteroids with telescopic images? How do we determine the orbit of an asteroid? Asteroids are recognizable in telescopic images because they move noticeably relative to the stars in just a short time (Figure 12.2). Once we detect an asteroid, we can calculate its orbit by applying Kepler's laws [Section 5.3]—even if we've observed only a small part of one complete orbit. Most asteroids appear as little more than points of light even to our largest Earth-based telescopes, so the best way to study an asteroid in depth is to send a spacecraft out to meet it. Spacecraft have visited only a handful of asteroids close-up in their native environment of the asteroid belt and a few other presumed asteroids "in captivity" in orbit around other planets (e.g., Phobos and Deimos orbiting Mars, and the backward outer satellites of Jupiter). 5. Briefly describe how we can estimate an asteroid's size, mass, density, and shape. We can directly measure the size of an asteroid only when we've seen it close up or in the rare cases when an asteroid is large enough to be resolved in a telescope. (We calculate physical size from the asteroid's angular size and distance [Section 7.1].) In many other cases, we can indirectly determine asteroid sizes by analyzing their light. The total amount of sunlight that an asteroid reflects depends on its size and albedo [Section 10.2]. For example, if two asteroids have the same albedo, the one that reflects more light must be larger. We can determine an asteroid's albedo by taking advantage of the fact that asteroids not only reflect visible light from the Sun, but also emit their own infrared thermal radiation. Asteroid masses can be measured only if we have observed the asteroid's gravitational effect on a passing spacecraft or, in very rare cases, if the asteroid has its own tiny moon. One case of an asteroid with a moon is Ida, with its moon Dactyl Determining an asteroid's density can offer valuable insights into its origin and makeup but is possible only if we can measure the asteroid's mass as well as its size. Mass measurements have been made only in a few cases, because they require observing an asteroid's gravitational effect on another object, either a passing spacecraft or a tiny "moon" orbiting the asteroid (Figure 12.6). But these few cases have already revealed that different asteroids can have very different densities. For example, observations from the NEAR flyby of Mathilde yielded a density of 1.5 g/cm3, which is so low that the asteroid cannot be a solid rocky object. Indeed, the impact that formed the huge crater on Mathilde's surface (see Figure 12.4b) would have disintegrated a solid object. Mathilde must be a loosely bound "rubble pile" that could absorb the shock of impact without completely disintegrating. In contrast, NEAR found a relatively high density of 2.4 g/cm3 for Eros, which is close to the value expected for solid rock. Determining asteroid shapes is even more challenging. One technique involves looking for brightness variations as an asteroid rotates. A uniform spherical asteroid will not change its brightness as it rotates, but a potato-shaped asteroid will reflect more light when it presents its larger side toward the Sun and our telescope (Figure 12.4b). Astronomers can also determine asteroid shapes by examining the shape of the shadows cast in starlight when an asteroid happens to pass right in front of a star. By combining the exact times of the star's disappearance and reappearance as clocked with telescopes in several different locations around the world, they can calculate the shape and size of the shadow and therefore the outline of the asteroid itself. Shape measurements show that only the largest asteroid (Ceres, 940-km diameter) is approximately spherical. 6. Describe the compositions of the three main groups of asteroids, as distinguished by spectroscopy. Thousands of asteroids have been analyzed in this way, and they fall into three main categories: About 75% of asteroids are very dark and show absorption bands from carbon-rich materials. Another 15% are more reflective and show absorption bands characteristic of rocky materials. The remaining 10% include asteroids with spectral characteristics of metals such as iron. Overall, the wide range of asteroid properties reveals their varied histories and underscores planetary scientists' interest in visiting more asteroids. 7. How can we distinguish a meteorite from a terrestrial rock? Why do we find so many meteorites in Antarctica? Most meteorites are difficult to distinguish from terrestrial rocks without detailed scientific analysis, but a few clues can help. Meteorites are usually covered with a dark, pitted crust resulting from their fiery passage through the atmosphere. Some can be readily distinguished from terrestrial rocks by their high metal content. (Most types of meteorites contain enough metal to attract a magnet hanging on a string. If you suspect that you have found a meteorite, most science museums will analyze a small chip free of charge.) The ultimate judge of extraterrestrial origin is laboratory analysis of the rock's composition. Terrestrial rocks may differ from one another in composition, but all contain isotopes of particular elements in roughly the same ratios. Meteorites can be identified by their very different isotope ratios. The presence of certain rare elements, such as iridium. Antarctica offers the greatest treasure trove of meteorites, not because more fall there but because the icy surface makes meteorites easier to identify and the movement of glaciers carries rocky debris into a few small areas. The majority of meteorites in museums and laboratories come from Antarctica. 8. Distinguish between primitive meteorites and processed meteorites in terms of composition. How do the origins of these two groups of meteorites differ? primitive meteorites are Meteorites that formed at the same time as the solar system itself, about 4.6 billion years ago. processed meteorites are Meteorites that apparently once were part of a larger object that processed the original material of the solar nebula into another form. Most primitive meteorites are composed of rocky minerals with an important difference from Earth rocks: A small but noticeable fraction of pure metallic flakes is mixed in. (Iron in Earth rocks is chemically bound in minerals.) Some primitive meteorites also contain substantial amounts of carbon compounds, and some even contain a small amount of water. radioactive dating shows that they formed at the same time as the solar system itself—about 4.6 billion years ago . 9. Why do primitive meteorites come in carbon-rich and rocky varieties? where they formed in the solar nebula. Carbon compounds condensed only at the relatively low temperatures that were found in the solar nebula beyond about 3 AU from the Sun. carbon-rich meteorites must come from the outer portion of the asteroid belt (beyond about 3 AU from the Sun). Laboratory spectra of these carbon-rich primitive meteorites confirm that they are a good match to the compositions of asteroids in the outer part of the asteroid belt. The remainder of the primitive meteorites lack carbon compounds, so they presumably formed in the warmer, inner part of the asteroid belt. Curiously, most of the meteorites collected on Earth are of the rocky variety, even though most asteroids are of the carbon-rich variety. Evidently, orbital resonances are more effective at pitching asteroids our way from the inner part of the asteroid belt. All the primitive meteorites apparently survived untouched since the beginning of the solar system—at least until they came crashing down to Earth. 10. How is the study of a processed meteorite an opportunity to look at a piece of a "dissected planet"? Terrestrial rocks may differ from one another in composition, but all contain isotopes of particular elements in roughly the same ratios. Meteorites can be identified by their very different isotope ratios. The presence of certain rare elements, such as iridium, also indicates extraterrestrial origin; nearly all of Earth's iridium sank to the core long ago and is absent from surface rocks. Some processed meteorites resemble the Earth's core in composition: an iron/nickel mixture with trace amounts of other metals. 11. How did Halley's comet get its name? How are comets named today? Halley's comet, named for the English scientist Edmund Halley (1656–1742). Halley did not "discover" his comet but rather gained fame for recognizing that a comet seen in 1682 was the same one seen on a number of previous occasions. He used Newton's law of gravitation to calculate the comet's 76-year orbit and, in a book published in 1705, predicted that the comet would return in 1758. The comet was given his name when it reappeared as predicted, 16 years after his death. Halley's comet has returned on schedule ever since, including twice in the twentieth century—spectacularly in 1910 when it passed near the Earth, and unimpressively in 1986 when it passed by at a much greater distance. It will next visit in 2061. The first discoverers (up to three) who report their findings to the International Astronomical Union have the comet named after them. 12. Describe the anatomy of a comet. How does gas escape from the interior of the nucleus into space? Why do the tails point away from the Sun? Comets are icy planetesimals from the outer solar system. Their composition has been described as "dirty snowballs": ices mixed with rocky dust. Comets are completely frozen when they are far from the Sun, and most are just a few kilometers across. But a comet takes on an entirely different appearance when it comes closer to the Sun (Figure 12.13). The dirty snowball is the comet's nucleus. The sublimation of ices in the nucleus creates a rapidly escaping dusty atmosphere called the coma, along with a tail that points away from the Sun regardless of which way the comet is moving through its orbit. In most cases, we actually see two tails: a plasma tail made of ionized gas, and a dust tail made of small solid particles. Although much of comet science focuses on the dramatic tail and coma, we will begin our closer look at comets with the humbler nucleus. Comet nuclei are rarely observable with telescopes, because they are quite small and are shrouded by the dusty coma. These ionized gases form the plasma tail, which may extend hundreds of millions of kilometers away from the Sun. Dust-size particles experience a much weaker push caused by the pressure of sunlight itself (called radiation pressure so the dust tail is swept away from the Sun in a slightly different direction. The comet wheels around the Sun, always keeping its tails of dust and plasma pointed roughly away from the Sun. Comets also eject some larger, pebble-size particles that are not pushed away from the Sun. These form another, invisible "tail" extending along the comet's orbit; as we'll discuss in Section 12.6, these particles are responsible for meteor showers. 13. Why can't an active comet last forever? What happens to comets after many passes near the Sun? Comets spend most of their lives in the frigid outer limits of our solar system. As a comet accelerates toward the Sun, its surface temperature increases and ices begin to sublime into gaseous form. By the time the comet comes within about 5 AU of the Sun, sublimation begins to form a noticeable atmosphere that easily escapes the comet's weak gravity. The escaping atmosphere drags away dust particles that were mixed with the ice and begins to create the dusty coma around the nucleus. Sublimation rates increase as the comet approaches the Sun, and gases jet away from patches on the nucleus at speeds of hundreds of meters per second (Figure 12.14). The jets can make faint pinwheel patterns within the coma, due to the slow rotation of comet nuclei. The rapid sublimation carries away so much dust that a spacecraft flyby is dangerous. The Giotto spacecraft, which approached Halley's nucleus at a relative speed of nearly 250,000 km/hr (70 km/sec), was sent reeling by dust impacts just minutes before closest approach, breaking radio contact with Earth. As gas and dust move away from the comet, they are influenced by the Sun in different ways. The gases are ionized by ultraviolet photons from the Sun and then carried straight outward away from the Sun with the solar wind at speeds of hundreds of kilometers per second. 14. Describe the Kuiper belt and the Oort cloud in terms of location and comet orbits. Explain how we infer the existence of these two comet reservoirs. How do we think comets came to exist in these two distinct reservoirs? Kuiper belt is The comet-rich region of our solar system that spans distances of about 30–100 AU from the Sun; Kuiper belt comets have orbits that lie fairly close to the plane of planetary orbits and travel around the Sun in the same direction as the planets. Oort cloud is A huge, spherical region centered on the Sun, extending perhaps halfway to the nearest stars, in which trillions of comets orbit the Sun with random inclinations, orbital directions, and eccentricities. comets must come from enormous reservoirs at much greater distances: the Kuiper belt and the Oort cloud (Figure 12.15). The existence of these reservoirs was first inferred by analysis of the orbits of comets that pass close to the Sun. Most comet orbits fit no pattern—they do not orbit the Sun in the same direction as the planets, and their elliptical orbits can be pointed in any direction. Comets Hyakutake and Hale–Bopp both fall into this class. It is believed that such comets are visitors from the Oort cloud. Other comets have a pattern to their orbits: They travel around the Sun in the same plane and direction as the planets, though on very elliptical orbits that take them beyond the orbit of Pluto. They also return much more frequently—typically every few decades or centuries—and are thought to be visitors from the Kuiper belt. 15. Describe Pluto and Charon. How were they discovered? Why won't Pluto collide with Neptune even though their orbits cross? How did Charon probably form? Pluto and Charon are small and far away. due to similarities in the compositions of one of Neptune's moons and Pluto, both of these objects originally formed in the Kuiper belt. Pluto's is noticeably elliptical. Its orbit is also the one that is at the most dramatic angle to the Earth's orbital plane. Finally, it's much smaller than even Mercury - about ½ its radius and less than 10% of its mass. The current theory to explain these disagreements is that Pluto didn't form the way the rest of the planets did and is more likely a captured traveler from the outskirts of the Solar System. If it didn't form in the same area, it's not such a big surprise that it doesn't fit in with the other planets. In 1930, the American astronomer Clyde Tombaugh, working with improved equipment and photographic techniques at the Lowell Observatory, finally succeeded in finding the ninth planet Pluto. Pluto's average density of 2000 kg/m3 is too low for a terrestrial planet but far too high for a jovian one. Instead, the mass, radius, and density of Pluto are just what we expect for one of the icy moons of a jovian planet. Indeed, Pluto is comparable in both mass and radius to Neptune's large moon, Triton. Pluto Atmosphere Surface Pressure: ~3 microbar Average temperature: ~50 K (-223 C) Scale height: ~60 km Mean molecular weight: ~16-25 g/mole Atmospheric composition: Methane (CH4), Nitrogen (N2) 16. Briefly summarize the evidence suggesting that Pluto is a Kuiper belt comet. Pluto is small in size and is near the edge of the solar system, and near Neptune. 17. Describe the impact of comet Shoemaker–Levy 9 on Jupiter. How was the impact studied? What did we learn from this impact? 18. Explain how meteor showers are linked to comets. Why do meteor showers seem to originate from a particular location in the sky? meteor is a bright streak in the sky, often referred to as a shooting star, resulting from a small piece of interplanetary debris entering Earth's atmosphere and heating air molecules, which emit light as they return to their ground states. meteorite Any part of a meteoroid that survives passage through the atmosphere and lands on the surface of Earth. Comets contain many of the basic ingredients for life, but they spend almost all of their time frozen, far from the Sun. A small fraction of the meteorites that survive the plunge to Earth’s surface also contain organic compounds. A similar method is also useful for meteorites the exposed surface is constantly being hit by high-energy particles called cosmic rays these are strong enough to break a nucleus of a heavy element into a few smaller nuclei (ligher elements). 19. Describe the evidence suggesting that the mass extinction that killed off the dinosaurs was caused by the impact of an asteroid or comet. How did the impact lead to the mass extinction? Craters in Arizona and Mexico. As asteroids revolve around the Sun in elliptical orbits, giant Jupiter’s gravity and occasional close encounters with Mars or with another asteroid change the asteroids’ orbits, knocking them out of the Main Belt and hurling them into space across the orbits of the planets. For example, Mars’ moons Phobos and Deimos may be captured asteroids. Scientists believe that stray asteroids or fragments of asteroids have slammed into Earth in the past, playing a major role both in altering the geological history of our planet and in the evolution of life on it. The extinction of the dinosaurs 65 million years ago has been linked to a devastating impact near the Yucatan peninsula in Mexico. After Asteroid hits the Earth a lot of dust, and particles fly up into the Earth's atmosphere blocking out sunlight which made the Earth become cold, and lead to the extinction of the dinosaurs. Plants were unable to grow. 20. How often should we expect impacts of various sizes on Earth? How could we alleviate the risk of major impacts? Discussion Questions 1. Impact Risk. How can we compare the risk of death from an impact to the risk of death from other hazards? One proposed way to evaluate the risk is to multiply the probability of an impact by the number of people it would kill. For example, the probability of a major impact that could kill half the world's population, or some 3 billion people, is estimated to be about 0.0000001 (10–7) in any given year. If we multiply this low probability by the 3 billion people that would be killed, we find the "average" risk from such an impact to be 10–7 X (3 X 109) = 300 people killed per year—about the same as the average number of people killed in airplane crashes. Do you think it is valid to say that the risk of being killed by a major impact is about the same as the risk of being killed in an airplane crash? Should we pay to limit this risk, as we pay to limit airline crashes? Defend your opinions. 2. Observational Bias. Meteorites and long-tailed comets represent "free samples" of more distant objects. 1. Carbon-rich asteroids make up about 5% of meteorite falls on the Earth. How does this compare with the observed fraction of carbon-rich asteroids in the asteroid belt? The odds of a particular comet we observe originating from the Oort cloud versus the Kuiper belt are about 50–50. How does this compare with the relative number of objects in these two regions? 2. Your answers to part (a) should show that meteorite samples and comet observations suffer from bias—that is, what we learn from their study may not accurately reflect the complete populations of the objects they represent. How might a similar bias play a role in more down-to-earth situations? For example, do you and your classmates form a representative sample of your city, nation, or planet? How might this affect the accuracy of a report on world events you might write together or the fairness of a decision you might vote on? In what ways can the effects of bias be removed? 3. Rise of the Mammals. Suppose the impact 65 million years ago had not occurred. How do you think our planet would be different? For example, do you think that mammals would still have eventually come to dominate the Earth? Would we be here? Defend your opinions. Problems Surprising Discoveries? For problems 1–8, suppose we made the discoveries described. (These are not real discoveries.) Decide whether the discovery should be considered reasonable or surprising. Explain. 1. A small asteroid that orbits within the asteroid belt has an active volcano. 2. Scientists discover a meteorite that, based on radioactive dating, is 7.9 billion years old. 3. An object that resembles a comet in size and composition is discovered to be orbiting in the inner solar system. 4. Studies of a large object in the Kuiper belt reveal that it is made almost entirely of rocky (as opposed to icy) material. 5. Astronomers discover a previously unknown comet that will produce a spectacular display in Earth's skies about 2 years from now. 6. A mission to Pluto finds that it has lakes of liquid water on its surface. 7. Geologists discover a crater from a 5-km object that impacted the Earth more than 100 million years ago. 8. Archaeologists learn that the fall of ancient Rome was caused in large part by an asteroid impact in southern Africa. 9. Orbital Resonances. How would our solar system be different if orbital resonances had never been important (for example, if Jupiter and asteroids continued to orbit the Sun but did not affect each other through resonances)? Describe at least five ways in which our solar system would be different. Which differences do you consider superficial, and which differences more profound? Consider the effects of orbital resonances discussed both in this chapter and in Chapter 11. 10. Life Story of an Iron Atom. Imagine that you are an iron atom in an iron meteorite recently fallen to Earth. Tell the story of how you got here, beginning from the time when you were in a gaseous state in the solar nebula 4.6 billion years ago. Include as much detail as possible. Your story should be scientifically accurate but also creative and interesting. 11. Asteroid Discovery. You have discovered two new asteroids and have named them Barkley and Jordan. Both lie at the same distance from the Earth and have the same brightness when you look at them through your telescope. But Barkley is twice as bright as Jordan at infrared wavelengths. What can you deduce about the two asteroids' relative reflectivities and sizes? Which would make a better target for a mission to mine metal? Which would make a better target for a mission to obtain a sample of a carbon-rich planetesimal? Explain your answers. 12. The "Near Miss" of Toutatis. The 5-km asteroid Toutatis passed a mere 3 million km from the Earth in 1992. 1. In one or two paragraphs, describe what would have happened to the Earth if Toutatis had hit it. 2. Suppose Toutatis was destined to pass somewhere within 3 million km of Earth. Calculate the probability that this somewhere would have meant that it slammed into Earth. Based on your result, do you think it is fair to say that the 1992 passage was a near miss? Explain. (Hint: You can calculate the probability by considering an imaginary dartboard of radius 3 million km on which the bull's-eye has the Earth's radius of 6,378 km.) 13. Comet Temperatures. Compare the strength of sunlight at 50,000 AU in the Oort cloud with its strength at 3 AU and 1 AU. Compare the "no greenhouse" temperatures for comets (see Mathematical Insight 10.1) at the three positions. At which location will the temperature be high enough for water ice to sublime (about 150 K)? Assume that the comets rotate rapidly and have an albedo of 3%. 14. Project: Tracking a Meteor Shower. Armed with an expendable star chart and a flashlight covered in red plastic, set yourself up comfortably to watch a meteor shower listed in Table 12.1. Each time you see a meteor, record its path on your star chart. Record at least a dozen, and try to determine the radiant of the shower—the point in the sky from which the meteors appear to radiate. Also record the direction of the Earth's motion, which you can find by determining which sign of the zodiac rises at midnight. 15. Project: Dirty Snowballs. If there is snow where you live or study, make a filthy snowball. (The ice chunks that form behind tires work well.) How much dirt does it take to darken snow? Find out by allowing your dirty snowball to melt and measuring the approximate proportions of water and dirt afterward. Web Projects Find useful links for Web projects on the text Web site. 1. The NEAR Mission. Learn about the NEAR mission to the asteroid Eros. How did the mission reach Eros? How did it end? What did it accomplish? Write a one- to two-page summary of your findings. 2. Stardust. Learn about NASA's Stardust mission (launched in 1999) to bring back cometary material to Earth. What is the current status of the spacecraft? What do we hope to learn after it returns? Write a report about the mission status and its science. 3. Asteroid and Comet Missions. Learn about another proposed space mission to study asteroids or comets. Write a short report about the mission plans, goals, and prospects for success. 4. Pluto Express. NASA has gone back and forth for years about a mission to Pluto, the only planet not yet visited by spacecraft. Find the latest on plans for a mission to Pluto. Does the mission seem likely to take place anytime soon? Write a short report about the current status of a Pluto mission. Discuss the scientific goals of such a mission and the political realities that may dictate whether it occurs. Chapter 13 Review Questions 1. Briefly summarize how Earth is different from the other terrestrial planets. In particular, define hydrosphere and biosphere. The abundant white clouds overlying the expanse of oceans show a planet unlike any other in our solar system. It is, of course, our own planet Earth. the Earth's surface is shaped by the same four geological processes (impact cratering, volcanism, tectonics, and erosion) that shape other worlds, but Earth is the only planet on which the lithosphere is clearly broken into plates that move around in what we call plate tectonics. The Earth's atmosphere shows even more substantial differences from the atmospheres of its neighbors: It is the only planet with significant atmospheric oxygen and the only terrestrial world with an ultraviolet-absorbing stratosphere. But the greatest differences between Earth and other worlds lie in two features totally unique to Earth. First, the surface of the Earth is covered by huge amounts of water. Oceans cover nearly three-fourths of the Earth's surface, with an average depth of about 3 kilometers (1.8 miles). Water is also significant on land, where it flows through streams and rivers, fills lakes and underground water tables, and sometimes lies frozen in glaciers. Frozen water covers nearly the entire continent of Antarctica in the form of the southern ice cap. The northern ice cap sits atop the Arctic Ocean and covers the large island of Greenland. Water plays such an important role on Earth that some scientists treat it as a distinct planetary layer, called the hydrosphere, between the lithosphere and the atmosphere. The second totally unique feature of Earth is its diversity of life. We find life nearly everywhere on Earth's surface, throughout the oceans, and even underground. The layer of life on Earth is sometimes called the biosphere. As we will see shortly, the biosphere helps shape many of the Earth's physical characteristics. For example, the biosphere explains the presence of oxygen in Earth's atmosphere. Without life, Earth's atmosphere would be very different. 2. Briefly describe the interior structure of the Earth, including its molten outer core and its lithosphere. The Earth's thin crust and the uppermost portion of the mantle make up a relatively cool and rigid lithosphere about 100 km thick [Section 9.2]. Below the lithosphere, the mantle is warm and partially molten in places; it supplies the magma for volcanic eruptions. Deeper in the mantle, higher pressures force the rock into the solid phase despite even higher temperatures. But even in solid form the mantle slowly flows, and convection continually carries heat up from below. The Earth's metallic core underlies the lower mantle. The outer region of the core is molten, but high pressures in the inner core force the metal into solid form. The Earth has all the ingredients needed for exciting geology: a hot interior to supply energy for volcanism, convection to help generate tectonic stresses, and a relatively thin lithosphere that does not inhibit geological activity. Earth is the only terrestrial planet on which the lithosphere is split into distinct plates. Earth also has a crust that comes in two very different varieties: a relatively thick, low-density crust underlying the continents, and a thinner, denser crust underlying the seafloors Seafloor crust is made of basalt and is typically only 5–10 km thick, whereas continental crust is made of lower-density rock (such as granite) and is 20–70 km thick. To understand these and other unique features of Earth's geology, we must look in more detail at how the four geological processes affect our planet. 3. How does seafloor crust differ from continental crust? Why do we find fewer craters on the seafloor than on the continents? Earth also has a crust that comes in two very different varieties: a relatively thick, low-density crust underlying the continents, and a thinner, denser crust underlying the seafloors (Figure 13.3). Seafloor crust is made of basalt and is typically only 5–10 km thick, whereas continental crust is made of lower-density rock (such as granite) and is 20–70 km thick. To understand these and other unique features of Earth's geology, we must look in more detail at how the four geological processes affect our planet. Four billion years ago, the Earth's surface may have been as saturated with craters as the densely cratered lunar highlands are today [Section 9.5]. We find no 4-billion-year-old craters on Earth now, so these ancient impacts must have been erased by other geological processes. The impact rate fell substantially after the early bombardment, but occasional impacts still occur—sometimes with devastating consequences [Section 12.6]. The effects of erosion make impact craters surprisingly difficult to identify on Earth. Nevertheless, remnants of more than 100 impact craters have been found (see Figure 12.8). Large impacts should have occurred more or less uniformly over the Earth's surface, including both continents and seafloors, because large impactors are not stopped by the oceans. The relative absence of craters on the seafloor suggests that seafloor crust is much younger than is continental crust; it must have formed later than most of the impacts. 4. Why is erosion more important on Earth than on Venus or Mars? Describe how erosion affects the Earth's geology. The rampant erosion on Earth arises primarily from processes involving water, but atmospheric winds also contribute. Wind tears away at geological features created by other processes, blows dust and sand across the globe, and builds features such as sand dunes. Note that wind erosion is more effective on Earth than on either Venus or Mars: Venus has very little surface wind because of its slow rotation, and wind on Mars does little damage because of the low atmospheric pressure. On Earth, water contributes to erosion through a remarkable variety of processes (Figure 13.5). Perhaps the most obvious are rain and rivers breaking down mountains, carving canyons, and transporting sand and silt across continents to deposit them in the sea. But water erosion occurs on microscopic levels too: Water seeps into cracks and crevices in rocks and breaks them down from the inside, especially when this water freezes and expands. Further examples of water-erosion processes include the slow movement of glaciers, the flow of underground rivers, and the pounding of the ocean surf. 5. Briefly describe the conveyor-like process of plate tectonics. What are spreading centers and subduction zones? plate tectonics is The geological process in which plates are moved around by stresses in a planet's mantle. subduction (of tectonic plates) The process in which one plate slides under another. subduction zones Places where one plate slides under another. spreading centers (geological) Places where hot mantle material rises upward between plates and then spreads sideways, creating new seafloor crust. 6. Describe how subduction has created the continents over billions of years. Give examples of how this process has affected Japan, the Philippines, and the western United States. Over millions of years, plate tectonics acts like a giant conveyor belt for the Earth's crust, carrying rock up from the mantle, transporting it across the seafloor, and then returning it down into the mantle (Figure 13.8). The mid-ocean ridges mark spreading centers between plates—places where hot mantle material rises upward and then spreads sideways, pushing the plates apart. New seafloor crust forms as the partially molten mantle material emerges through a long string of underwater volcanoes, forming crust made of basalt [Section 9.4]. subduction (of tectonic plates) The process in which one plate slides under another As the process continues, islands can grow and merge; this occurred with both Japan and the Philippines, each of which once contained many small islands that merged into the fewer islands we see today. As these islands continue to grow and merge, they may eventually create a new continent. In other cases, a plate carrying islands may run up against an existing continental plate. The dense seafloor crust surrounding the islands subducts below the continents, but the islands resist subduction because they are made of low-density rock. 7. Briefly describe how tectonic stresses can create rift valleys, tall mountain ranges, and faults. Give examples of places that have been affected in each of these ways. tectonics are The disruption of a planet's surface by internal stresses. Tectonic Stresses on Continents Continental crust is relatively thick, strong, and low-density, so it resists both spreading and subduction. Instead of simply separating like seafloor crust on either side of a mid-ocean ridge, continental crust thins and creates a rift valley when mantle convection tugs it apart. One such rift valley runs through Africa; it will eventually tear the continent apart and create a seafloor spreading center. A similar process tore the Arabian peninsula from Africa in the past, creating the Red Sea. 8. What is a hot spot? Describe how hot spots affect Hawaii and Yellowstone. hot spot (geological) A place within a plate of the lithosphere where a localized plume of hot mantle material rises. Hot Spots and Mantle Plumes Not all volcanoes occur near plate boundaries. Sometimes, a plume of hot mantle material may rise in what we call a hot spot within a plate. The Hawaiian Islands are the result of a hot spot that has been erupting basaltic lava for tens of millions of years (Figure 13.13). The low viscosity of this lava produces broad shield volcanoes [Section 9.4]. Today, most of the lava erupts on the "Big Island" of Hawaii, giving much of this island a young, rocky surface. But about a million years ago, the mantle plume lay farther to the northwest—or, equivalently, the entire plate lay farther to the southeast. Back then, the eruptions built the island of Maui, parts of which are now heavily eroded and covered in lush vegetation. 9. What is a runaway greenhouse effect? Why did it occur on Venus but not on Earth? runaway greenhouse effect A positive feedback cycle in which heating caused by the greenhouse effect causes more green-house gases to enter the atmosphere, which further enhances the greenhouse effect. On Earth, moderate temperatures allowed most of the water vapor to condense as rain, leading to the accumulation of liquid water in the oceans. A small amount of water vapor remained in the atmosphere and caused greenhouse warming, but not enough to create a runaway greenhouse effect. Additional water vapor released from volcanoes therefore also condensed, gradually forming the oceans and the other components of the hydrosphere. Venus lost its oceans because it was too hot, Mars lost its oceans because it was too cold, and Earth retained its oceans because conditions were just right. 10. Describe how the carbonate–silicate cycle helps maintain the relatively small CO2 content of our atmosphere. carbonate–silicate cycle is The process that cycles carbon dioxide between the Earth's atmosphere and surface rocks. There the minerals react with dissolved carbon dioxide to form carbonate minerals, which fall to the ocean floor, building up thick layers of carbonate rock such as limestone. This is part of the carbonate–silicate cycle. Because the process requires liquid water, it operates only on Earth, where it has removed about as much CO2 from Earth's atmosphere as now remains in Venus's atmosphere. (If Venus's CO2 could somehow be removed, the remaining atmosphere would have about as much nitrogen as Earth's.) Had Earth been slightly closer to the Sun, its warmer temperature might have evaporated the oceans, leaving the CO2 in the atmosphere and causing a runaway greenhouse effect as on Venus. 11. What are oxidation reactions? If there were no life on Earth, would Earth's atmosphere still contain significant amounts of oxygen or ozone? oxidation Refers to chemical reactions, often with the surface of a planet, that remove oxygen from the atmosphere. The answer to the oxygen mystery is life. The process that supplies oxygen to the atmosphere is photosynthesis, which converts CO2 to O2. The carbon becomes incorporated into amino acids, proteins, and other components of living organisms. Today, plants and single-celled photosynthetic organisms return oxygen to the atmosphere in approximate balance with the rate at which animals and oxidation reactions consume oxygen, so the oxygen content of the atmosphere stays relatively steady. Earth originally developed its oxygen atmosphere when photosynthesis added oxygen at a rate greater than these processes could remove it from the atmosphere. It would contain oxygen. 12. Give examples of positive and negative feedback relationships. How does feedback affect the CO2 balance in our atmosphere? What is "snowball Earth"? feedback relationships are Processes in which one property amplifies (positive feedback) or counteracts (negative feedback) the behavior of properties. A planet's carbon dioxide balance, and its greenhouse-induced temperature, is also subject to both positive and negative feedback. The hotter a planet's surface, the more of its greenhouse gases will be in the atmosphere instead of in the oceans and crust. But this increase in greenhouse gases further increases the temperature—an example of positive feedback (which ultimately led to the runaway greenhouse effect on Venus). However, in some cases, warming temperatures can also lead to negative feedback, at least on planets with liquid water. The warmer temperature leads to more evaporation and cloud formation, and the higher albedo of clouds causes cooling as more sunlight is reflected back to space. Furthermore, higher temperatures increase the rate of carbonate rock formation, pulling more CO2 from the atmosphere and cooling the planet. The complexity of these relationships makes predicting planetary climates difficult. snowball Earth Name given to a hypothesis suggesting that, some 600–700 million years ago, the Earth experienced a period in which it became cold enough for glaciers to exist worldwide, even in equatorial regions. 13. Approximately when did life arise on Earth? How do we know? The key to reconstructing the history of life is to determine the dates at which fossil organisms lived. The relative ages of fossils found in different layers can be determined easily: Deeper layers formed earlier and contain more ancient fossils. Radioactive dating confirms these relative ages and gives us fairly accurate absolute ages for fossils. For relatively recent geological history, such as the age of the dinosaurs that began about 250 million years ago and ended abruptly 65 million years ago, the numerous fossil skeletons of extinct animals prove that life on Earth has undergone dramatic changes. Life in earlier epochs is more difficult to characterize. Primitive life-forms without skeletons leave fewer fossils, erosion erases much old fossil evidence, and subduction destroys other fossil evidence deep beneath the Earth's surface. 14. What evidence tells us that all life today shares a common ancestor? How do biologists compare DNA sequences to establish the "tree of life"? Where do plants and animals fall on this diagram? Life arose on Earth at least 3.5 billion years ago, and possibly much earlier than that. We've found recognizable fossils in rocks as old as 3.5 billion years—microscopic fossils of single-celled bacteria and larger fossils of bacterial "colonies" called stromatolites. indirect evidence suggests that life originated at least 350 million years earlier (3.85 billion years ago), even though such ancient rock samples are too contorted for fossils to remain recognizable. This evidence comes from analysis of different isotopes of carbon [Section 4.3]. Most carbon atoms are atoms of carbon-12 (6 protons and 6 neutrons), but a small proportion of carbon atoms are instead carbon-13 (6 protons and 7 neutrons). organisms use virtually the same limited set of chemical building blocks. For example, proteins are made from building blocks called amino acids, and all living organisms use the same set of 20 different amino acids—even though more than 70 amino acids exist. Similarly, all living organisms use the same basic molecule (called ATP) to store energy within cells, and all use molecules of DNA to transmit their genes from one generation to the next. A second line of evidence for a common ancestor comes from the fact that all living organisms share nearly the same genetic code—the "language" that living cells use to read the instructions chemically encoded in DNA. You are probably familiar with the structure of DNA, which consists of two long strands that look somewhat like train tracks, wound together in the shape of a double helix (Figure 13.18). Each letter shown along the DNA strands represents one of four chemical bases, denoted by A, G, T, and C (for the first letters of their chemical names). The instructions for assembling the cell are written in the precise arrangement of these four chemical bases: 15. What are mutations? How do mutations drive the process of natural selection? mutations are Errors in the copying process when a living cell replicates itself. the transmission of DNA from one generation to the next is not always perfect. Mutations—errors in the copying process—can change the arrangement of chemical bases in a strand of DNA, making the genetic information in a new cell slightly different from that of its parent. Mutations can be caused by many factors, including high-energy cosmic rays from space, ultraviolet light from the Sun, particles emitted by the decay of radioactive elements in the Earth, and various toxic chemicals. Most mutations are lethal, killing the cell in which the mutation occurs. However, some mutations may make a cell better able to survive in its surroundings, and the cell then passes on this improvement to its offspring. 16. Briefly describe how life gradually altered the Earth's atmosphere until it reached its current state. Oxygen is a highly reactive gas, and for a long time it was pulled back out of the atmosphere by reactions with surface rocks. However, by about 2 billion years ago, the oxidation of surface rocks was fairly complete, and oxygen began to accumulate in the atmosphere. Today it constitutes about 20% of the atmosphere, but this fraction may vary over periods of millions of years. The buildup of oxygen had two far-reaching effects for life on Earth. First, it made possible the development of oxygen-breathing animals (Figure 13.21). No one knows precisely how or when the first oxygen-breathing organism appeared, but for that animal the world was filled with food. You can imagine how quickly these creatures must have spread around the world, and the fact that other organisms could now be eaten changed the "rules of the game" for evolution. The second major effect of the oxygen buildup was the formation of the ozone layer, which made it safe for life to move onto the land. Although it took more than a billion years, natural selection eventually led to plants that could survive and thrive on land, and animals followed soon after, taking advantage of this new food source. This epoch highlights the ability of life to fundamentally alter a planet. Not only did life change the Earth's atmosphere, but in doing so it made two other kinds of life possible: oxygen-breathing animals and land organisms. 17. Summarize the slow evolution of life on the early Earth. What was the Cambrian explosion? the remarkable slowness with which evolution progressed for most of Earth's history. But the fossil record reveals a dramatic diversification of life beginning about 540 million years ago. Although this change occurred over a period of about 40 million years, it was so dramatic in comparison to the events of the previous 3 billion years that it is often called the Cambrian explosion. (Cambrian is the name geologists give the period from about 540 million to 500 million years ago.) We can trace the origin of most of today's plant and animal species—from insects to trees to vertebrates—back to this period. Apparently, once life began to diversify, the increased competition among the many more complex species accelerated the process of natural selection and the evolution of new species. Dinosaurs dominated the landscape of the Earth for more than 100 million years. But their sudden demise 65 million years ago paved the way for the evolution of large mammals—including us. The earliest humans appeared on the scene only a few million years ago . 18. What is global warming? Briefly describe some of the potential dangers of global warming and why so many uncertainties are involved in knowing whether global warming represents a real threat. Venus stands as a searing example of the effects of large amounts of atmospheric carbon dioxide. Earth remains habitable only because natural processes have locked up most of its carbon dioxide on the seafloor. However, humans are now tinkering with this difference between the two planets by adding carbon dioxide and other greenhouse gases to the Earth's atmosphere. The primary way we release carbon dioxide is through the burning of fossil fuels (coal, natural gas, and oil)—the carbon-rich remains of plants buried millions of years ago. But other human actions, such as deforestation and the subsequent burning of trees, also affect the carbon dioxide balance of our atmosphere. The inescapable result is that the amount of atmospheric carbon dioxide has risen steadily since the dawn of the industrial age—and continues to rise (Figure 13.23)—nearly 20% in the past 50 years alone. Although it may seem logical to conclude that an increase in the concentration of greenhouse gases should warm the Earth, the Earth is a very complex system. The question of whether human activity is inducing global warming is not merely academic: The consequences of a significant continued warming could be widespread and disastrous. The primary way scientists try to predict the effects of global warming is by making sophisticated computer models of the climate. Different models give different results, but some predict a warming of more than 5°C during the next hundred years. Past ice ages occurred when the average temperature dropped by about 5°C; a similar increase could melt polar ice and flood the Earth's densely populated coastal regions. Such warming would also increase evaporation from the oceans, tending to make storms of all types both more frequent and more destructive: The most obvious way to prevent global warming is to stop burning the fossil fuels that add greenhouse gases to the atmosphere. But much of the world economy depends on energy produced from fossil fuels. 19. Briefly describe the phenomena and causes of the Antarctic ozone hole and worldwide ozone depletion. ozone The molecule O3, which is a particularly good absorber of ultraviolet light. ozone depletion Refers to the declining levels of atmospheric ozone found worldwide on Earth, especially in Antarctica, in recent years. ozone hole A place where the concentration of ozone in the stratosphere is dramatically lower than is the norm. The apparent cause of the ozone depletion is human-made chemicals known as CFCs (chlorofluorocarbons). CFCs were invented in the 1930s and have been widely used in air conditioners and refrigerators, in the manufacture of packaging foam, as propellants in spray cans, in industrial solvents used in the computer industry, and for many other purposes. Indeed, CFCs once seemed like an almost ideal chemical: They are useful in many industries, cheap and easy to produce, and chemically inert they do not burn, break down, or react with anything on the Earth's surface. 20. Is the Earth currently undergoing a mass extinction? Explain. Scientific ideas about evolution are undergoing a similar transformation. Biologists once assumed that evolution always proceeded gradually, with new species arising slowly and others occasionally becoming extinct. It now appears that the vast majority of all species in Earth's history died out in sudden mass extinctions—for which impacts are the prime suspect. The mass extinction that killed off the dinosaurs is only the most famous of these events [Section 12.6]; the fossil record shows evidence of at least a dozen other mass extinctions, some with even greater species loss than in the dinosaur event. While some species died out from direct effects of the impact, most probably died due to the disappearance from their ecosystem of species on which they depended. Furthermore, the survival or extinction of species appears to be random during mass extinctions: Surviving species show no discernible advantage over those that perish. mass extinction is An event in which a large fraction of the species living on Earth go extinct, such as the event in which the dinosaurs died out about 65 million years ago. 21. Summarize why we now think that life can survive in a much broader range of conditions than we did just a few decades ago. Why is this important to the prospect of finding life elsewhere? While some species died out from direct effects of the impact, most probably died due to the disappearance from their ecosystem of species on which they depended. Furthermore, the survival or extinction of species appears to be random during mass extinctions: Surviving species show no discernible advantage over those that perish. In a sense, mass extinctions clear the blackboard, allowing evolution to get a fresh start with a new set of species. If we re-formed the Earth from scratch, life (and even intelligent life) might well arise again, but there is no scientific basis for thinking that evolution would follow the same course. global warming alters the climate significantly or if ozone depletion leads to more genetic damage in plants and animals, the rate of species extinction might increase even more. 22. Describe the evidence from Martian meteorites suggesting that life may once have existed on Mars. Explain how life might have originated on one terrestrial planet and been transferred to others. Martian meteorite found in Antarctica in 1984. The meteorite apparently landed in Antarctica 13,000 years ago, following a 16-million-year journey through space after being blasted from Mars by an impact. The rock itself dates to 4.5 billion years ago, indicating that it solidified shortly after Mars formed and therefore was present during the time when Mars was warmer and wetter. Painstaking analysis of the meteorite reveals indirect evidence of past life on Mars, including layered carbonate minerals and complex molecules (called polycyclic aromatic hydrocarbons), both of which are associated with life when they are found in Earth rocks. Even more intriguing, highly magnified images of the meteorite reveal eerily lifelike forms (Figure 13.25a). These forms bear a superficial resemblance to terrestrial bacteria, although they are about a hundred times smaller—about the same size as recently discovered terrestrial "nanobacteria" and viruses. Magnetic crystals have also been found within the rock—crystals that on Earth are only made by bacteria (Figure 13.25b). Nevertheless, many scientists dispute the conclusion that these features suggest the past existence of life on Mars, claiming that nonbiological causes can also explain the meteorite's unusual features. Martian meteorites also remind us that the planets may occasionally exchange rocks dislodged by major impacts. The harsh conditions under which some life on Earth exists suggest that living organisms might survive such impacts and even survive the journey from one planet to another. Earth's basalt-dwelling bacteria, for example, could probably survive an impact-cratering event, the ensuing millions of years in space, and a violent impact on Mars. If a meteorite from Earth once landed in hospitable conditions on Mars, it might have introduced life to Mars or wiped out life already present. 23. Why are Europa and Titan considered prospects for harboring life? Several of them may meet the requirements of having liquid water, appropriate chemicals, and energy sources for life. Europa may have a planet-wide ocean beneath its icy crust. The ice and rock from which Europa formed undoubtedly included the necessary chemicals, and its internal heating might lead to undersea volcanic vents. found evidence of complex chemical reactions on Titan, many involving the same elements used by life on Earth. Liquid water and energy are in shorter supply, but both might have been supplied by impacts that heated and melted the icy surface early in Titan's history. Life might have arisen in a slushy pond during the brief period that it remained liquid and might have survived after the pond froze. Unlike the case on Earth, where early impacts probably sterilized the planet, impacts on Titan may have made life possible. 24. What is a habitable zone? Using this idea, briefly describe the prospect of finding life on planets around other stars. habitable zone is The region around a star in which planets could potentially have surface temperatures at which liquid water could exist. Interstellar clouds throughout the galaxy contain the basic chemical ingredients of life—carbon, oxygen, nitrogen, and hydrogen, as well as other elements. All stars are born from such interstellar clouds, so it seems likely that other solar nebulae should have given rise to planetary systems similar to our own. Even if a planet is large enough to outgas substantial quantities of water and retain its atmosphere, the stories of Venus and Mars tell us that oceans are not guaranteed. To keep oceans for billions of years, the planet must lie within a range of distances from its star, sometimes called the habitable zone, that has temperatures just right for liquid water. Discussion Questions 1. Evidence of Our Civilization. Imagine a future archaeologist, say 10,000 years from now, trying to piece together a picture of human civilization at our time (i.e., around the year 2000). What types of evidence of our civilization are most likely to survive for 10,000 years? (Will our buildings survive? Our infrastructure, such as highways and water pipes? Information in the form of books or computer data?) What geological processes are likely to destroy evidence over the next 10,000 years? Next, discuss the evidence that will remain—and why—for an archaeologist living 100 million years from now. Be sure to consider the effects of all four geological processes, as well as continental drift. 2. Cancer of the Earth? In the text, we discussed how the spread of humans over the Earth resembles, at least in some ways, the spread of cancer in a human body. Cancers end up killing themselves because of the damage they do to their hosts. Do you think we are in danger of killing ourselves through our actions on the Earth? If so, what should we do to alleviate this danger? Overall, do you think the cancer analogy is valid or invalid? Defend your opinions. 3. Contact. Suppose we discover definitive evidence for microbial life on Mars or Europa. Would this discovery alter your view of our place in the universe? If so, how? What if we made contact with an intelligent species from another world? Do you think it is likely that either kind of life exists elsewhere in the universe? Do you think either kind will be discovered in your lifetime? Explain. Problems Surprising Discoveries? For problems 1–8, suppose we made the discoveries described. (These are not real discoveries.) Decide whether the discovery should be considered reasonable or surprising. Explain. (In some cases, either view can be defended.) 1. A fossil of an organism that died more than 300 million years ago, found in the crust near a mid-ocean ridge. 2. Evidence that fish once swam in a region that is now high on a mountaintop. 3. A "lost continent" on which humans had a great city just a few thousand years ago but that now resides deep underground near a subduction zone. 4. A planet in another solar system that has an Earth-like atmosphere but no life. 5. A planet in another solar system that has an ozone layer but no ordinary oxygen (O2) in its atmosphere. 6. Evidence that the early Earth had more carbon dioxide in its atmosphere than the Earth does today. 7. Discovery of life on Mars that also uses DNA as its generic molecule and that uses a genetic code very similar to that used by life on Earth. 8. Evidence of photosynthesis occurring on a planet in another solar system that lies outside that solar system's habitable zone. 9. Change in Formation Properties. Consider Earth's four formation properties of size, distance, composition, and rotation rate. Choose one property, and suppose it had been different (e.g., smaller size, greater distance). Describe how this change might have affected Earth's subsequent history and the possibility of life on Earth. 10. Growing Population. Since about 1950, human population has grown with a doubling time of about 40 years; that is, the population doubles every 40 years. The current population is about 6 billion. If population continues to grow with a doubling time of 40 years, what will it be in 40 years? In 80 years? Do you think this will actually happen? Why or why not? 11. Feedback Processes in the Atmosphere. 1. Give an everyday example (not used in this book) of a positive or negative feedback process. Explain how the process works. 2. As the Sun gradually brightens, how can the carbonate–silicate cycle respond to reduce the warming effect? Which parts of the cycle will be affected? Is this an example of positive or negative feedback? 12. Defining Life. Write a definition of life and explain the basis of your definition in a few sentences. Then evaluate whether each of the following three cases meets your definition. Explain why or why not in a paragraph for each case. (i) The first self-replicating molecule on Earth lies near the boundary of life and nonlife. Does it meet your definition of life? (ii) Modern-day viruses are essentially packets of DNA encased in a microscopic shell of protein. Viruses cannot replicate themselves; instead, they reproduce by infecting living cells and "hijacking" the cell's reproduction machinery to make copies of the viral DNA and proteins. Are viruses alive? (iii) Imagine that humans someday travel to other stars and discover a planet populated by what appear to be robots programmed to mine metal, refine it, and assemble copies of themselves. Examination of fossil "robots" shows that they have improved, perhaps because cosmic rays have caused errors in their programs. Is this race of robots alive? Would your answer depend on whether another race had built the first robots? 13. Ozone Signature. Suppose a powerful future telescope is able to take a spectrum of a terrestrial planet around another star. The spectrum reveals the presence of significant amounts of ozone. Why would this discovery strongly suggest the presence of life on this planet? Would it tell us whether the life is microscopic or more advanced? Summarize your answers in one or two paragraphs. 14. Explaining Ourselves to the Aliens. Imagine that someday we make contact with intelligent aliens and even learn to communicate. Even so, many facets of life we take for granted may be utterly incomprehensible to them: music (perhaps they have no sense of hearing), money (perhaps there has never been a need), love (perhaps they don't feel this emotion), meals (perhaps they photosynthesize). Write a page attempting to explain one of these concepts, or another of your choosing. Remember that even the words in your explanation require definition; start at the lowest possible level. Web Projects Find useful links for Web projects on the text Web site. 1. Life on Mars. Find the latest information regarding the controversy over evidence for life in Martian meteorites. Write a one- to two-page report summarizing the current state of the controversy and your own opinion as to whether life once existed on Mars. 2. Search for Life. Learn about a proposed mission to search for life on Mars, Europa, or elsewhere in our solar system or beyond. Write a one- to two-page summary of the mission and its prospects for success. 3. Human Threats to the Earth. Write an in-depth research report, three to five pages in length, about current understanding and controversy regarding one of the following issues: global warming, ozone depletion, or the loss of species on Earth due to human activity. Be sure to address both the latest knowledge about the issue and proposals for alleviating any dangers associated with it. End your report by making your own recommendations about what, if anything, needs to be done to prevent damage to the Earth. 4. Local Geology. Write a one- to two-page report about the geology of an area you know well—perhaps the location of your campus or your hometown. Which of the four geological processes has played the most important role, in your opinion? Has plate tectonics played a direct role in shaping the area? Chapter 14 Review Questions 1. Briefly describe how gravitational contraction generates energy and when it was important in the Sun's history. gravitational contraction The process in which gravity causes an object to contract, thereby converting gravitational potential energy into thermal energy. the Sun generates energy by contracting in size, a process called gravitational contraction. If the Sun were shrinking, it would constantly be converting gravitational potential energy into thermal energy, thereby keeping the Sun hot. Because of its large mass, the Sun would need to contract only very slightly each year to maintain its temperature—so slightly that it would be unnoticeable. 2. What two forces are balanced in gravitational equilibrium? How does gravitational equilibrium determine the pressure at any depth within a planet or star? gravitational equilibrium Describes a state of balance in which the force of gravity pulling inward is precisely counteracted by pressure pushing outward. the Sun's size is generally stable, maintained by a balance between the competing forces of gravity pulling inward and pressure pushing outward. This balance is called gravitational equilibrium (also referred to as hydrostatic equilibrium). It means that, at any point within the Sun, the weight of overlying material is supported by the underlying pressure. 3. What is the Sun made of? How do we know? Gases Helium Gas, Hydrogen Gas. Our Sun was born from a collapsing cloud of interstellar gas. The contraction of the cloud released gravitational potential energy, raising the interior temperature higher and higher. When the central temperature and density reached the values necessary to sustain nuclear fusion, the newly released energy provided enough pressure to halt the collapse. That is, the onset of fusion brought the Sun into gravitational equilibrium. About 5 billion years from now, when the Sun finally exhausts its nuclear fuel, the internal pressure will drop, and gravitational contraction will begin once again. As we will see later, some of the most important and spectacular processes in astronomy hinge on this ongoing "battle" between the crush of gravity and a star's internal sources of pressure. Why does the Sun shine?" is that about 4.6 billion years ago gravitational contraction made the Sun hot enough to sustain nuclear fusion in its core. Ever since, energy liberated by fusion has maintained the Sun's gravitational equilibrium and kept the Sun shining steadily, supplying the light and heat that sustain life on Earth. 4. Briefly describe the Sun's luminosity, mass, radius, and average surface temperature. luminosity is The total power output of an object, usually measured in watts or in units of solar luminosities (LSun = 3.8 1026 watts). 4.6 billion years ago gravitational contraction made the Sun hot enough to sustain nuclear fusion in its core. Ever since, energy liberated by fusion has maintained the Sun's gravitational equilibrium and kept the Sun shining steadily, supplying the light and heat that sustain life on Earth. 5. Briefly describe the distinguishing features of each of the Sun's major layers shown in Figure 14.4. A few million kilometers above the solar surface, you enter the solar corona, the tenuous uppermost layer of the Sun's atmosphere (Figure 14.4). Here you find the temperature to be astonishingly high—about 1 million Kelvin. This region emits most of the Sun's X rays. However, the density here is so low that your spaceship feels relatively little heat despite the million-degree temperature [Section 4.2]. Nearer the surface, the temperature suddenly drops to about 10,000 K in the chromosphere, the primary source of the Sun's ultraviolet radiation. At last, you plunge through the visible surface of the Sun, called the photosphere, where the temperature averages just under 6,000 K. Although the photosphere looks like a well-defined surface from Earth, it consists of gas far less dense than the Earth's atmosphere. 6. What are sunspots? Why do they appear dark in pictures of the Sun? sunspots Blotches on the surface of the Sun that appear darker than surrounding regions. 7. Distinguish between nuclear fission and nuclear fusion. Which one is used in nuclear power plants? Which one is used by the Sun? nuclear fusion is in the sun. nuclear fission is in power plants. nuclear fission The process in which a larger nucleus splits into two (or more) smaller particles. nuclear fusion The process in which two (or more) smaller nuclei slam together and make one larger nucleus. 8. Why does fusion require high temperatures and pressures? What rule does the strong force play? The high pressures and temperatures in the solar core are just right for fusion of hydrogen nuclei into helium nuclei. The high temperature is important because the nuclei must collide at very high speeds if they are to come close enough together to fuse. Quantum tunneling is also important to this process. The higher the temperature, the harder the collisions, making fusion reactions more likely at higher temperatures. strong force One of the four fundamental forces; it is the force that holds atomic nuclei together. 9. What is the overall nuclear fusion reaction in the Sun? Briefly describe the proton–proton chain. proton–proton chain The chain of reactions by which low-mass stars (including the Sun) fuse hydrogen into helium. collisions between two nuclei are far more common than three- or four-way collisions, so this overall reaction proceeds through steps that involve just two nuclei at a time. The sequence of steps that occurs in the Sun is called the proton–proton chain because it begins with collisions between individual protons. Hydrogen fuses into helium in the Sun by way of the proton–proton chain. In step 1, two protons fuse to create a deuterium nucleus consisting of a proton and a neutron. In step 2, the deuterium nucleus and a protos fuse to form helium-3, a rare form of helium. In step 3, two helium-3 nuclei fuse to form helium-4, the common form of helium. 10. How does the idea of gravitational equilibrium explain why the Sun's core temperature and fusion rate are self-regulating, like a thermostat? The rate of nuclear fusion in the solar core, which determines the energy output of the Sun, is very sensitive to temperature. A slight increase in temperature would mean a much higher fusion rate, and a slight decrease in temperature would mean a much lower fusion rate. The response of the core pressure to changes in the nuclear fusion rate is essentially a thermostat that keeps the Sun's central temperature steady. Any change in the core temperature is automatically corrected by the change in the fusion rate and the accompanying change in pressure. While the processes involved in gravitational equilibrium prevent erratic changes in the fusion rate, they also ensure that the fusion rate gradually rises over billions of years. Because each fusion reaction converts four hydrogen nuclei into one helium nucleus, the total number of independent particles in the solar core is gradually falling. 11. Explain how mathematical models allow us to predict conditions inside the Sun. How can we be confident that the models are on the right track? The primary way we learn about the interior of the Sun and other stars is by creating mathematical models that use the laws of physics to predict the internal conditions. A basic model uses the Sun's observed composition and mass as inputs to equations that describe gravitational equilibrium and the solar thermostat. With the aid of a computer, we can use the model to calculate the Sun's temperature, pressure, and density at any depth. We can then predict the rate of nuclear fusion in the solar core by combining these calculations with knowledge about nuclear fusion gathered in laboratories here on Earth. Remarkably, such models correctly "predict" the radius, surface temperature, luminosity, age, and many other properties of the Sun. However, current models do not predict everything about the Sun correctly, so scientists are constantly working to discover what is missing from them. The fact that the models successfully predict so many observed characteristics of the Sun gives us confidence that they are on the right track and that we really do understand what is going on inside the Sun. 12. How are "sun quakes" similar to earthquakes? How are they different? Describe how we can observe them and how they help us learn about the solar interior. A second way to learn about the inside of the Sun is to observe "sun quakes"—vibrations of the Sun that are similar to the vibrations of the Earth caused by earthquakes, although they are generated very differently. Earthquakes occur when the Earth's crust suddenly shifts, generating seismic waves that propagate through the Earth's interior [Section 13.2]. We can learn about the Earth's interior by recording seismic waves on the Earth's surface with seismographs. Sun quakes result from waves of pressure (sound waves) that propagate deep within the Sun at all times. These waves cause the solar surface to vibrate when they reach it. Although we cannot set up seismographs on the Sun, we can detect the vibrations of the surface by measuring Doppler shifts [Section 6.5]: Light from portions of the surface that are rising toward us is slightly blueshifted, while light from portions that are falling away from us is slightly red-shifted. The vibrations are relatively small but measurable (Figure 14.8). 13. What is the solar neutrino problem? Describe a possible solution to this problem. The Solar Neutrino Problem Another way to study the solar interior is to observe the neutrinos coming from fusion reactions in the core. Don't panic, but as you read this sentence about a thousand trillion solar neutrinos will zip through your body. Fortunately, they won't do any damage, because neutrinos rarely interact with anything. Neutrinos created by fusion in the solar core fly quickly through the Sun as if passing through empty space. In fact, while an inch of lead will stop an X ray, stopping an average neutrino would require a slab of lead more than a light-year thick! Clearly, counting neutrinos is dauntingly difficult, because virtually all of them stream right through any detector built to capture them. neutrinos do occasionally interact with matter, and it is possible to capture a few solar neutrinos with a large enough detector. Neutrino detectors are usually placed deep inside mines so that the overlying layers of rock block all other kinds of particles coming from outer space except neutrinos, which pass through rock easily. The first major solar neutrino detector, built in the 1960s, was located 1,500 meters underground in the Homestake gold mine in South Dakota (Figure 14.9). The detector for this "Homestake experiment" consisted of a 400,000-liter vat of chlorine-containing dry-cleaning fluid. It turns out that, on very rare occasions, a chlorine nucleus can capture a neutrino and change into a nucleus of radioactive argon. By looking for radioactive argon in the tank of cleaning fluid, experimenters could count the number of neutrinos captured in the detector. solar neutrino problem Refers to the disagreement between the predicted and observed number of neutrinos coming from the Sun. 14. Why does the energy produced by fusion in the solar core take so long to reach the solar surface? Describe the process of radiative diffusion. photons can also interact with any charged particle, and a photon that "collides" with an electron can be deflected into a completely new direction. Deep in the solar interior, the plasma is so dense that the gamma-ray photons resulting from fusion travel only a fraction of a millimeter before colliding with an electron. Because each collision sends the photon in a random new direction, the photon bounces around the core in a haphazard way, sometimes called a random walk (Figure 14.11). With each random bounce, the photon drifts farther and farther, on average, from its point of origin. As a result, photons from the solar core gradually work their way outward. 15. What is convection? Describe how convection transports energy through the Sun's convection zone. convection The energy transport process in which warm material expands and rises, while cooler material contracts and falls. convection zone (of a star) A region in which energy is transported outward by convection. 16. Describe the appearance and temperature of the Sun's photosphere. What is granulation? How would granulation appear in a movie? photosphere is The visible surface of the Sun, where the temperature averages just under 6,000 K. granulation (on the Sun) The bubbling pattern visible in the photosphere, produced by the underlying convection. 17. Briefly describe how magnetic field lines are related to what we would see if we placed compasses in a magnetic field. magnetic field Describes the region surrounding a magnet in which it can affect other magnets or charged particles in its vicinity. magnetic field lines Lines that represent how the needles on a series of compasses would point if they were laid out in a magnetic field. 18. How are magnetic fields related to sunspots? Describe how magnetic fields explain each of the following: the fact that sunspot plasma is cool, the existence and appearance of prominences, and the dramatic explosions of solar flares. solar prominences Vaulted loops of hot gas that rise above the Sun's surface and follow magnetic field lines. The magnetic field lines act somewhat like elastic bands, twisted into contortions and knots by turbulent motions in the solar atmosphere. Sunspots occur where the most taut and tightly wound magnetic fields poke nearly straight out from the solar interior (Figure 14.15a). Note that sunspots tend to occur in pairs connected by a loop of magnetic field lines. These tight magnetic field lines suppress convection within each sunspot and prevent surrounding plasma from sliding sideways into the sunspot. With hot plasma unable to enter the region, the sunspot plasma becomes cooler than that of the rest of the photosphere. plasma A gas consisting of ions and electrons. plasma tail (of a comet) One of two tails seen when a comet passes near the Sun (the other is the dust tail); composed of ionized gas blown away from the Sun by the solar wind. solar flares Huge and sudden releases of energy on the solar surface, probably caused when energy stored in magnetic fields is suddenly released. magnetic field Describes the region surrounding a magnet in which it can affect other magnets or charged particles in its vicinity. 19. Why is the chromosphere best viewed with ultraviolet telescopes? Why is the corona best viewed with X-ray telescopes? The gas of the chromosphere and corona is so tenuous that we cannot see it with our eyes except during a total eclipse, when we can see the faint visible light scattered by electrons in the corona. 20. Describe the current theory of how the chromosphere and corona are heated. What evidence supports it? the roughly 10,000-K plasma of the chromosphere emits strongly in the ultraviolet, and the million-K plasma of the corona is the source of virtually all X rays coming from the Sun. Figure 14.18 shows an X-ray image of the Sun: As the solar heating model predicts, the brightest regions of the corona tend to be directly above sunspot groups. Some regions of the corona, called coronal holes, barely show up in X-ray images. More detailed analyses show that the magnetic field lines in coronal holes project out into space like broken rubber bands, allowing particles spiraling along them to escape the Sun altogether. These particles streaming outward from the corona constitute the solar wind, which blows through the solar system at an average speed of about 500 kilometers per second and has important effects on planetary surfaces, atmospheres, and magnetospheres. Somewhere beyond the orbit of Neptune, the pressure of interstellar gas must eventually halt the solar wind. The Pioneer and Voyager spacecraft that visited the outer planets in the 1970s and 1980s are still traveling outward from our solar system and may soon encounter this "boundary" (called the heliopause) of the realm of the Sun. It's also worth noting that, in the same way that meteorites provide us with samples of asteroids we've never visited, solar wind particles captured by satellites provide us with a sample of material from the Sun. Analysis of these solar particles has reassuringly verified that the Sun is made mostly of hydrogen, just as we conclude from studying the Sun's spectrum. 21. What are coronal holes? How are they related to the solar wind? coronal holes are Regions of the corona that barely show up in X-ray images because they are nearly devoid of hot coronal gas. solar wind is A stream of charged particles ejected from the Sun. 22. What do we mean by solar activity? Explain how it is similar to weather on short time scales and to climate on longer time scales. solar activity Refers to short-lived phenomena on the Sun, including the emergence and disappearance of individual sunspots, prominences, and flares; sometimes called solar weather. 23. Describe the sunspot cycle. What do we mean by solar maximum and solar minimum? Explain why the complete cycle is really 22 years rather than 11 years. sunspot cycle is The period of about 11 years over which the number of sunspots on the Sun rises and falls. solar maximum is The time during each sunspot cycle at which the number of sunspots is the greatest. solar minimum is The time during each sunspot cycle at which the number of sunspots is the smallest. 24. Describe a few known ways solar activity affects the Earth. Why is it so difficult to establish links between solar activity and the Earth's climate? if solar activity really is affecting Earth's climate, it must be through some very subtle mechanism. For example, perhaps the expansion of the Earth's upper atmosphere that occurs with solar maximum somehow causes changes in weather. The question of how solar activity is linked to the Earth's climate is very important, because we need to know whether global warming is affected by solar activity in addition to human activity. Unfortunately, for the time being at least, we can say little about this question. Discussion Questions 1. The Solar Neutrino Problem. Discuss the solar neutrino problem and its potential solutions. How serious do you consider this problem? Do you think current theoretical models of the Sun could be wrong in any fundamental way? Why or why not? 2. The Sun and Global Warming. One of the most pressing environmental issues on Earth concerns the extent to which human emissions of greenhouse gases are warming our planet. Some people claim that part or all of the observed warming over the past century may be due to changes on the Sun, rather than to anything humans have done. Discuss how a better understanding of the Sun might help us understand the threat posed by greenhouse gas emissions. Why is it so difficult to develop a clear understanding of how the Sun affects the Earth's climate? Problems Sensible Statements? For problems 1–7, decide whether the statement is sensible and explain why it is or is not. 1. Before Einstein, gravitational contraction appeared to be a perfectly plausible mechanism for solar energy generation. 2. A sudden temperature rise in the Sun's core is nothing to worry about, because conditions in the core will soon return to normal. 3. If fusion in the solar core ceased today, worldwide panic would break out tomorrow as the Sun began to grow dimmer. 4. Astronomers have recently photographed magnetic fields churning deep beneath the solar photosphere. 5. Neutrinos probably can't harm me, but just to be safe I think I'll wear a lead vest. 6. If you want to see lots of sunspots, just wait for solar maximum! 7. News of a major solar flare today caused concern among professionals in the fields of communications and electrical power generation. 8. Differential Rotation. The Sun and Jupiter exhibit differential rotation, but Earth does not. 1. Explain clearly what we mean by differential rotation. 2. Briefly explain why it is possible for jovian planets to rotate differentially, but it is not possible for terrestrial planets to do so. 3. Would you expect differential rotation to be common among other stars? Why or why not? 9. Number of Fusion Reactions in the Sun. Use the fact that each cycle of the proton–proton chain converts 4.7 X 10–29 kg of mass into energy (see Mathematical Insight 14.1), along with the fact that the Sun loses a total of about 4.2 X 109 kg of mass each second, to calculate the total number of times the proton–proton chain occurs each second in the Sun. 10. The Lifetime of the Sun. The total mass of the Sun is about 2 X 1030 kg, of which about 75% was hydrogen when the Sun formed. However, only about 13% of this hydrogen ever becomes available for fusion in the core; the rest remains in layers of the Sun where the temperature is too low for fusion. 1. Based on the given information, calculate the total mass of hydrogen available for fusion over the lifetime of the Sun. 2. Combine your results from part (a) and the fact that the Sun fuses about 600 billion kg of hydrogen each second to calculate how long the Sun's initial supply of hydrogen can last. Give your answer in both seconds and years. 3. Given that our solar system is now about 4.6 billion years old, when will we need to worry about the Sun running out of hydrogen for fusion? 11. Solar Power Collectors. This problem leads you through the calculation and discussion of how much solar power can be collected by solar cells on Earth. 1. Imagine a giant sphere surrounding the Sun with a radius of 1 AU. What is the surface area of this sphere, in square meters? (Hint: The formula for the surface area of a sphere is 4r 2.) 2. Because this imaginary giant sphere surrounds the Sun, the Sun's entire luminosity of 3.8 1026 watts must pass through it. Calculate the power passing through each square meter of this imaginary sphere in watts per square meter. Explain why this number represents the maximum power per square meter that can be collected by a solar collector in Earth orbit. 3. List several reasons why the average power per square meter collected by a solar collector on the ground will always be less than what you found in part (b). 4. Suppose you want to put a solar collector on your roof. If you want to optimize the amount of power you can collect, how should you orient the collector? (Hint: The optimum orientation depends on both your latitude and the time of year and day.) 12. Solar Power for the United States. The total annual U.S. energy consumption is about 2 X 1020 joules. 1. What is the average power requirement for the United States, in watts? (Hint: 1 watt = 1 joule/s.) 2. With current technologies and solar collectors on the ground, the best we can hope is that solar cells will generate an average (day and night) power of about 200 watts/m2. (You might compare this to the maximum power per square meter you found in problem 11b.) What total area would we need to cover with solar cells to supply all the power needed for the United States? Give your answer in both square meters and square kilometers. 3. The total surface area of the United States is about 2 107 km2. What fraction of the U.S. area would have to be covered by solar collectors to generate all of the U.S. power needs? In one page or less, describe potential environmental impacts of covering so much area with solar collectors. Also discuss whether you think these environmental impacts would be greater or lesser than the impacts of using current energy sources such as coal, oil, nuclear power, and hydroelectric power. 13. The Color of the Sun. The Sun's average surface temperature is about 5,800 K. Use Wien's law (see Mathematical Insight 6.2) to calculate the wavelength of peak thermal emission from the Sun. What color does this wavelength correspond to in the visible-light spectrum? In light of your answer, why do you think the Sun appears white or yellow to our eyes? Web Projects Find useful links for Web projects on the text Web site. 1. Current Solar Activity. Daily information about solar activity is available at NASA's Web site Where are we in the sunspot cycle right now? When is the next solar maximum or minimum expected? Have there been any major solar storms in the past few months? If so, did they have any significant effects on Earth? Summarize your findings in a one- to two-page report. 2. Solar Observatories in Space. Visit NASA's Web site for the Sun–Earth connection and explore some of the current and planned space missions designed to observe the Sun. Choose one mission to study in greater depth, and write a one- to two-page report on the mission status and goals and what it has taught or will teach us about the Sun. 3. Sudbury Neutrino Observatory. Visit the Web site for the Sudbury Neutrino Observatory (SNO) and learn how it may help solve the solar neutrino problem. Write a one- to two-page report describing the observatory, any recent results, and what we can expect from it in the future. Chapter 15 Review Questions 1. Briefly explain how we can learn about the lives of stars, despite the fact that stellar lives are far longer than human lives. Compared with stellar lifetimes of millions or billions of years, the few hundred years humans have spent studying stars with telescopes is rather like the aliens' 1-minute glimpse of humanity. We see only a brief moment in any star's life, and our collective snapshot of the heavens consists of such frozen moments for billions of stars. From this snapshot, we try to reconstruct the life cycles of stars while also analyzing what makes one star different from another. 2. What basic composition are all stars born with? Given that all stars begin their lives with this same basic composition, why do stars differ from one another? Thanks to the efforts of hundreds of astronomers studying this snapshot of the heavens, stars are no longer mysterious points of light in the sky. We now know that all stars form in great clouds of gas and dust. All stars begin their life with roughly the same chemical composition: About three-quarters of the star's mass at birth is hydrogen, and about one-quarter is helium, with no more than about 2% consisting of elements heavier than helium. 3. What do we mean by a star's luminosity? What are the standard units for luminosity? Explain what we mean when we measure luminosity in units of L Sun. luminosity is The total power output of an object, usually measured in watts or in units of solar luminosities (LSun = 3.8 1026 watts). A star's luminosity is the total amount of power it radiates into space, which can be stated in watts. For example, the Sun's luminosity is 3.8 X 1026 watts. We cannot measure a star's luminosity directly, because its brightness in our sky depends on its distance as well as its true luminosity. For example, our Sun and Alpha Centauri A the brightest of the three stars in the Alpha Centauri system are similar in luminosity. Today, astronomers classify a star primarily according to its luminosity and surface temperature. Our task in this chapter is to learn how this extraordinarily effective classification system reveals the true natures of stars and their life cycles. We begin by investigating how to determine a star's luminosity, surface temperature, and mass brighter stars tend to appear larger than dimmer stars. 4. What do we mean by a star's apparent brightness? What are the standard units for apparent brightness? Explain how a star's apparent brightness depends on its distance from us. apparent brightness is The amount of light reaching us per unit area from a luminous object; often measured in units of watts/m2. we define the apparent brightness of any star in our sky as the amount of light reaching us per unit area. (A more technical term for apparent brightness is flux.) The apparent brightness of any light source obeys an inverse square law with distance, similar to the inverse square law that describes the force of gravity. If we viewed the Sun from twice the Earth's distance, it would appear dimmer by a factor of 22 = 4. If we viewed it from 10 times the Earth's distance, it would appear 102 = 100 times dimmer. From 270,000 times the Earth's distance, it would look like Alpha Centauri A—dimmer by a factor of 270,0002, or about 70 billion. 5. State the luminosity–distance formula, and explain why it is so important. luminosity–distance formula is The formula that relates apparent brightness, luminosity, and distance: the standard units of luminosity are watts, the units of apparent brightness are watts per square meter. Because we can always measure the apparent brightness of a star, this formula provides a way to calculate a star's luminosity if we can first measure its distance or to calculate a star's distance if we somehow know its luminosity. The luminosity–distance formula is strictly correct only if interstellar dust does not absorb or scatter the starlight along its path to Earth. 6. What do we mean by a star's visible-light luminosity or visible-light apparent brightness? By its X-ray luminosity or X-ray apparent brightness? Explain why we sometimes talk about such wavelength-specific measures, rather than total luminosity and total apparent brightness. when we perceive a star's brightness, our eyes are measuring the apparent brightness only in the visible region of the spectrum. Clearly, when we measure the apparent brightness in visible light, we can calculate only the star's visible-light luminosity. Similarly, when we observe a star with a spaceborne X-ray telescope, we measure only the apparent brightness in X rays and can calculate only the star's X-ray luminosity. We will use the terms total luminosity and total apparent brightness to describe the luminosity and apparent brightness we would measure if we could detect photons across the entire electromagnetic spectrum. Astronomers refer to the total luminosity as the bolometric luminosity. 7. Briefly explain how we calculate a star's distance in parsecs by measuring its parallax angle in arcseconds. Once we have measured a star's apparent brightness, the next step in determining its luminosity is to measure its distance. The most direct way to measure the distances to stars is with stellar parallax, the small annual shifts in a star's apparent position caused by the Earth's motion around the Sun. parallax is The apparent shifting of an object against the background, due to viewing it from different positions. See also stellar parallax parallax angle is Half of a star's annual back-and-forth shift due to stellar parallax; related to the star's distance according to the formula where p is the parallax angle in arcseconds. parsec (pc) is Approximately equal to 3.26 light-years; it is the distance to an object with a parallax angle of 1 arcsecond. 8. What is the magnitude system? What are its origins? Briefly explain what we mean by the apparent magnitude and absolute magnitude of a star. magnitude system is A system of describing stellar brightness by using numbers, called magnitudes, based on an ancient Greek way of describing the brightnesses of stars in the sky. This system uses apparent magnitude to describe a star's apparent brightness and absolute magnitude to describe a star's luminosity. apparent magnitude is A measure of the apparent brightness of an object in the sky, based on the ancient system developed by Hipparchus. absolute magnitude A measure of an object's luminosity; defined to be the apparent magnitude the object would have if it were located exactly 10 parsecs away. 9. Briefly describe how a star's spectral type is related to its surface temperature. List the seven basic spectral types in order of decreasing temperature. How are the spectral types subdivided by number (e.g., A3, G5)? spectral type A way of classifying a star by the lines that appear in its spectrum; it is related to surface temperature. The basic spectral types are designated by a letter (OBAFGKM, with O for the hottest stars and M for the coolest) and are subdivided with numbers from 0 through 9. O B A F G K M B0, B1, . . . , B9). The larger the number, the cooler the star. For example, the Sun is designated spectral type G2, which means it is slightly hotter than a G3 star but cooler than a G1 star. 10. Briefly summarize the roles of Annie Jump Cannon and Cecilia Payne-Gaposchkin in discovering the spectral sequence and its meaning. the task of finding a better classification scheme fell to Annie Jump Cannon (1863–1941), who joined Pickering's team in 1896 (Figure 15.4). Building on the work of Fleming and another of Pickering's computers, Antonia Maury (1866–1952), Cannon soon realized that the spectral classes fell into a natural order—but it was not the alphabetical order determined by hydrogen lines alone. Moreover, she found that some of the original classes overlapped others and could be eliminated. Cannon discovered that the natural sequence consisted of just a few of Pickering's original classes in the order OBAFGKM; she also added the subdivisions by number. Cannon became so adept that she could properly classify a stellar spectrum with little more than a momentary glance. During her lifetime, she personally classified over 400,000 stars. She became the first woman ever awarded an honorary degree by Oxford University, and in 1929 the League of Women Voters named her one of the 12 greatest living American women. The astronomical community adopted Cannon's system of stellar classification in 1910. However, no one at that time knew why spectra followed the OBAFGKM sequence. Many astronomers guessed, incorrectly, that the different sets of spectral lines reflected different compositions for the stars. The correct answer—that all stars are made primarily of hydrogen and helium and that a star's surface temperature determines the strength of its spectral lines—was discovered by Cecilia Payne-Gaposchkin (1900–1979), another woman working at Harvard Observatory. Relying on insights from what was then the newly developing science of quantum mechanics, Payne-Gaposchkin showed that the differences in spectral lines from star to star merely reflected changes in the ionization level of the emitting atoms. For example, O stars have weak hydrogen lines because, at their high surface temperatures, nearly all their hydrogen is ionized. Without an electron to "jump" between energy levels, ionized hydrogen can neither emit nor absorb its usual specific wavelengths of light. At the other end of the spectral sequence, M stars are cool enough for some particularly stable molecules to form, explaining their strong molecular absorption lines. Payne-Gaposchkin described her work and her conclusions in a dissertation published in 1925. A later review of twentieth-century astronomy called her work "undoubtedly the most brilliant Ph.D. thesis ever written in astronomy." 11. Describe and distinguish between visual binary systems, eclipsing binary systems, and spectroscopic binary systems. visual binary A binary star system in which we can resolve both stars through a telescope. eclipsing binary A binary star system in which the two stars happen to be orbiting in the plane of our line of sight, so that each star will periodically eclipse the other. spectroscopic binary A binary star system whose binary nature is revealed because we detect the spectral lines of one or both stars alternately becoming blueshifted and redshifted as the stars orbit each other. 12. Describe how we measure stellar masses and why eclipsing binaries are so important to such measurements. Measuring orbital period is fairly easy: In a visual binary, we simply observe how long each orbit takes (or extrapolate from part of an orbit); in an eclipsing binary, we measure the time between eclipses; and in a spectroscopic binary, we measure the time it takes the spectral lines to shift back and forth. Determining the average separation of the stars in a binary system is usually much more difficult. Except in rare cases in which we can measure the separation directly, we can calculate the separation only if we know the actual orbital speeds of the stars from their Doppler shifts. Unfortunately, a Doppler shift tells us only the portion of a star's velocity that is directly toward us or away from us. Because orbiting stars generally do not move directly along our line of sight, their actual velocities can be significantly greater than those we measure through the Doppler effect. The exceptions are eclipsing binary stars; because they orbit in the plane of our line of sight, their Doppler shifts can tell us their true orbital velocities.(*footnote) Eclipsing binaries are therefore particularly important to the study of stellar masses. As an added bonus, eclipsing binaries allow us to measure stellar radii directly: Because we know how fast the stars are moving across our line of sight as one eclipses the other, we can determine their radii by timing how long each eclipse lasts. 13. Draw a sketch of a basic Hertzsprung–Russell diagram (H–R diagram). Label the main sequence, giants, supergiants, and white dwarfs. Where on this diagram do we find stars that are cool and dim? Cool and luminous? Hot and dim? Hot and bright? The horizontal axis represents stellar surface temperature, which corresponds to spectral type. Temperature increases from right to left because Hertzsprung and Russell based their diagrams on the spectral sequence OBAFGKM. The vertical axis represents stellar luminosity, in units of the Sun's luminosity (L Sun). Stellar luminosities span a wide range, so we keep the graph compact by making each tick mark represent a luminosity 10 times larger than the prior tick mark. Each dot on the diagram represents the spectral type and luminosity of a single star. For example, the dot representing the Sun in Figure 15.9 corresponds to the Sun's spectral type, G2, and its luminosity, 1L Sun. Because luminosity increases upward on the diagram and surface temperature increases leftward, stars near the upper left are hot and luminous. Similarly, stars near the upper right are cool and luminous, stars near the lower right are cool and dim, and stars near the lower left are hot and dim. Hertzsprung–Russell (H–R) diagram A graph plotting individual stars as points, with stellar luminosity on the vertical axis and spectral type (or surface temperature) on the horizontal axis. 14. What do we mean by a star's luminosity class? On your sketch of the H–R diagram, identify the regions for luminosity classes I, III, and V. measuring the masses of stars in binary systems, astronomers have discovered that stellar masses increase upward along the main sequence (Figure 15.10). At the upper end of the main sequence, the hot, luminous O stars can have masses as high as 100 times that of the Sun (100M Sun). On the lower end, cool, dim M stars may have as little as 0.08 times the mass of the Sun (0.08M Sun). Many more stars fall on the lower end of the main sequence than on the upper end, which tells us that low-mass stars are much more common than high-mass stars. 15. Explain how mass determines the luminosity and surface temperature of a main-sequence star. How do masses differ as we look along the main sequence on an H–R diagram? The orderly arrangement of stellar masses along the main sequence tells us that mass is the most important attribute of a hydrogen-burning star. Luminosity depends directly on mass because the weight of a star's outer layers determines the nuclear burning rate in its core; more weight means the star must sustain a higher nuclear burning rate in order to maintain gravitational equilibrium. The nuclear burning rate, and hence the luminosity, is very sensitive to mass. For example, a 10M Sun star on the main sequence is about 10,000 times more luminous than the Sun. 16. What do we mean by a star's main-sequence lifetime? Explain why more massive stars live shorter lives. The precise point on the H–R diagram at which the Pleiades' main sequence diverges from the standard main sequence is called the main-sequence turnoff point. In this cluster, it occurs around spectral type B6. The main-sequence lifetime of a B6 star is roughly 100 million years, so this must be the age of the Pleiades. Any star in the Pleiades that was born with a main-sequence spectral type hotter than B6 had a lifetime shorter than 100 million years and is no longer found on the main sequence. Stars with lifetimes longer than 100 million years are still fusing hydrogen and remain as main-sequence stars. main-sequence lifetime The length of time for which a star of a particular mass can shine by fusing hydrogen into helium in its core. 17. What are pulsating variable stars? Why do they vary periodically in brightness? pulsating variable stars Stars that alternately grow brighter and dimmer as their outer layers expand and contract in size. 18. What are Cepheid variables? What is the period–luminosity relation for Cepheids, and why is it useful for distance measurements? Cepheid variable A particularly luminous type of pulsating variable star that follows a period–luminosity relation and is very useful for measuring cosmic distances. 19. Describe in general terms how open clusters and globular clusters differ in their numbers of stars, ages, and locations in the galaxy. Why are star clusters so important to astronomers? open cluster A cluster of up to several thousand stars; open clusters are found only in the disks of galaxies and often contain young stars. globular cluster A spherically shaped cluster of up to a million or more stars; globular clusters are found primarily in the halos of galaxies and contain only very old stars. star cluster See cluster of stars. cluster of stars A group of anywhere from several hundred to a million or so stars; star clusters come in two types—open clusters and globular clusters. 20. Explain why H–R diagrams look different for star clusters of different ages. How does the location of the main-sequence turnoff point tell us the age of the star cluster? globular-cluster stars are older than 10 billion years. More precise studies of the turnoff points in globular clusters, coupled with theoretical calculations of stellar lifetimes, place the ages of these clusters at between 12 and 16 billion years, making them the oldest known objects in the galaxy. In fact, globular clusters place a constraint on the possible age of the universe: If stars in globular clusters are 12 billion years old, then the universe must be at least this old. stars in a particular cluster that once resided above the turnoff point on the main sequence have already exhausted their core supply of hydrogen, while stars below the turnoff point remain on the main sequence. main-sequence turnoff A method for measuring the age of a cluster of stars from the point on its H–R diagram where its stars turn off from the main sequence; the age of the cluster is equal to the main-sequence lifetime of stars at the main-sequence turnoff point. Discussion Question 1. Classification. Edward Pickering's team of female "computers" at Harvard University made many important contributions to astronomy, particularly in the area of systematic stellar classification. Why do you think rapid advances in our understanding of stars followed so quickly on the heels of their efforts? Can you think of other areas in science where huge advances in understanding followed directly from improved systems of classification? Problems True Statements? For problems 1–10, decide whether the statements are true or false and clearly explain how you know. 1. Two stars that look very different must be made out of different kinds of elements. 2. Sirius is the brightest star in the night sky, but if we moved it 10 times farther away it would look only one-tenth as bright. 3. Sirius looks brighter than Alpha Centauri, but we know that Alpha Centauri is closer because its apparent position in the sky shifts by a larger amount as the Earth orbits the Sun. 4. Stars that look red-hot have hotter surfaces than stars that look blue. 5. Some of the stars on the main sequence of the H–R diagram are not converting hydrogen into helium. 6. The smallest, hottest stars are plotted in the lower left-hand portion of the H–R diagram. 7. Stars that begin their lives with the most mass live longer than less massive stars because it takes them a lot longer to use up their hydrogen fuel. 8. Star clusters with lots of bright, blue stars are generally younger than clusters that don't have any such stars. 9. All giants, supergiants, and white dwarfs were once main-sequence stars. 10. Most of the stars in the sky are more massive than the Sun. 11. Stellar Data. Consider the following data table for several bright stars. Note that M v is absolute magnitude and m v is apparent magnitude.Answer each of the following questions, including a brief explanation with each answer. Spectral Data Star Mv mv Spectral Type Luminosity Class Aldebaran –0.2 +0.9 K5 III Alpha Centauri A +4.4 0.0 G2 V Antares –4.5 +0.9 M1 I Canopus –3.1 –0.7 F0 II Fomalhaut +2.0 +1.2 A3 V Regulus –0.6 +1.4 B7 V Sirius +1.4 –1.4 A1 V Spica –3.6 +0.9 B1 V 1. Which star appears brightest in our sky? 2. Which star appears faintest in our sky? 3. Which star has the greatest luminosity? 4. Which star has the smallest luminosity? 5. Which star has the highest surface temperature? 6. Which star has the lowest surface temperature? 7. Which star is most similar to the Sun? 8. Which star is a red supergiant? 9. Which star has the largest radius? 10. Which stars have finished burning hydrogen in their cores? 11. Among the main-sequence stars listed, which one is the most massive? 12. Among the main-sequence stars listed, which one has the longest lifetime? 12. Data Tables. Study the spectral types listed in Appendix D for the 20 brightest stars and for the stars within 12 light-years. Why do you think the two lists are so different? Explain. 13. The Inverse Square Law for Light. The Earth is about 150 million km from the Sun, and the apparent brightness of the Sun in our sky is about 1,300 watts/m2. Using these two facts and the inverse square law for light, determine the apparent brightness we would measure for the Sun if we were located at the following positions. 1. Half the Earth's distance from the Sun. 2. Twice the Earth's distance from the Sun. 3. Five times the Earth's distance from the Sun. 14. The Luminosity of Alpha Centauri A. Alpha Centauri A lies at a distance of 4.4 light-years and has an apparent brightness in our night sky of 2.7 X 10–8 watt/m2. Recall that 1 light-year = 9.5 X 1012 km = 9.5 X 1015 m. 1. Use the luminosity–distance formula to calculate the luminosity of Alpha Centauri A. 2. Suppose you have a light bulb that emits 100 watts of visible light. (Note: This is not the case for a standard 100-watt light bulb, in which most of its 100 watts goes to heat and only about 10–15 watts is emitted as visible light.) How far away would you have to put the light bulb for it to have the same apparent brightness as Alpha Centauri A in our sky? (Hint: Use the 100 watts as L in the luminosity–distance formula, and use the apparent brightness given above for Alpha Centauri A. Then solve for the distance.) 15. More Practice with the Luminosity–Distance Formula. Use the luminosity–distance formula to answer each of the following questions. 1. Suppose a star has the same luminosity as our Sun (3.8 1026 watts) but is located at a distance of 10 light-years. What is its apparent brightness? 2. Suppose a star has the same apparent brightness as Alpha Centauri A (2.7 10–8 watt/m2) but is located at a distance of 200 light-years. What is its luminosity? 3. Suppose a star has a luminosity of 8 1026 watts and an apparent brightness of 3.5 10–12 watt/m2. How far away is it? Give your answer in both kilometers and light-years. 4. Suppose a star has a luminosity of 5 1029 watts and an apparent brightness of 9 10–15 watt/m2. How far away is it? Give your answer in both kilometers and light-years. 16. Parallax and Distance. Use the parallax formula to calculate the distance to each of the following stars. Give your answers in both parsecs and light-years. 1. Alpha Centauri: parallax angle of 0.7420. 2. Procyon: parallax angle of 0.2860. 17. The Magnitude System. Use the definitions of the magnitude system to answer each of the following questions. 1. Which is brighter in our sky, a star with apparent magnitude 2 or a star with apparent magnitude 7? By how much? 2. Which has a greater luminosity, a star with absolute magnitude +4 or a star with absolute magnitude –6? By how much? 18. Measuring Stellar Mass. The spectral lines of two stars in a particular eclipsing binary system shift back and forth with a period of 6 months. The lines of both stars shift by equal amounts, and the amount of the Doppler shift indicates that each star has an orbital speed of 80,000 m/s. What are the masses of the two stars? Assume that each of the two stars traces a circular orbit around their center of mass. (Hint: See Mathematical Insight 15.4.) 19. Calculating Stellar Radii. Sirius A has a luminosity of 26L Sun and a surface temperature of about 9,000 K. What is its radius? (Hint: See Mathematical Insight 15.5.) Web Projects Find useful links for Web projects on the text Web site. 1. Women in Astronomy. Until fairly recently, men greatly outnumbered women in professional astronomy. Nevertheless, many women made crucial discoveries in astronomy throughout history. Do some research about the life and discoveries of a woman astronomer from any time period, and write a two- to three-page scientific biography. 2. The Hipparcos Mission. The European Space Agency's Hipparcos mission, which operated from 1989–1993, made precise parallax measurements for more than 40,000 stars. Learn about how Hipparcos allowed astronomers to measure smaller parallax angles than they could from the ground and how Hipparcos discoveries have affected our knowledge of the universe. Write a one- to two-page report on your findings. 3. Future Parallax Missions. Astronomers have plans for missions that will further extend our ability to measure distances through parallax. Write a one- to two-page report on one such mission, such as NASA's Space Interferometry Mission (SIM; launch planned for 2009) or the European Space Agency's GAIA mission (launch scheduled for 2012). Chapter 16 Review Questions 1. What is thermal pressure? What are the two energy sources that can help a star maintain its internal thermal pressure? thermal pressure The ordinary pressure in a gas arising from motions of particles that can be attributed to the object's temperature. a star's life is in many ways the story of an extended battle between two opposing forces: gravity and pressure. The most common type of pressure in stars is thermal pressure—the familiar type of pressure that keeps a balloon inflated and that increases when the temperature or thermal energy increases. A star can maintain its internal thermal pressure only if it continually generates new thermal energy to replace the energy it radiates into space. This energy can come from two sources: nuclear fusion of light elements into heavier ones and the process of gravitational contraction, which converts gravitational potential energy into thermal energy. 2. What is a molecular cloud? Briefly describe the process by which a protostar and protostellar disk form from gas in a molecular cloud. molecular clouds Cool, dense interstellar clouds in which the low temperatures allow hydrogen atoms to pair up into hydrogen molecules (H2). protostar A forming star that has not yet reached the point where sustained fusion can occur in its core. protostellar disk A disk of material surrounding a protostar; essentially the same as a protoplanetary disk, but may not necessarily lead to planet formation. 3. Under what conditions does a close binary form? close binary A binary star system in which the two stars are very close together. Rotation is likely to be responsible for the formation of some binary star systems. Protostars that are unable to rid themselves of enough angular momentum spin too fast to become a stable single star and tend to split in two. Each of these two fragments can go on to form a separate star. If the stars are particularly close together, the resulting pair is called a close binary system, in which two stars coexist in close proximity, rapidly orbiting each other. Observations show that the latter stages of a star's formation can be surprisingly violent. Besides the strong wind, many young stars also fire high-speed streams, or jets, of gas into interstellar space 4. Describe some of the activity seen in protostars, such as strong protostellar winds and jets. protostar A forming star that has not yet reached the point where sustained fusion can occur in its core. protostellar disk A disk of material surrounding a protostar; essentially the same as a protoplanetary disk, but may not necessarily lead to planet formation. protostellar wind The relatively strong wind from a protostar. The protostellar disk probably plays a large role in eventually slowing the rotation of the protostar. The protostar's rapid rotation generates a strong magnetic field. As the magnetic field lines sweep through the protostellar disk, they transfer some of the protostar's angular momentum outward, slowing its rotation. The strong magnetic field also helps generate a strong protostellar wind—an outward flow of particles similar to the solar wind that may carry additional angular momentum from the protostar to interstellar space. 5. What do we mean by a star's life track on an H–R diagram? How does an H–R diagram that shows life tracks differ from a standard H–R diagram? life track A track drawn on an H–R diagram to represent the changes in a star's surface temperature and luminosity during its life; also called an evolutionary track. The length of time from the formation of a protostar to the birth of a main-sequence star depends on the star's mass. Remember that massive stars do everything faster. The collapse of a high-mass protostar may take only a million years or less. Collapse into a star like our Sun takes about 50 million years, and collapse into a small star of spectral type M may take more than a hundred million years. The most massive stars in a young star cluster may live and die before the smallest stars finish their prenatal period. We can summarize the transitions that occur during star birth with a special type of H–R diagram. Recall that a standard H–R diagram shows luminosities and surface temperatures for many different stars. In contrast, this special H–R diagram shows part of a life track (also called an evolutionary track) for a single star; for reference, the diagram also shows the standard main sequence. Each point along a star's life track represents its surface temperature and luminosity at some moment during its life. Figure 16.5 shows a life track for the prenatal period in the life of a 1M Sun star like our Sun. Note that this period includes four distinct stages: 6. Describe the observed trends in the number of stars that are born with different masses. What types of stars are most common? What types are least common? Stars of different masses follow a similar set of stages during their prenatal periods. Figure 16.6 illustrates life tracks on an H–R diagram for the prenatal stages of several stars of different masses. a 1M Sun star like our Sun. 7. What is degeneracy pressure? How does it differ from thermal pressure? Explain why degeneracy pressure can support a stellar core against gravity even when the core becomes very cold. degeneracy pressure A type of pressure unrelated to an object's temperature, which arises when electrons (electron degeneracy pressure) or neutrons (neutron degeneracy pressure) are packed so tightly that the exclusion and uncertainty principles come into play. thermal pressure The ordinary pressure in a gas arising from motions of particles that can be attributed to the object's temperature. 8. What is a brown dwarf? Explain why brown dwarfs may be common, even though they are difficult to detect. brown dwarf An object too small to become an ordinary star because electron degeneracy pressure halts its gravitational collapse before fusion becomes self-sustaining; brown dwarfs have mass less than 0.08MSun. Because degeneracy pressure halts the collapse of a protostellar core with less than 0.08M Sun before fusion becomes self-sustaining, the result is a "failed star" that slowly radiates away its internal thermal energy, gradually cooling with time. Such objects, called brown dwarfs, occupy a fuzzy gap between what we call a planet and what we call a star. (Note that 0.08M Sun is about 80 times the mass of Jupiter.) Because degeneracy pressure does not rise and fall with temperature, the gradual cooling of a brown dwarf's interior does not weaken its degeneracy pressure. In the constant battle of any "star" to resist the crush of gravity, brown dwarfs are winners, albeit dim ones: Their degeneracy pressure will not diminish with time, so gravity will never gain the upper hand. 9. What happens to the core of a star when it exhausts its hydrogen supply? Why does hydrogen shell burning begin around the inert core? A low-mass star gradually consumes its core hydrogen, converting it into helium over a period of billions of years. In the process, the declining number of independent particles in the core (four independent protons fuse into just one independent helium nucleus) causes the core to shrink and heat very gradually, pushing the luminosity of the main-sequence star slowly upward as it ages. But the most dramatic changes occur when nuclear fusion exhausts the hydrogen in the star's core. Red Giant Stage The energy released by hydrogen fusion during a star's main-sequence life maintains the thermal pressure that holds gravity at bay. But when the core hydrogen is finally depleted, nuclear fusion ceases in the star's core. With no fusion to supply thermal energy, the core pressure can no longer resist the crush of gravity, and the core begins to shrink more rapidly. 10. Why does helium fusion require much higher temperatures than hydrogen fusion? Briefly describe the overall reaction by which helium fuses into carbon. The greater charge means that helium nuclei repel one another more strongly than hydrogen nuclei. Helium fusion therefore occurs only when nuclei slam into one another at much higher speeds than those needed for hydrogen fusion. Therefore, helium fusion requires much higher temperatures. The helium fusion process (often called the "triple-alpha" reaction because helium nuclei are sometimes called "alpha particles") converts three helium nuclei into one carbon nucleus: 11. Why does helium burning begin with a helium flash in low-mass stars? How do the core structure and rate of fusion change after the helium flash? Because degeneracy pressure does not increase with temperature, the onset of helium fusion heats the core rapidly without causing it to inflate. The rising temperature causes the helium fusion rate to rocket upward in what is called a helium flash. The helium flash dumps enormous amounts of new thermal energy into the core. In a matter of seconds, the rapidly rising thermal pressure becomes the dominant pressure pushing back against gravity; the core is no longer degenerate and begins to expand. helium flash The event that marks the sudden onset of helium fusion in the previously inert helium core of a low-mass star. 12. Explain why a star's overall radius shrinks from its peak size as a red giant after helium fusion begins. Why do helium-burning stars in a star cluster all fall on a horizontal branch on an H–R diagram? Red Giant Stage The energy released by hydrogen fusion during a star's main-sequence life maintains the thermal pressure that holds gravity at bay. But when the core hydrogen is finally depleted, nuclear fusion ceases in the star's core. With no fusion to supply thermal energy, the core pressure can no longer resist the crush of gravity, and the core begins to shrink more rapidly. the star's outer layers expand outward while the core is shrinking. On an H–R diagram, the star's life track moves almost horizontally to the right as the star grows in size to become a subgiant. Then, as the expansion of the outer layers continues, the star's luminosity begins to increase substantially, and the star slowly becomes a red giant. For a 1M Sun star, this process takes about a billion years, during which the star's radius increases about 100-fold and its luminosity grows by an even greater factor. The core and shell continue to shrink in size and grow in luminosity, while thermal pressure continues to push the star's upper layers outward. This cycle breaks down only when the inert helium core reaches a temperature of about 100 million K, at which point helium nuclei can fuse together. (In a very low mass star, the inert helium core may never become hot enough to fuse helium. The core collapse will instead be halted by degeneracy pressure, ultimately leaving the star a helium white dwarf.) Throughout the expansion phase, red-giant winds carry away much more matter than the solar wind does for our Sun, but at much slower speeds. Helium Burning Recall that fusion occurs only when two nuclei come close enough together for the attractive strong force to overcome electromagnetic repulsion. Helium nuclei have two protons (and two neutrons) and hence a greater positive charge than the single proton of a hydrogen nucleus. The greater charge means that helium nuclei repel one another more strongly than hydrogen nuclei. Helium fusion therefore occurs only when nuclei slam into one another at much higher speeds than those needed for hydrogen fusion. Therefore, helium fusion requires much higher temperatures. The helium fusion process (often called the "triple-alpha" reaction because helium nuclei are sometimes called "alpha particles") converts three helium nuclei into one carbon nucleus: Because the helium-burning star is now smaller and hotter than it was as a red giant, its life track on the H–R diagram drops downward and to the left (Figure 16.11a). The helium cores of all low-mass stars fuse helium into carbon at about the same rate, so these stars all have about the same luminosity. However, the outer layers of these stars can have different masses, depending on how much mass they lost through their red-giant winds. Stars that lost more mass end up with smaller radii and higher surface temperatures and hence are farther to the left on the H–R diagram. In a cluster of stars, those stars that are currently in their helium-burning phase therefore all have about the same luminosity but differ in surface temperature. Thus, on an H–R diagram for a cluster of stars, the helium-burning stars are arranged along a horizontal branch (Figure 16.11b). Note that the cluster H–R diagram clearly shows the main-sequence turnoff point. Stars that have recently left the main sequence are subgiants on their way to becoming red giants. In the upper-right corner of the red giant region are stars that are almost ready for the helium flash. The stars that have already become helium-burning, horizontal-branch stars are slightly dimmer and hotter. 13. What is a planetary nebula? What happens to the core of a star after a planetary nebula occurs? planetary nebula The glowing cloud of gas ejected from a low-mass star at the end of its life. Before a low-mass star dies, it treats us to one last spectacle. Through winds and other processes, the star ejects its outer layers into space. The result is a huge shell of gas expanding away from the inert, degenerate carbon core. The exposed core is still very hot and therefore emits intense ultraviolet radiation that ionizes the gas in the expanding shell, causing it to glow brightly as what we call a planetary nebula. Despite their name, planetary nebulae have nothing to do with planets. 14. Briefly describe how the Sun will change, and how Earth will be affected by these changes, over the next several billion years. The Fate of Life on Earth The evolutionary stages of low-mass stars are immensely important to the Earth, because we orbit a low-mass star—the Sun. The Sun will gradually brighten during its remaining time as a main-sequence star; it has already been doing so for the past 4 billion years with no serious consequences for life on Earth. (Apparently, Earth's climate self-adjusts to maintain stable temperatures as the Sun heats over long time scales.) However, somewhere around the year a.d. 5,000,000,000, the hydrogen in the solar core will run out. The Sun will then expand to a subgiant about three times as large and twice as bright as it is today. This increased luminosity will evaporate the oceans, perhaps leading to a runaway greenhouse effect that could raise Earth's average temperature to something similar to that of Venus and probably hotter. If any life survives, it will have to be very tolerant of heat. Things will only get worse as the Sun grows into a red giant over the next several hundred million years. Just before helium flash, the Sun will be about 100 times larger in radius and over 1,000 times more luminous than it is today. Earth's surface temperature will exceed 1,000 K, and the oceans will long since have boiled away. By this time, any surviving humans will need to have found a new home. Saturn's moon Titan might not be a bad choice: Its surface temperature will have risen from well below freezing today to about the present temperature of Earth. The Sun will shrink somewhat after helium burning begins, providing a temporary lull in incineration while the Sun spends 100 million years as a helium-burning star. Anyone who survives the Sun's helium-burning phase will need to prepare for one final disaster. After exhausting its core helium, the Sun will expand again during its last million years. Its luminosity will soar to thousands of times what it is today, and it will grow so large that solar prominences might lap at the Earth's surface. Then it will eject its outer layers as a planetary nebula that will engulf Jupiter and Saturn and drift on past Pluto into interstellar space. If the Earth is not destroyed, its charred surface will be cold and dark in the faint, fading light of the white dwarf that the Sun has become. From then on, the Earth will be little more than a chunk of rock circling the corpse of our once-brilliant star. 15. What is radiation pressure? Why is it more important in high-mass stars than in low-mass stars? What effects does radiation pressure have on the structure of a high-mass star? radiation pressure Pressure exerted by photons of light. high-mass stars produce the full array of elements on which life depends. The combined jolts from the huge number of photons streaming outward through a high-mass star apply a type of pressure called radiation pressure. We have now discussed three types of pressure: thermal pressure, degeneracy pressure, and radiation pressure. Before continuing, briefly review each type of pressure and describe the conditions under which each is important. Radiation pressure can have dramatic effects on high-mass stars. In the most massive stars, radiation pressure is even more important than thermal pressure in keeping gravity at bay. Near the photosphere, the radiation pressure can drive strong, fast-moving stellar winds. The wind from a very massive star can expel as much as 10–5 solar mass of gas per year at speeds greater than 1,000 km/s. 16. Describe some of the nuclear reactions that can occur in high-mass stars after they exhaust their core helium. Why does this continued nuclear burning occur in high-mass stars but not in low-mass stars? The exhaustion of core hydrogen in a high-mass star sets in motion the same processes that turn a low-mass star into a red giant, but the transformation proceeds much more quickly. The star develops a hydrogen-burning shell, and its outer layers begin to expand outward. At the same time, the core contracts, and this gravitational contraction releases energy that raises the core temperature until it becomes hot enough to fuse helium into carbon. However, there is no helium flash in stars of more than 2 solar masses. The high core temperatures induced by core contraction keep the thermal pressure high, preventing degeneracy pressure from being a factor. Helium burning therefore ignites gradually, just as hydrogen burning did at the beginning of the star's main-sequence life. A high-mass star fuses helium into carbon so rapidly that it is left with an inert carbon core after just a few hundred thousand years or less. Once again, the absence of fusion leaves the core without a thermal energy source to fight off the crush of gravity. 17. What special feature of iron nuclei determines how massive stars end their lives? What happens during a supernova? iron is unique, remember that only two basic processes can release nuclear energy: fusion of light elements into heavier ones, and fission of very heavy elements into not-so-heavy ones. Recall that hydrogen fusion converts four protons (hydrogen nuclei) into a helium nucleus that consists of two protons and two neutrons. Iron has the lowest mass per nuclear particle of all nuclei and therefore cannot release energy by either fusion or fission. The gravitational collapse of the core releases an enormous amount of energy—more than a hundred times what the Sun will radiate over its entire 10-billion-year lifetime! Where does this energy go? It drives the outer layers off into space in a titanic explosion—a supernova. The ball of neutrons left behind is called a neutron star. In some cases, the remaining mass may be so large that gravity also overcomes neutron degeneracy pressure, and the core continues to collapse until it becomes a black hole. supernova The explosion of a star. 18. Summarize some of the observational evidence supporting our ideas about how the elements formed and showing that supernovae really occur. the signature of nuclear reactions in massive stars is written in the patterns of elemental abundances across the universe. For example, if massive stars really produce heavy elements (that is, elements heavier than hydrogen and helium) and scatter these elements into space when they die, the total amount of these heavy elements in interstellar gas should gradually increase with time (because additional massive stars have died). we should expect stars born recently to contain a greater proportion of heavy elements than stars born in the distant past because they formed from interstellar gas that contained more heavy elements. Stellar spectra confirm this prediction: Older stars do indeed contain smaller amounts of heavy elements than younger stars. For very old stars in globular clusters, elements besides hydrogen and helium typically make up as little as 0.1% of the total mass. In contrast, about 2–3% of the mass of young stars that formed in the recent past is in the form of heavy elements. The Crab Nebula is a supernova remnant—an expanding cloud of debris from a supernova explosion. A spinning neutron star lies at the center of the Crab Nebula, providing evidence that supernovae really do create neutron stars. Photographs taken years apart show that the nebula is growing larger at a rate of several thousand kilometers per second. 19. What is the Algol paradox? What is its resolution? Use your answer to summarize how the lives of stars in close binaries can differ from the lives of single stars. This so-called Algol paradox reveals some of the complications in ordinary stellar life cycles that can arise in close binary systems. The two stars in close binaries are near enough to exert significant tidal forces on each other. The gravity of each star attracts the near side of the other star more strongly than it attracts the far side. The stars therefore stretch into football-like shapes rather than remaining spherical. In addition, the stars become tidally locked so that they always show the same face to each other, much as the Moon always shows the same face to Earth. During the time that both stars are main-sequence stars, the tidal forces have little effect on their lives. But when the more massive star (which exhausts its core hydrogen sooner) begins to expand into a red giant, gas from its outer layers can spill over onto its companion. This mass exchange occurs when the giant grows so large that its tidally distorted outer layers succumb to the gravitational attraction of the smaller companion star. The companion then begins to gain mass at the expense of the giant. The solution to the Algol paradox should now be clear (Figure 16.24). The 0.8M Sun subgiant used to be much more massive. As the more massive star, it was the first to begin expanding into a red giant. But as it expanded, so much of its matter spilled over onto its companion that it is now the less massive star. The future may hold even more interesting events for Algol. The 3.7M Sun star is still gaining mass from its subgiant companion. its life cycle is actually accelerating as its increasing gravity raises its core hydrogen fusion rate. Millions of years from now, it will exhaust its hydrogen and begin to expand into a red giant itself. At that point, it can begin to transfer mass back to its companion. Even stranger things can happen in other mass-exchange systems, particularly when one of the stars is a white dwarf or a neutron star. Discussion Questions 1. Connections to the Stars. In ancient times, many people believed that our lives were somehow influenced by the patterns of the stars in the sky, a belief that survives to this day in astrology. Modern science has not found any evidence to support this belief but instead has found that we have a connection to the stars on a much deeper level: In the words of Carl Sagan, we are "star stuff." Discuss in some detail our real connections to the stars as established by modern astronomy. Do you think these connections have any philosophical implications in terms of how we view our lives and our civilization? Explain. 2. Humanity in a.d. 5,000,000,000. Do you think it is likely that humanity will survive until the Sun begins to expand into a red giant 5 billion years from now? Why or why not? If the human race does survive, how do you think people in a.d. 5,000,000,000 will differ from people today? What do you think they will do when faced with the impending death of the Sun? Debate these questions, and see if you and your friends can come to any agreement on possible answers. Problems Sensible Statements? For problems 1–6, decide whether the statement is sensible and explain why it is or is not. 1. The iron in my blood came from a star that blew up over 4 billion years ago. 2. A protostellar cloud spins faster as it contracts because it is gaining angular momentum. 3. When helium fusion begins in the core of a low-mass star, the extra energy generated causes the star's luminosity to rise. 4. Humanity will eventually have to find another planet to live on, because one day the Sun will blow up as a supernova. 5. I sure am glad hydrogen has a higher mass per nuclear particle than many other elements. If it had the lowest mass per nuclear particle, none of us would be here. 6. I just discovered a 3.5M Sun main-sequence star orbiting a 2.5M Sun red giant. I'll bet that red giant was more massive than 3M Sun when it was a main-sequence star. Homes to Civilizations. We do not yet know how many stars have Earth-like planets, nor do we know the likelihood that such planets might harbor advanced civilizations like our own. However, some stars can probably be ruled out as candidates for advanced civilizations. For example, given that it took a few billion years for humans to evolve on Earth, it seems unlikely that advanced life would have had time to evolve around a star that is only a few million years old. For each of the stars in problems 7–12, decide whether you think it is possible that it could harbor an advanced civilization, and explain your reasoning in one or two paragraphs. 1. A 10M Sun main-sequence star. 2. A flare star. 3. A carbon star. 4. A 1.5M Sun red giant. 5. A 1M Sun horizontal branch star. 6. A red supergiant. 7. Rare Elements. Lithium, beryllium, and boron are elements with atomic numbers 3, 4, and 5, respectively. But despite their being three of the five simplest elements, Figure 16.20 shows that they are rare compared to many heavier elements. Suggest a reason for their rarity. (Hint: Consider the process by which helium fuses into carbon.) 8. Future Skies. As a red giant, the Sun's angular size in the Earth's sky will be about 30°. What will sunset and sunrise be like? About how long will they take? Do you think the color of the sky will be different from what it is today? Explain. 9. Research: Historical Supernovae. As discussed in the text, historical accounts exist for supernovae in the years 1006, 1054, 1572, and 1604. Choose one of these supernovae and learn more about historical records of the event. Did the supernova influence human history in any way? Write a two- to three-page summary of your research findings. Web Projects Find useful links for Web projects on the text Web site. 1. Coming Fireworks in Supernova 1987A. Astronomers believe that the show from Supernova 1987A is not yet over. In particular, sometime between now and about 2010, the expanding cloud of gas from the supernova is expected to ram into surrounding material, and the heat generated by the impact is expected to create a new light show. Learn more about how Supernova 1987A is changing and what we might expect to see from it in the future. Summarize your findings in a one- to two-page report. 2. Picturing Star Birth and Death. Photographs of stellar birthplaces (i.e., molecular clouds) and death places (e.g., planetary nebulae and supernova remnants) can be strikingly beautiful, but only a few such photographs are included in this chapter. Search the Web for additional photographs of these types; look not only for photos taken in visible light, but also for false-color photographs made from observations in other wavelengths of light. Put each photograph you find into a personal on-line journal, along with a one-paragraph description of what the photograph shows. Try to compile a journal of at least 20 such photographs. Chapter 17 Review Questions 1. What is the difference between electron degeneracy pressure and neutron degeneracy pressure? Which type supports a white dwarf? Why are neutron stars so much smaller in size than white dwarfs? electron degeneracy pressure Degeneracy pressure exerted by electrons, as in brown dwarfs and white dwarfs. neutron degeneracy pressure Degeneracy pressure exerted by neutrons, as in neutron stars. More specifically, white dwarfs are supported against the crush of gravity by electron degeneracy pressure, in which the pressure arises from densely packed electrons. In neutron stars, it is neutrons that are packed tightly together, thereby generating neutron degeneracy pressure. White dwarfs and neutron stars would be strange enough if the story ended here, but it does not. Sometimes, gravity wins the battle with degeneracy pressure, and the stellar corpse collapses without end, crushing itself out of existence and forming a black hole. A black hole is truly a hole in the universe. If you enter a black hole, you leave our observable universe and can never return. In this chapter, we will study the bizarre properties and occasional catastrophes of the stellar corpses known as white dwarfs, neutron stars, and black holes. 2. With degeneracy pressure, how are the speeds of electrons (or neutrons) related to the mass of the degenerate object? Explain why this relationship between speed and mass implies upper limits on the possible masses of white dwarfs and neutron stars. What is the white dwarf limit? What is the neutron star limit? Gravity and electron degeneracy pressure have battled to a draw in white dwarfs. Electron degeneracy pressure finally halts the collapse of a 1M Sun stellar corpse when it shrinks to about the size of the Earth. If you recall that our Earth is smaller than a typical sunspot, it should be clear that it's no small feat to pack the entire mass of the Sun into the volume of the Earth. The density of such a white dwarf is so high that a pair of standard dice made from its material would weigh about 5 tons. Surprisingly, more massive white dwarfs are smaller in size than less massive ones. For example, a 1.3M Sun white dwarf is half the diameter of a 1.0M Sun white dwarf (Figure 17.2). The more massive white dwarf is smaller—even though it contains more matter—because its greater gravity can compress this matter to a much greater density. As a white dwarf becomes denser, its electrons must move faster, and degeneracy pressure becomes stronger [Section S4.5]. The most massive white dwarfs are therefore the smallest, because they must be extremely dense for degeneracy pressure to balance their greater gravity. white dwarfs The hot, compact corpses of low-mass stars, typically with a mass similar to the Sun compressed to a volume the size of the Earth. Theoretical calculations show that the mass of a white dwarf cannot exceed a white dwarf limit of about 1.4M Sun, commonly called the Chandrasekhar limit after its discoverer. The limit comes about because the electron speeds are higher in more massive white dwarfs, and these speeds approach the speed of light in white dwarfs with masses approaching 1.4M Sun. Neither electrons nor anything else can travel faster than the speed of light, so electrons can do nothing to halt the crush of gravity in a stellar corpse with a mass above the white dwarf limit. 3. Explain why more massive white dwarfs are smaller in size. How does this idea explain why red giants become more luminous as they age? A white dwarf in a close binary system can gain substantial quantities of mass if its companion is a main-sequence or giant star. When a clump of mass first spills over from the companion to the white dwarf, it has some small orbital velocity. The law of conservation of angular momentum dictates that the clump must orbit faster and faster as it falls toward the white dwarf's surface. The infalling matter therefore forms a whirlpool-like disk around the white dwarf. 4. What is an accretion disk? Under what conditions does an accretion disk form? Explain how the accretion disk provides a white dwarf with a new source of energy that we can detect from Earth. accretion disk A rapidly rotating disk of material that gradually falls inward as it orbits a starlike object (e.g., white dwarf, neutron star, or black hole). The infalling matter therefore forms a whirlpool-like disk around the white dwarf (Figure 17.3). The process in which material falls onto another body is called accretion [Section 8.4], so this rapidly rotating disk is called an accretion disk. 5. Describe the process of a nova. Why do novae only occur in close binary star systems? Can the same star system undergo a nova event more than once? Explain. nova The dramatic brightening of a star that lasts for a few weeks and then subsides; occurs when a burst of hydrogen fusion ignites in a shell on the surface of an accreting white dwarf in a binary star system. A nova occurs when hydrogen fusion ignites on the surface of a white dwarf in a binary star system. supernovae generate far more power than novae—the light of 10 billion Suns in a supernova versus 100,000 Suns in a nova—a very distant supernova can appear as bright in our sky as a nova that is relatively close. Thus, people could not distinguish between novae and supernovae prior to modern times. 6. Contrast the process of a white dwarf supernova with that of a massive star supernova. Observationally, how can we distinguish between these two types of supernovae? White Dwarf Supernovae Each time a nova occurs, the white dwarf ejects some of its mass. Each time a nova subsides, the white dwarf begins to accrete matter again. Theoretical models cannot yet tell us whether the net result is a gradual increase or decrease in the white dwarf's mass. Nevertheless, in at least some cases, accreting white dwarfs in binary systems continue to gain mass as time passes. If such a white dwarf gains enough mass, it can one day reach the 1.4M Sun white dwarf limit. This day is the white dwarf's last. The electron degeneracy pressure that has been supporting the white dwarf gives out as soon as it reaches the 1.4M Sun limit. Gravity is suddenly unopposed, and the white dwarf begins to collapse. A white dwarf supernova shines as brilliantly as a supernova that occurs at the end of a high-mass star's life [Section 16.4]. To distinguish the two types, we'll refer to the latter as a massive star supernova. Both white dwarf supernovae and massive star supernovae result in the destruction of a star. A massive star supernova is thought inevitably to leave behind either a neutron star or a black hole, but nothing remains after the "carbon bomb" detonation of a white dwarf supernova. Astronomers can distinguish between white dwarf and massive star supernovae by studying their light.(*footnote) Because white dwarfs contain almost no hydrogen, the spectra of white dwarf supernovae show no spectral lines of hydrogen. In contrast, massive stars usually have plenty of hydrogen in their outer layers at the time they explode, so hydrogen lines are prominent in the spectra of most massive star supernovae. A second way to distinguish the two types of supernovae is to plot light curves that show how their luminosity fades with time. 7. What is a pulsar? Briefly describe how pulsars were discovered and how they get their name. How do we know that pulsars must be neutron stars? pulsar A neutron star from which we see rapid pulses of radiation as it rotates. A neutron star is the ball of neutrons created by the collapse of the iron core in a massive star supernova (Figure 17.6). Typically just 10 kilometers across yet more massive than the Sun, neutron stars are essentially giant atomic nuclei, with two important differences: (1) They are made almost entirely of neutrons, and (2) gravity, not the strong force, is what binds them together. build a radio telescope ideal for discovering fluctuating sources of radio waves. to interpret the flood of data pouring out of this instrument in October 1967 when she noticed a peculiar signal. After ruling out other possibilities, she concluded that pulses of radio waves were arriving from somewhere near the direction of the constellation Cygnus at precise 1.337301-second intervals. No known astronomical object pulsated so regularly. 8. Explain why neutron stars in close binary systems are often called X-ray binaries. neutron star The compact corpse of a high-mass star left over after a supernova; typically contains a mass comparable to the mass of the Sun in a volume just a few kilometers in radius. Neutron Stars in Close Binary Systems Like their white dwarf brethren, neutron stars in close binary systems can brilliantly burst back to life. As is the case with white dwarfs, gas overflowing from a companion star can create a hot, swirling accretion disk around the neutron star. However, in the neutron star's mighty gravitational field, infalling matter releases an amazing amount of gravitational potential energy. Dropping a brick onto a neutron star would liberate as much energy as an atomic bomb. Because the gravitational energies of accretion disks around neutron stars are so tremendous, they are much hotter and much more luminous than those around white dwarfs. The high temperatures in the inner regions of the accretion disk make it radiate powerfully in X rays. Some close binaries with neutron stars emit 100,000 times more energy in X rays than our Sun emits in all wavelengths of light combined. Due to this intense X-ray emission, close binaries that contain accreting neutron stars are often called X-ray binaries. Their existence confirms many of the strange properties of neutron stars. Today we know of hundreds of X-ray binaries in the Milky Way. These neutron star systems are concentrated in the disk, just like most of our galaxy's stars, gas, and dust. X-ray sources are usually named by their constellation and order of discovery. For example, Sco X-1 was the first X-ray source discovered in the direction of the constellation Scorpio. Sco X-1 is now known to be an X-ray binary in which a low-mass star orbits a neutron star about every 19 hours. 9. What is an X-ray burster? How is the process of an X-ray burst similar to that of a nova? How do X-ray bursts differ from novae observationally? X-ray burster An object that emits a burst of X rays every few hours to every few days; each burst lasts a few seconds and is thought to be caused by helium fusion on the surface of an accreting neutron star in a binary system. Like accreting white dwarfs that occasionally erupt into novae, accreting neutron stars sporadically erupt with enormous luminosities. Hydrogen-rich material from the companion star builds up on the surface of the neutron star. Pressures at the bottom of this accreted hydrogen shell, only a meter thick, maintain steady fusion. Helium accumulates beneath the hydrogen-burning shell, and helium fusion suddenly ignites when the temperature builds to 100 million K. The helium burns rapidly to carbon and heavier elements, generating a burst of energy that flows from the neutron star in the form of X rays. These X-ray bursters typically flare every few hours to every few days. Each burst lasts only a few seconds, but during that short time the system radiates power equivalent to 100,000 Suns, all in X rays. Within a minute after a burst, the X-ray burster cools back down and resumes accreting. 10. Briefly explain the process by which the core of a very high mass star can collapse to form a black hole. 11. What is the event horizon of a black hole? How does it get its name? How is it related to the Schwarzschild radius? 12. Suppose you are orbiting a black hole. Describe how you will see the passage of time on an object approaching the black hole. What will you notice about light from the object? Explain why an object falling toward the black hole will eventually fade from view yet never cross the event horizon from your point of view. 13. Suppose you are falling into a black hole. How will you perceive the passage of your own time? How will you perceive the passage of time in the universe around you? Briefly explain why your trip will be lethal if the black hole is relatively small in mass, and why you may survive to cross the event horizon of a supermassive black hole. 14. What do we mean by the singularity of a black hole? How do we know that our current theories are inadequate to explain what happens at the singularity? 15. Briefly describe the observational evidence supporting the idea that Cygnus X-1 contains a black hole. 16. What are gamma-ray bursts? Why are they so mysterious? Discussion Questions 1. Too Strange to Be True? Despite strong theoretical arguments for their existence, many scientists rejected the possibility that neutron stars or black holes could really exist until they were confronted with very strong observational evidence. Some people claim that this type of scientific skepticism demonstrates that scientists are too unwilling to give up their deeply held scientific beliefs. Others claim that this type of skepticism is necessary for scientific advancement. What do you think? Defend your opinion. 2. Black Holes in Popular Culture. Phrases such as "it disappeared into a black hole" are now common in popular culture. Give a few examples in which the term black hole is used in popular culture but is not meant to be taken literally. In what ways are these uses correct in their analogies to real black holes? In what ways are they incorrect? Why do you think such an esoteric scientific idea as that of a black hole has so captured the public imagination? Problems Sensible Statements? For problems 1–8, decide whether the statement is sensible and explain why it is or is not. 1. Most white dwarf stars have masses close to that of our Sun, but a few white dwarf stars are up to three times more massive than the Sun. 2. The radii of white dwarf stars in close binary systems gradually increase as they accrete matter. 3. White dwarf supernovae are useful distance indicators. 4. Before pulsars were discovered, no one knew for sure whether neutron stars existed. 5. If you want to find a pulsar, you might want to look near the remnant of a supernova described by ancient Chinese astronomers. 6. If a black hole 10 times more massive than our Sun were lurking just beyond Pluto's orbit, we'd have no way of knowing it was there. 7. If the Sun suddenly became a 1 M Sun black hole, the orbits of the nine planets would not change at all. 8. We can detect black holes with X-ray telescopes because matter falling into a black hole emits X rays after it smashes into the event horizon. Life Stories of Stars. Write a one- to two-page short story for the scenarios in problems 9 and 10. Each story should be detailed and scientifically correct, but also creative. That is, it should be entertaining while at the same time proving that you understand stellar evolution. Be sure to state whether "you" are a member of a binary system. 1. You are a white dwarf of 0.8M Sun. Tell your life story. 2. You are a neutron star of 1.5M Sun. Tell your life story. 3. Neutron Star Density. A typical neutron star has a mass of about 1.5M Sun and a radius of 10 km. 1. Calculate the average density of a neutron star, in kilograms per cubic centimeter. 2. Compare the mass of 1 cm3 of neutron star material to the mass of Mount Everest ( 5 1010 kg). 4. A Black Hole? You've just discovered a new X-ray binary, which we will call Hyp-X1 ("Hyp" for hypothetical). The system Hyp-X1 contains a bright, B2 main-sequence star orbiting an unseen companion. The separation of the stars is estimated to be 20 million km, and the orbital period of the visible star is 4 days. 1. Use Newton's version of Kepler's third law to calculate the sum of the masses of the two stars in the system. (Hint: See Mathematical Insight 15.4.) Give your answer in both kilograms and solar masses (M Sun = 2.0 1030 kg). 2. Determine the mass of the unseen companion. Is it a neutron star or a black hole? Explain. (Hint: A main-sequence star with spectral type B2 has a mass of about 10M Sun.) 5. Schwarzschild Radii. Calculate the Schwarzschild radius (in km) for each of the following. 1. A 108 M Sun black hole in the center of a quasar. 2. A 5M Sun black hole that formed in the supernova of a massive star. 3. A mini–black hole with the mass of the Moon. 4. A mini–black hole formed when a superadvanced civilization decides to punish you (unfairly) by squeezing you until you become so small that you disappear inside your own event horizon. 6. Challenge Problem: A Neutron Star Comes to Town. Suppose a neutron star were suddenly to appear in your hometown. How thick a layer would the Earth form as it wraps around the neutron star's surface? To make the problem easier, you may assume that the layer formed by the Earth has the same average density as the neutron star. (Hint: Consider the mass of the Earth to be distributed in a spherical shell over the surface of the neutron star and then calculate the thickness of such a shell with the same mass as the Earth. The volume of a spherical shell is approximately its surface area times its thickness: V shell @ 4p r 2 X thickness. Because the shell will be thin, you can assume that its radius is the radius of the neutron star.) Web Projects Find useful links for Web projects on the text Web site. 1. Gamma-ray Bursts. Go to the Web site for NASA's High Energy Transient Experiment (HETE) or another mission studying gamma-ray bursts and find the latest information about gamma-ray bursts. Write a one- to two-page essay on recent discoveries and how they may shed light on the mystery of gamma-ray bursts. 2. White Dwarf Supernovae. Learn more about how astronomers are using white dwarf supernovae to determine distances for distant galaxies. What have these observations taught us about the universe? What have they taught us about white dwarf supernovae? Chapter 18 Review Questions 1. Draw simple sketches of our galaxy as it would appear face-on and edge-on, identifying the disk, bulge, halo, and spiral arms. disk component (of a galaxy) The portion of a spiral galaxy that looks like a disk and contains an interstellar medium with cool gas and dust; stars of many ages are found in the disk component. bulge (of a spiral galaxy) The central portion of a spiral galaxy that is roughly spherical (or football shaped) and bulges above and below the plane of the galactic disk. halo (of a galaxy) The spherical region surrounding the disk of a spiral galaxy. spiral arms The bright, prominent arms, usually in a spiral pattern, found in most spiral galaxies. 2. What do we mean by the interstellar medium? How does it affect our view of the galaxy? interstellar medium Refers to gas and dust that fills the space between stars in a galaxy. obscuring our view when we try to peer directly through it. The smoggy nature of the interstellar medium hides most of our galaxy from us. 3. What do we mean by heavy elements? How much of the Milky Way's gas is in the form of heavy elements? Where are heavy elements made? heavy elements In astronomy, heavy elements generally refers to all elements except hydrogen and helium. the overall composition of the galaxy is about 70% hydrogen, 28% helium, and 2% heavy elements by mass. The process of adding to the abundance of heavy elements, called chemical enrichment, is an inevitable by-product of continual star formation. in stars. 4. What is the star–gas–star cycle, and how does it lead to chemical enrichment? Use the idea of chemical enrichment to explain why stars that formed early in the history of the galaxy contain a smaller proportion of heavy elements than stars that formed more recently. The hot gas cools first into clouds of atomic hydrogen (that is, neutral hydrogen atoms as opposed to ionized hydrogen or hydrogen molecules) and then into clouds of molecular hydrogen (H2). The cooling of interstellar gas into clouds of molecular hydrogen takes millions of years. These clouds subsequently give birth to new stars more highly enriched in heavy elements, completing the star–gas–star cycle. 5. Distinguish between the following forms of gas: ionized hydrogen, atomic hydrogen, and molecular hydrogen. Atomic hydrogen gas tends to be found in two distinct forms: large, tenuous clouds of warm (10,000 K) atomic hydrogen and smaller, denser clouds of cool (100 K) atomic hydrogen. If you were to take an interstellar voyage across the Milky Way, you would spend the majority of your time cruising through regions of warm atomic hydrogen interspersed with bubbles of hot, ionized gas. Every thousand light-years or so, you would encounter a cooler, denser cloud of atomic hydrogen. In the warm regions, you would detect about one atom per cubic centimeter and a weak magnetic field (weaker than Earth's magnetic field by a factor of about 100,000). In the cooler clouds, you would find a density of about 100 atoms per cubic centimeter and a stronger magnetic field. Molecular hydrogen (H2) is by far the most abundant molecule in molecular clouds, but it is difficult to detect because temperatures are usually too cold for the gas to produce H2 emission lines. As a result, most of what we know about molecular clouds comes from observing spectral lines of molecules that make up only a tiny fraction of a cloud's mass. The most abundant of these molecules is carbon monoxide (CO, also a common ingredient in car exhaust), which produces strong emission lines in the radio portion of the spectrum at the 10–30 K temperatures of molecular clouds like blowouts continually cycle gas between the Milky Way's disk and the halo, an idea summarized in a model known as the galactic fountain. According to this model, fountains of hot, ionized gas rise from the disk into the halo through the elongated bubbles carved by blowouts. The gravity of the galactic disk slows the rise of the gas, eventually pulling it back down. Near the top of its trajectory, the ejected gas starts to cool and form clouds of atomic hydrogen. These clouds cool further as they plunge back down, ultimately rejoining the layer of atomic hydrogen gas in the disk. 6. What are cosmic rays? Where do we think they come from? cosmic rays Particles such as electrons, protons, and atomic nuclei that zip through interstellar space at close to the speed of light. Supernova remnants may also generate the cosmic rays that permeate the interstellar medium and bombard the Earth's atmosphere. 7. What is a superbubble? How is it made? Describe what happens in a blowout in which a superbubble breaks out of the galactic disk. superbubble Essentially a giant interstellar bubble, formed when the shock waves of many individual bubbles merge to form a single, giant shock wave. In many places in our galactic disk, we see what appear to be elongated bubbles extending from young clusters of stars to distances of 3,000 light-years (1 kpc) or more above the disk. These probably are places where superbubbles have grown so large that they cannot be contained within the disk of the Milky Way. Once the superbubble breaks out of the disk, where nearly all of the Milky Way's gas resides, nothing remains to slow its expansion except gravity. Such a blowout is in some ways similar to a volcanic eruption, but on a galactic scale: Hot plasma erupts from the disk and shoots high into the galactic halo. 8. Describe the galactic fountain model. What evidence supports this model? galactic fountain Refers to a model for the cycling of gas in the Milky Way Galaxy in which fountains of hot, ionized gas rise from the disk into the halo and then cool and form clouds as they sink back into the disk. The galactic fountain model is plausible but difficult to verify. We do indeed see some hot gas high above the galaxy's disk. We also see cooler clouds that appear to be raining down from the halo. However, we can see this "rain" only directly above and below us, making it difficult to demonstrate beyond a doubt that galactic fountains circulate the products of supernovae throughout the Milky Way. 9. What is the most common form of gas in the interstellar medium? What is the wavelength of the radio emission line characteristic of this gas? all interstellar material actually has a composition of about 70% hydrogen, 28% helium, and 2% heavy elements. 10. What are dust grains? Where do they form? dust Tiny solid flecks of material; in astronomy, we often discuss interplanetary dust (found within a star system) or interstellar dust (found between the stars in a galaxy). Some of the heavy elements in regions of atomic hydrogen are in the form of tiny, solid dust grains: flecks of carbon and silicon minerals that resemble particles of smoke and form in the winds of red giant stars. Once formed, dust grains remain in the interstellar medium unless they are heated and destroyed by a passing shock wave or incorporated into a protostar. Although dust grains make up only about 1% of the mass of the atomic hydrogen clouds, they are responsible for the absorption of visible light that prevents us from seeing through the disk of the galaxy. 11. How do molecular clouds form? How do we observe them? Why do molecular clouds tend to settle toward the central layers of the Milky Way's disk? As the temperature drops further in the center of a cool cloud of atomic hydrogen, hydrogen atoms combine into molecules, making a molecular cloud. Molecular clouds are the coldest, densest collections of gas in the interstellar medium, and they often congregate into giant molecular clouds that hold up to a million solar masses of gas. The total mass of molecular clouds in the Milky Way is somewhat uncertain, but it is probably about the same as the total mass of atomic hydrogen gas—about 5 billion solar masses. Throughout much of this molecular gas, temperatures hover only a few degrees above absolute zero, and gas densities are a few hundred molecules per cubic centimeter. 12. Will the star–gas–star cycle continue forever? Why or why not? the star–gas–star cycle cannot go on forever. 13. Describe the stars we find in the halo in terms of mass, luminosity, color, and proportion of heavy elements. Why do halo stars have these characteristics? Most of the halo stars are old, red, and dim and much smaller in mass than our Sun. Halo stars also contain far fewer heavy elements than our Sun, sometimes having heavy-element proportions as low as 0.02% (in contrast to about 2% in the Sun). The relative lack of chemical enrichment in the halo indicates that its stars formed early in the galaxy's history—before many supernovae had exploded, adding heavy elements to star-forming clouds. The halo's gas content corroborates this view. The halo is virtually gas-free compared to the disk, with very few detectable molecular clouds. Apparently, the bulk of the Milky Way's gas settled into the disk long ago. The halo environment is a place where lack of gas caused star formation to cease early in our galaxy's life. 14. What is an ionization nebula? Why are such nebulae found near massive young stars? What produces their striking colors? ionization nebula is A colorful, wispy cloud of gas that glows because neighboring hot stars irradiate it with ultraviolet photons that can ionize hydrogen atoms. The energy that powers ionization nebulae comes from neighboring hot stars that irradiate them with ultraviolet photons. These photons ionize and excite the atoms in the nebulae, causing them to emit light. The Orion Nebula, about 1,500 light-years away in the "sword" of the constellation Orion Most of the striking colors in an ionization nebula come from particular spectral lines produced by particular atomic transitions. For example, the transition in which an electron falls from energy level 3 to energy level 2 in a hydrogen atom generates a red photon with a wavelength of 656 nanometers [Section 6.4]. Ionization nebulae appear predominantly red in photographs because of all the red photons released by this particular transition. (Jumps from level 2 to level 1 are even more common, but they produce ultraviolet photons that can be studied only with ultraviolet telescopes in space.) Transitions in other elements produce other spectral lines of different colors. 15. Contrast the general patterns of the orbits of stars in the disk with the orbits of stars in the halo. All the stars in the disk, including our Sun, orbit the center in the same direction. Moreover, like horses on a merry-go-round, individual stars bob up and down through the disk as they orbit. The general orbit of a star around the galaxy arises from its gravitational attraction toward the galactic center, while the bobbing arises from the localized pull of gravity within the disk itself (Figure 18.18): A star that is "too far" above the disk is pulled back into the disk by gravity; because the density of interstellar gas is too low to slow the star, it flies through the disk until it is "too far" below the disk on the other side. Gravity then pulls it back in the other direction. This ongoing process produces the bobbing of the stars. These up-and-down motions spread the disk stars over a thickness of about 1,000 light-years—quite thin in comparison to the 100,000-light-year diameter of the disk. Each orbit takes over 200 million years in the vicinity of our Sun, and each up-and-down "bob" takes a few tens of millions of years. The orbits of stars in the halo and bulge are much less organized than the orbits of stars in the disk. Individual bulge and halo stars travel around the galactic center on more or less elliptical paths, but the orientations of these paths are relatively random. Neighboring halo stars can circle the galactic center in opposite directions. They swoop from high above the disk to far below it and back again, plunging through the disk at velocities so high that the disk's gravity hardly alters their trajectories. Near the Sun, we see several fast-moving halo stars in the course of hasty excursions through the local region of the disk. One such star is Arcturus, the fourth-brightest star in the night sky. 16. At what speed does the Sun travel around the solar circle? About how long does one orbit take? Briefly explain how we can use the characteristics of the Sun's orbit to determine the mass of the Milky Way contained within the solar circle. What is the result? the Sun and its neighbors orbit the center of the Milky Way at a speed of about 220 km/s (about 800,000 km/hr. Even at this speed, it takes the Sun about 230 million years to complete one orbit around the galactic center. Early dinosaurs ruled the Earth when it last visited this side of the galaxy. solar circle The Sun's orbital path around the galaxy, which has a radius of about 28,000 light-years. 17. What is a rotation curve? Describe the rotation curve of the Milky Way, and explain how it indicates that most of the Milky Way's mass lies outside the solar circle. What do we mean by dark matter? rotation curve A graph that plots rotational (or orbital) velocity against distance from the center for any object or set of objects. we can use the orbital motion of any other star to measure the mass of the Milky Way within the star's own orbital circle. In principle, we could determine the complete distribution of mass in the Milky Way by applying the orbital velocity law to the orbits of stars at every different distance from the galactic center. In practice, interstellar dust obscures our view of disk stars beyond a few thousand light-years, making it very difficult to measure stellar velocities. However, radio waves penetrate this dust, so we can see the 21-cm line from atomic hydrogen gas no matter where the gas is located in the galaxy. Such studies allow us to build a map of atomic hydrogen clouds. It is such maps that reveal our galaxy's large-scale spiral structure and also its overall pattern of rotation. dark matter Matter that we infer to exist from its gravitational effects but from which we have not detected any light; dark matter apparently dominates the total mass of the universe. 18. How do we know that spiral arms are not simple "pinwheels" as they appear at first glance? What features do we see in images of spiral arms that suggest that they result from waves of star formation propagating through galaxies? The disks of spiral galaxies like the Milky Way display sweeping spiral arms that can stretch tens of thousands of light-years from their bulges. At first glance, spiral arms look as if they ought to rotate with the stars, like the fins of a giant pinwheel in space. However, because stars near the center of the galaxy take less time to complete an orbit than more distant stars, the arms would gradually wind themselves up if they really did rotate with the stars in the disk. By the time a spiral galaxy was a few billion years old, the spiral arms would look like a tightly wound coil. Because we do not see such tightly coiled spiral arms, the explanation for spiral structure must be more complex. Detailed images show the spiral arms to be home to most of the young, bright, blue stars in a galaxy (Figure 18.20). Clusters of these hot, short-lived massive stars populate the spiral arms. Between the arms, we find many fewer hot stars. We also see enhanced amounts of molecular and atomic gas in the spiral arms, and streaks of interstellar dust often obscure the inner sides of the arms themselves (Figure 18.21). All these clues suggest that spiral arms result from waves of star formation that propagate through the disks of spiral galaxies. 19. What is Sgr A*? What evidence suggests that it contains a massive black hole? Deep in the galactic center, we find swirling clouds of gas and a cluster of several million stars. Bright radio emission traces out the magnetic fields that thread this turbulent region. At the core of it all sits a source of bright radio emission named Sagittarius A* (pronounced "Sagittarius A-star"), or Sgr A* for short, that is quite unlike any other radio source in our galaxy. The motions of the gas and stars in Sgr A* indicate that it contains a few million solar masses within a region no larger than about 3 light-years across. The star cluster in Sgr A* cannot account for all that mass. Many astronomers therefore suspect that Sgr A* contains a black hole weighing around 2.5 million solar masses. the behavior of this suspected black hole is somewhat puzzling. The most plausible black-hole candidates in our galaxy—those in binary systems like Cygnus X-1 —accrete matter from their companions. The resulting accretion disks radiate brightly in X rays. If Sgr A* truly is a giant black hole, we might expect it to be accreting some of the surrounding gas from the galactic center. Because of its large mass, it would have a large accretion disk and would shine brightly in X rays. It is possible that Sgr A* contains a huge black hole that simply has run out of gas to accrete. Even more intriguingly, the black hole might be consuming the energy contained in the accreting matter before it has a chance to escape as radiation. In any case, if Sgr A* is indeed a black hole, it does not behave like other black holes whose accretion disks are more apparent. Because the black hole at the center of our galaxy is so well hidden from us, the nature of Sgr A* remains mysterious. Discussion Questions 1. Galactic Ecosystem. The introduction to this chapter likened the star–gas–star cycle in our Milky Way to the ecosystem that sustains life on Earth. Here on our planet, water molecules cycle from the sea to the sky to the ground and back to the sea. Our bodies convert atmospheric oxygen molecules into carbon dioxide, and plants convert the carbon dioxide back into oxygen molecules. How are the cycles of matter on Earth similar to the cycles of matter in the galaxy? How do they differ? Do you think the term ecosystem is appropriate to discussions of the galaxy? 2. Galaxy Stuff. In the chapters on stars, we learned why we are "star stuff." Based on what you've learned in this chapter, explain why we are also "galaxy stuff." Does the fact that the entire galaxy was involved in bringing forth life on Earth change your perspective on the Earth or on life in any way? If so, how? If not, why not? Problems Sensible Statements? For problems 1–7, decide whether the statement is sensible and explain why it is or is not. 1. We did not understand the true size and shape of our galaxy until NASA satellites were launched into the galactic halo, enabling us to see what the Milky Way looks like from the outside. 2. Planets like Earth probably didn't form around the very first stars because there were so few heavy elements back then. 3. If I could see infrared light, the galactic center would look much more impressive. 4. Many spectacular ionization nebulae are seen throughout the Milky Way's halo. 5. The carbon in my diamond ring was once part of an interstellar dust grain. 6. The Sun's velocity around the Milky Way tells us that most of our galaxy's dark matter lies within the solar circle. 7. We know that a black hole lies at our galaxy's center because a few of the stars it is sucking in have vanished over the last several years. 8. Unenriched Stars. Suppose you discovered a star made purely of hydrogen and helium. How old do you think it would be? Explain your reasoning. 9. Enrichment of Star Clusters. The gravitational pull of an isolated globular cluster is rather weak—a single supernova explosion can blow all the interstellar gas out of a globular cluster. How might this fact be related to observations indicating that stars ceased to form in globular clusters long ago? How might it be related to the fact that globular clusters are deficient in elements heavier than hydrogen and helium? Summarize your answers in one or two paragraphs. 10. High-velocity Star. The average speed of stars relative to the Sun in the solar neighborhood is about 20 km/s (i.e., the speed at which we see stars moving toward or away from the Sun—not their orbital speed around the galaxy). Suppose you discover a star in the solar neighborhood that is moving relative to the Sun at a much higher speed, say 200 km/s. What kind of orbit does this star probably have around the Milky Way? In what part of the galaxy does it spend most of its time? Explain. 11. Mass from Rotation Curve. Using velocities shown on the Milky Way's rotation curve in Figure 18.19c, along with the orbital velocity law (see Mathematical Insight 18.1), calculate the mass of the Milky Way Galaxy within each of the following distances. Give your answers in both kilograms and solar masses. 1. 10,000 light-years. 2. 30,000 light-years. 3. 50,000 light-years. 12. Research: Discovering the Milky Way. Humans have been looking at the Milky Way since long before recorded history, but only in the past century did we verify the true shape of the galaxy and our location within it. Learn more about how conceptions of the Milky Way developed through history. What names did different cultures give the band of light they saw? What stories did they tell about it? How have ideas about the galaxy changed in the past few centuries? Try to locate diagrams that illustrate these changes. Write a two- to three-page summary of your findings. Web Projects Find useful links to Web projects on the text Web site. 1. Images of the Star–Gas–Star Cycle. Explore the Web to find pictures of nebulae and other forms of interstellar gas in different stages of the star–gas–star cycle. Assemble the pictures into a sequence that tells the story of interstellar recycling, with a one-paragraph explanation accompanying each image. 2. The Galactic Center. Search the Web for recent images of the galactic center, along with information about whether the center hides a massive black hole. Present a two- to three-page report, with pictures, giving an update on current knowledge about the center of the Milky Way Galaxy. Chapter 19 Review Questions 1. Distinguish between spiral galaxies and elliptical galaxies in terms of their shapes and colors. What are irregular galaxies? spiral galaxies Galaxies that look like flat, white disks with yellowish bulges at their centers. The disks are filled with cool gas and dust, interspersed with hotter ionized gas, and usually display beautiful spiral arms. elliptical galaxies Galaxies that appear rounded in shape, often longer in one direction, like a football. They have no disks and contain very little cool gas and dust compared to spiral galaxies, though they often contain very hot, ionized gas. irregular galaxies Galaxies that look neither spiral nor elliptical. Spiral galaxies look like flat white disks with yellowish bulges at their centers (Figure 19.2). The disks are filled with cool gas and dust, interspersed with hotter ionized gas as in the Milky Way, and usually display beautiful spiral arms. Elliptical galaxies are redder, more rounded, and often longer in one direction than in the other, like a football. Compared with spiral galaxies, elliptical galaxies contain very little cool gas and dust, though they often contain very hot, ionized gas. Galaxies that appear neither disklike nor rounded are classified as irregular galaxies. Spiral and irregular galaxies look white because they contain stars of all different colors and ages; elliptical galaxies look redder because they contain very few young, blue stars. 2. Distinguish between the disk component and the spheroidal component of a spiral galaxy. Which component includes the galaxy's spiral arms? Which includes its bulge? Which includes its halo? The bulge itself merges smoothly into a halo that can extend to a radius of over 100,000 light-years. Together, the bulge and halo of a spiral galaxy make up its spheroidal component, so named because of its rounded shape. Although no clear boundary divides the pieces of the spheroidal component, astronomers usually consider stars within 10,000 light-years of the center to be members of the bulge and those outside this radius to be members of the halo. The disk component of a spiral galaxy slices directly through the halo and bulge. The disk of a large spiral galaxy like the Milky Way can extend 50,000 light-years or more from the center. The disks of all spiral galaxies contain an interstellar medium of gas and dust, but the amounts and proportions of the interstellar medium in molecular, atomic, and ionized forms differ from one spiral galaxy to the next. disk component (of a galaxy) The portion of a spiral galaxy that looks like a disk and contains an interstellar medium with cool gas and dust; stars of many ages are found in the disk component. spheroidal component (of a galaxy) The portion of any galaxy that is spherical (or football-like) in shape and contains very little cool gas; generally contains only very old stars. Elliptical galaxies have only a spheroidal component, while spiral galaxies also have a disk component. 3. How does a barred spiral galaxy differ from a normal spiral galaxy? How does a lenticular galaxy differ from a normal spiral galaxy? Some spiral galaxies appear to have a straight bar of stars cutting across the center, with spiral arms curling away from the ends of the bar. Such galaxies are known as barred spiral galaxies. Other galaxies have disks but appear to lack spiral arms. These are called lenticular galaxies, because they look lens-shaped when seen edge-on (lenticular means "lens-shaped"). Although they look like spiral galaxies without arms, lenticular galaxies might more appropriately be considered an intermediate class between spirals and ellipticals, because they tend to have less cool gas than normal spirals but more than ellipticals. 4. What is a group of galaxies? What is a cluster of galaxies? Spiral galaxies are often found in loose collections of several galaxies, called groups, that extend over a few million light-years group (of galaxies) A few to a few dozen galaxies bound together by gravity. See also cluster of galaxies. cluster of galaxies A collection of a few dozen or more galaxies bound together by gravity; smaller collections of galaxies are simply called groups. 5. What is the major difference between an elliptical galaxy and a spiral galaxy? How is an elliptical galaxy similar to the halo of the Milky Way? The major difference between elliptical and spiral galaxies is that ellipticals lack a significant disk component. an elliptical galaxy has only a spheroidal component and looks much like the bulge and halo of a spiral galaxy. (In fact, elliptical galaxies are sometimes called spheroidal galaxies.) Most of the interstellar medium in large elliptical galaxies consists of low-density, hot, X ray–emitting gas, making it much like the gas in bubbles and superbubbles in the Milky Way. Elliptical galaxies usually contain very little dust or cool gas, although they are not completely devoid of either. 6. Among large galaxies in the universe, about what proportion are spiral or lenticular? Elliptical? What do we mean by a dwarf elliptical galaxy? Elliptical galaxies appear to be more social than spiral galaxies: They are much more common in clusters of galaxies than outside clusters. Elliptical galaxies make up about half the large galaxies in the central regions of clusters, while they represent only a small minority (about 15%) of the large galaxies found outside clusters. However, ellipticals are more common among small galaxies. Particularly small elliptical galaxies with less than a billion stars, called dwarf elliptical galaxies, are often found near larger spiral galaxies. dwarf elliptical galaxy A small elliptical galaxy with less than about a billion stars. 7. What do we mean by a standard candle? Briefly explain how, once we identify an object as a standard candle, we can use the luminosity–distance formula to find its distance. standard candle An object for which we have some means of knowing its true luminosity, so that we can use its apparent brightness to determine its distance with the luminosity–distance formula. We can usually measure an object's apparent brightness with a detector, so we can use the luminosity–distance formula [Section 15.2] to calculate the object's luminosity if we know its distance, or to calculate its distance if we know its luminosity. For example, suppose we see a distant street lamp and know that all street lamps of its type put out 1,000 watts of light. Then, once we measure the apparent brightness of the street lamp (in units of watts/m2), we can calculate its distance with the luminosity–distance formula. 8. Why are Cepheid variables good standard candles? Briefly explain how Edwin Hubble used his discovery of a Cepheid in Andromeda to prove that the "spiral nebulae" were actually entire galaxies. we need very bright stars to serve as standard candles for distance measurements beyond the Milky Way, and the most useful bright stars are the Cepheid variables. The Cepheids are pulsating variable stars that follow a simple period–luminosity relation: The longer the time period between peaks in brightness, the greater the luminosity of the Cepheid variable star 9. Describe how we can use Hubble's law to determine the distance to a distant galaxy. What practical difficulties limit the use of Hubble's law for measuring distances? used the period–luminosity relation to determine the luminosities of these stars and then used these luminosities in the luminosity–distance formula to compute their distances. 10. What makes white dwarf supernovae good standard candles? Briefly describe how we have learned the true luminosities of white dwarf supernovae. white dwarf supernovae are thought to represent exploding white dwarf stars that have reached the 1.4-solar-mass limit and should all have nearly the same luminosity. white dwarf supernovae should be good standard candles—once we know their true luminosities. Although only a few supernovae have been detected during the past century in galaxies within about 50 million light-years of the Milky Way, astronomers have kept careful records of these events. Today, we can look back at the light curves for these events to determine which of these past supernovae were white dwarf supernovae. 11. What is our current best estimate of Hubble's constant? Summarize all the links in the distance chain that allow us to estimate distances to the farthest reaches of the universe. Hubble's Constant and Age To see how the universe's expansion rate is related to its age, let's return to the miniature scientists living on dot B. Three seconds after the balloon began to expand, they would measure the following: Dot A is 3 cm away and moving at 1 cm/s. Dot C is 3 cm away and moving at 1 cm/s. Dot D is 6 cm away and moving at 2 cm/s. They could summarize these observations as follows: Every dot is moving away from our home with a speed that is 1 cm/s for each 3 cm of distance. And because the expansion of the balloon is uniform, scientists living on any other dot would come to the same conclusion. Each scientist living on the balloon would determine that the following formula relates the distances and velocities of other dots on the balloon where v and d are the velocity and distance of any dot, respectively. Hubble's constant A number that expresses the current rate of expansion of the universe; designated H0, it is usually stated in units of km/s/Mpc. The reciprocal of Hubble's constant is the age the universe would have if the expansion rate had never changed. 12. In what ways is the surface of an expanding balloon a good analogy to the universe? In what ways is this analogy limited? Explain why a miniature scientist living in a polka dot on the balloon would observe all other dots to be moving away, with more distant dots moving away faster. If the miniature scientists think of their balloon as a bubble, they might call the number relating distance to velocity—the term 1/3s in the above formula—the "bubble constant." An especially insightful miniature scientist might flip over the "bubble constant" and find that it is exactly equal to the time since the balloon started expanding. That is, the "bubble constant" of 1/3s tells them that the balloon has been expanding for 3 seconds. Perhaps you see where we are heading. Just as the inverse of the "bubble constant" tells the miniature scientists that their balloon has been expanding for 3 seconds, the inverse of the Hubble constant, or 1/H 0, tells us something about how long our universe has been expanding. The "bubble constant" for the balloon depends on when it is measured, but it is always equal to 1/(time since balloon started expanding). Similarly, the Hubble constant actually changes with time but stays roughly equal to 1/(age of the universe). We call it a constant because it is the same at all locations in the universe. 13. What is a lookback time? Why does it make more sense to talk about a distant object in terms of its lookback time than in terms of its distance? lookback time Refers to the amount of time since the light we see from a distant object was emitted. if an object has a lookback time of 400 million years, we are seeing it as it looked 400 million years ago. 14. What do we mean by a cosmological redshift? How does our interpretation of a distant galaxy's redshift differ if we think of it as a cosmological redshift rather than as a Doppler shift? cosmological redshift Refers to the redshifts we see from distant galaxies, caused by the fact that expansion of the universe stretches all the photons within it to longer, redder wavelengths. As the balloon inflates, these wavy lines stretch out, and their wavelengths increase. This stretching closely resembles what happens to photons in an expanding universe. The expansion of the universe stretches out all the photons within it, shifting them to longer, redder wavelengths. We call this effect a cosmological redshift. we have a choice when we interpret the redshift of a distant galaxy: We can think of the redshift either as being caused by the Doppler effect as the galaxy moves away from us or as being caused by a photon-stretching, cosmological redshift. 15. What is the cosmological horizon? Why can't we see past it? cosmological horizon The boundary of our observable universe, which is where the lookback time is equal to the age of the universe. Beyond this boundary in spacetime, we cannot see anything at all. the universe does have a horizon, a place beyond which we cannot see. This cosmological horizon is a boundary in time, not in space. It exists because we cannot see back to a time before the universe began. For example, if the universe is 14 billion years old, then no object can have lookback time greater than 14 billion years. we cannot see matter at the cosmological horizon, but if we could we would see it as it looked at the very beginning of time. One year from now, we would see this same matter as it looked 1 year after the beginning—which means the horizon will have moved somewhat farther from us. In fact, our horizon is continually expanding outward at the speed of light. Our observable universe therefore grows larger in radius by 1 light-year with each passing year. Discussion Questions 1. Cosmology and Philosophy. One hundred years ago, many scientists believed that the universe was infinite and eternal, with no beginning and no end. When Einstein first developed his general theory of relativity, he found it predicted that the universe should be either expanding or contracting. He believed so strongly in an eternal and unchanging universe that he modified the theory, a modification he would later call his "greatest blunder." Why do you think Einstein and others assumed that the universe had no beginning? Do you think that a universe with a definite beginning in time, some 15 billion or so years ago, has any important philosophical implications? Explain. 2. Tired Light. Hubble's law relates the redshifts of galaxies directly to their distances. The overwhelming majority of astronomers believe that these redshifts arise from the Doppler effect, an easily measurable and well-understood phenomenon that can be measured in the laboratory. However, a few astronomers argue that there might be some other explanation for galaxy redshifts based on physical effects that occur only on vast scales. For example, perhaps photons somehow get "tired" and lose energy as they cross immense intergalactic distances. Which explanation for redshifts do you prefer? Why is considering alternative explanations important in science? Problems Sensible Statements? For problems 1–8, decide whether the statement is sensible and explain why it is or is not. 1. If you want to find elliptical galaxies, you'll have better luck looking in clusters of galaxies than elsewhere in the universe. 2. Cepheid variables make good standard candles because they all have exactly the same luminosity. 3. If the standard candles you are using are less luminous than you think they are, then the distances you determine from them will be too small. 4. Galaxy A is moving away from me twice as fast as Galaxy B. That probably means it's twice as far away. 5. The lookback time to the Andromeda Galaxy is about 2.5 million years. 6. I'd love to live in one of the galaxies at the very edge of the universe, because I want to see the black void into which the universe is expanding. 7. We can't see galaxies beyond the cosmological horizon because they are moving away from us faster than the speed of light. 8. We see distant galaxies as they were when the universe was younger, and any people living in those galaxies today would see the Milky Way as it was when the universe was younger. 9. Distance Measurements. The techniques astronomers use to measure distances are not so different from the ones you use every day. Describe how parallax measurements are similar to your visual depth perception. Describe how standard-candle measurements are similar to the way you estimate the distance to an oncoming car at night. 10. Cepheids as Standard Candles. Suppose you are observing Cepheids in a nearby galaxy. You observe one Cepheid with a period of 8 days between peaks in brightness, and another with a period of 35 days. Estimate the luminosity of each star. Explain how you arrived at your estimate. (Hint: See Figure 19.10.) 11. Counting Galaxies. Estimate how many galaxies are pictured in Figure 19.1. Explain the method you used to arrive at this estimate. This picture shows about 1/30,000,000 of the sky, so multiply your estimate by 30,000,000 to obtain an estimate of how many galaxies like these fill the entire sky. 12. Cepheids in M 100. Scientists using the Hubble Space Telescope have observed Cepheids in the galaxy M 100. Here are actual data for three Cepheids in M 100:Compute the distance to M 100 with data from each of the three Cepheids. Do all three distance computations agree? Based on your results, estimate the uncertainty in the distance you have found. 13. Redshift and Hubble's Law. Imagine that you have obtained spectra for several galaxies and have measured the observed wavelength of a hydrogen emission line that has a rest wavelength of 656.3 nm. Here are your results: 1. Calculate the redshift, z, for each of the three galaxies. 2. From their redshifts, calculate the speed at which each of the galaxies is moving away from us. Give your answers both in km/s and as a fraction of the speed of light. 3. Estimate the distance to each galaxy from Hubble's law. Assume that H 0 = 65 km/s/Mpc. Web Projects Find useful links for Web projects on the text Web site. 1. Galaxy Gallery. Many fine images of galaxies are available on the Web. Collect several images of each major type and build a galaxy gallery of your own. Supply a descriptive paragraph about each galaxy. 2. Hubble's Constant. Measurements of Hubble's constant are rapidly growing more reliable. Find at least two measurements of H 0 determined in the past 2 years. Describe how these values were measured. What is the quoted uncertainty of each? By how much do they differ? 3. Greatest Lookback Time. Look for recent discoveries of objects with the largest lookback times (or redshifts). What is the current record for the most distant known object? What kind of object is it? Chapter 20 Review Questions 1. What do we mean by galaxy evolution? Briefly describe three unanswered questions about galaxy evolution. galaxy evolution is The formation and development of galaxies. galaxies come in a variety of shapes, colors, and sizes. the great variety of galaxies we see today formed from the hydrogen and helium gas present in the early universe. elliptical, spiral, and irregular galaxies. some galaxies turned out flattened and gas-rich while others did not. We also need to explain some of the stranger aspects of galaxies. For example, observations show that some galaxies, called starburst galaxies, are currently forming stars at a tremendous rate. Starbursts must be only a temporary phase in the lives of these galaxies, or they would have consumed all of the galaxies' gas long ago. We have also found that some galaxies have extremely bright centers, known as active galactic nuclei, that sometimes outshine all the stars in the galaxy combined. 2. How do theoretical models help us study galaxy birth? What two assumptions underlie theoretical models of galaxy formation? we must use theoretical modeling to study the earliest stages in galaxy evolution. The most successful models for galaxy formation assume the following: Hydrogen and helium gas filled all of space more or less uniformly when the universe was very young—say, in the first million years after its birth. This uniformity was not quite perfect, and certain regions of the universe were ever so slightly denser than others. Beginning from these assumptions, which are supported by a mounting body of evidence we can model galaxy formation using well-established laws of physics to trace how the denser regions in the early universe grew into galaxies. The models show that the regions of enhanced density originally expanded along with the rest of the universe. 3. How do disk population stars differ from spheroidal population stars? Briefly explain how the collapse of a protogalactic cloud is thought to lead to these two distinct populations of stars. How does this explain why the halo of our galaxy looks so much like an elliptical galaxy? disks of spiral galaxies appear whitish with flecks of blue. This indicates that the stars in the disks of spiral galaxies, sometimes referred to as the disk population (or Population I), include hot, blue stars as well as cool, red ones. Because only short-lived, massive stars look blue, we conclude that star formation must be an ongoing process in galactic disks—just as it is in the disk of the Milky Way. In contrast, the stars in elliptical galaxies and in the bulges and halos of spiral galaxies, called the spheroidal population (or Population II), look reddish in color. The absence of blue stars among the spheroidal population indicates that most of these stars are old and that their star formation must have ceased long ago—just as is the case in the halo of the Milky Way. The characteristic motions of stars in disks and spheroids provide another important clue to their nature. Disk stars generally orbit in orderly circles in the same direction; all galactic disks rotate much like the Milky Way's disk. Stars of spheroidal populations tend to orbit in random directions, much like stars in the bulge and halo of the Milky Way. Because the motions of stars in the populations are so different, disks and spheroids must have formed in very different ways. 4. What evidence suggests that the protogalactic cloud that formed our own Milky Way resulted from several collisions among smaller clouds? According to the most basic model for galaxy formation from a protogalactic cloud, the stars of the spheroidal population formed first. Early on, the gravity associated with a protogalactic cloud drew in matter from all directions, creating a cloud that was blobby in shape and had little or no measurable rotation. The orbits of stars forming within such a cloud could have had any orientation, accounting for the randomly oriented orbits of spheroidal population stars. Later, at least in spiral galaxies, conservation of angular momentum caused the remaining gas to flatten into a spinning disk as it contracted under the force of gravity. This process was much like the process that leads to protoplanetary disks around young stars, but on a much larger scale: Collisions among gas particles tended to average out their random motions, leading them to acquire orbits in the same direction and in the same plane. Stars that formed within this spinning disk were born on orbits moving at the same speed and in the same direction as their neighbors and became the disk population stars. 5. Describe the two scenarios in which the properties of a protogalactic cloud determine whether a galaxy becomes elliptical or spiral. What evidence supports these scenarios? Because most spiral galaxies in today's universe look similar to our own Milky Way Galaxy, we can test our theories about the formation of spiral galaxies by studying the "fossil record" written within the stars of the Milky Way. The clues found to date support the basic picture but suggest that the full story of galaxy formation may be somewhat more complex. All available evidence confirms that the stars in the Milky Way's halo are indeed old. The main-sequence turnoff points in H–R diagrams of globular clusters show that their stars were born at least 12 billion years ago. Individual halo stars (i.e., those not in globular clusters) and some of the bulge stars appear similarly old. Furthermore, the proportions of heavy elements in halo stars are much lower than in the Sun, indicating that they formed before many generations of supernovae had a chance to enrich the Milky Way's interstellar medium. However, careful study of heavy-element proportions suggests that our galaxy formed from a few different gas clouds. If the Milky Way had formed from a single protogalactic cloud, it would have steadily accumulated heavy elements during its inward collapse as stars formed and exploded within it. In that case, the outermost stars in the halo would be the oldest and the most deficient in heavy elements. Halo stars in globular clusters do indeed differ in age and heavy-element content, but these variations do not seem to depend on the stars' distance from the galactic center. The easiest way to account for the variations is to suppose that the Milky Way's earliest stars formed in relatively small protogalactic clouds, each with a few globular clusters, and that these clouds later collided and combined to create the full protogalactic cloud that became the Milky Way. 6. Briefly explain why we expect that collisions between galaxies should be relatively common, while collisions between stars are extremely rare. Why should galaxy collisions have been more common in the past than they are today? the average distances between galaxies are not tremendously larger than the sizes of galaxies, and collisions between galaxies are inevitable. Even the Milky Way Galaxy is not immune. About 80,000 light-years away, directly behind the galactic bulge, a small elliptical galaxy (called the Sagittarius dwarf elliptical) is currently crashing through the Milky Way's disk. Collisions between galaxies are spectacular events that unfold over hundreds of millions of years (Figure 20.6). In our short lifetimes, we can at best see a snapshot of a collision in progress, as evidenced by the distorted shape of the colliding galaxies. Galactic collisions must have been even more frequent when the universe was smaller and galaxies were even closer together. Photographs of galaxies at a variety of distances confirm that distorted-looking galaxies—probably galaxy collisions in progress—were more common in the early universe than they are today 7. Briefly describe how a collision between two spiral galaxies might lead to the creation of a single elliptical galaxy. What evidence supports this scenario for the formation of elliptical galaxies? We can learn much more about galactic collisions with the aid of computer simulations that allow us to "watch" collisions that take hundreds of millions of years to unfold in nature. These computer models show that a collision between two spiral galaxies can create an elliptical galaxy. Tremendous tidal forces between the colliding galaxies tear apart the two disks, randomizing the orbits of their stars. Meanwhile, a large fraction of their gas sinks to the center of the collision and rapidly forms new stars. Supernovae and stellar winds eventually blow away the rest of the gas. When the cataclysm finally settles down, the merger of the two spirals has produced a single elliptical galaxy: Little gas is left for a disk, and the orbits of the stars have random orientations. Observations seem to confirm the idea that at least some elliptical galaxies result from collisions and subsequent mergers. The fact that elliptical galaxies dominate the galaxy populations at the cores of dense clusters of galaxies, where collisions should be most frequent, may mean that any spirals once present became ellipticals through collisions. 8. What are central dominant galaxies? How do we think they formed? central dominant galaxy is A giant elliptical galaxy found at the center of a dense cluster of galaxies, apparently formed by the merger of several individual galaxies. Central dominant galaxies are gigantic elliptical galaxies that apparently grew to a huge size by consuming other galaxies through collisions. Central dominant galaxies frequently contain several tightly bound clumps of stars that probably were the centers of individual galaxies before being swallowed by the giant. 9. Briefly explain why starburst galaxies often appear ordinary when they are observed in visible light but extraordinary when they are observed in infrared light. Starburst galaxies are relatively new subjects of study. These voracious consumers of interstellar gas look peculiar at visible wavelengths because they are filled with star-forming molecular clouds, but these clouds conceal much of the action. Dust grains in the molecular clouds absorb most of the visible and ultraviolet radiation streaming from a starburst galaxy's many young stars. This radiation heats the dust grains to much higher temperatures than normal, and they ultimately reemit all the absorbed visible and ultraviolet energy as infrared light, with a peak wavelength of around 60,000 nanometers (60 micrometers). Infrared observations of Arp 220, a large starburst galaxy. a Image of Arp 220, a large starburst galaxy. b The spectrum of Arp 220 shows that it emits most of its radiation as infrared light, rather than visible light. starburst galaxy is A galaxy in which stars are forming at an unusually high rate. 10. What is a galactic wind? What causes it? How is it similar to a superbubble in the Milky Way, and how is it different? galactic wind is A wind of low-density but extremely hot gas flowing out from a starburst galaxy, created by the combined energy of many supernovae. Galactic Winds A star-formation rate 100 times that of the Milky Way also means an occurrence of supernovae at 100 times the Milky Way's rate. Just as in the Milky Way, each supernova in a starburst galaxy generates a shock wave that creates a bubble of hot gas. The shock waves from several nearby supernovae quickly overlap and blend into a much larger superbubble. The story usually ends here in the Milky Way, but in a starburst galaxy the drama is just beginning. Supernovae continue to explode inside the superbubble, adding to its thermal and kinetic energy. When the superbubble starts to break through the disrupted gaseous disk, it expands even faster. Hot gas erupts into intergalactic space, creating a galactic wind. Galactic winds consist of low-density but extremely hot gas, typically with temperatures of 10–100 million Kelvin. They do not emit much visible light, but they do generate X rays. X-ray telescopes in orbit have detected pockets of X-ray emission surrounding the disks of some starburst galaxies, presumably coming from the outflowing galactic wind (Figure 20.12a). Sometimes we also see the glowing remnants of a punctured superbubble extending out into space. 11. Why must starbursts cease after a relatively short time? What evidence suggests that small galaxies in our Local Group have undergone two or more starbursts in the past? Causes of Starbursts Many of the most luminous starburst galaxies look violently disturbed. They are neither flat disks with symmetric spiral arms nor smoothly rounded balls of stars, like elliptical galaxies. Streamers of stars are strewn everywhere. Such galaxies are filled with dusty molecular clouds, and deep inside them we see two distinct clumps of stars that look like two different galactic centers. Their appearance suggests that such starbursts result from a collision between two gas-rich spiral galaxies. The collision apparently compresses the gas inside the colliding galaxies, leading to the burst of star formation. The causes of smaller-scale starbursts are less clear. Some may result from direct collisions, while others may be caused by close encounters with other galaxies. The Large Magellanic Cloud is currently undergoing a period of rapid star formation, perhaps because of the tidal influence of the Milky Way. No matter what their exact causes turn out to be, starburst galaxies clearly represent an important piece in the overall puzzle of galaxy evolution. 12. Briefly describe the discovery of quasars. What evidence convinced astronomers that the high redshifts of quasars really do imply great distances? Why can we learn more about quasars by studying nearby active galactic nuclei? quasar is The brightest type of active galactic nucleus. some galaxies display even more incredible phenomena: extreme amounts of radiation, and sometimes powerful jets of material, emanating from deep in their centers. We generally refer to these unusually bright galactic centers as active galactic nuclei and reserve the term quasar for the very brightest of them. (Galaxies with active galactic nuclei are sometimes called active galaxies.) The brightest quasars shine more powerfully than 1,000 galaxies the size of the Milky Way. We find quasars primarily at great distances, telling us that these blazingly luminous objects were most common billions of years ago, when galaxies were in their youth. Because we find no nearby quasars and relatively few nearby galaxies with any type of active galactic nucleus we conclude that the objects that shine as quasars in young galaxies must become dormant as the galaxies age. many nearby galaxies that now look quite normal—we don't yet know which ones—must have centers that once shone brilliantly as quasars. 13. Briefly explain how we can use variations in luminosity to set limits on the size of an object's emitting region. For example, if an object doubles its luminosity in 1 hour, how big can it be? To understand how variations in luminosity give us clues about an object's size, imagine that you are a master of the universe and you want to signal one of your fellow masters a billion light-years away. An active galactic nucleus would make an excellent signal beacon, because it is so bright. However, suppose the smallest nucleus you can find is 1 light-year across. Each time you flash it on, the photons from the front end of the source reach your fellow master a full year before the photons from the back end. Thus, if you flash it on and off more than once a year, your signal will be smeared out. Similarly, if you find a source that is 1 light-day across, you can transmit signals that flash on and off no more than once a day. If you want to send signals just a few hours apart, you need a source no more than a few light-hours across. Occasionally, the luminosity of an active galactic nucleus doubles in a matter of hours. The fact that we see a clear signal indicates that the source must be less than a few light-hours across. In other words, the incredible luminosities of active galactic nuclei and quasars are apparently being generated in a volume of space not much bigger than our solar system. 14. What is a radio galaxy? Describe jets and radio lobes. Why do we think that the ultimate energy sources of radio galaxies lie in quasarlike galactic nuclei? radio galaxy is A galaxy that emits unusually large quantities of radio waves; thought to contain an active galactic nucleus powered by a supermassive black hole. much of the radio emission comes not from the galaxies themselves but rather from pairs of huge radio lobes, one on either side of the galaxy. The radio waves from the lobes are produced by electrons and protons spiraling around magnetic field lines at nearly the speed of light. jets are High-speed streams of gas ejected from an object into space. radio galaxies must have powerful jets spurting from their nuclei that transport energy to their lobes. That is, although the lobes lie far outside the visible galaxy the ultimate source of their energy would be found in the galaxy's tiny nucleus, which must therefore be as powerful as a quasar. 15. Briefly explain the general picture of how supermassive black holes enable quasars to produce their huge luminosities. Summarize the evidence supporting the idea that supermassive black holes lie at the center of radio galaxies, quasars, and other active galactic nuclei. Astronomers have worked hard to envision physical processes that might explain how radio galaxies, quasars, and other active galactic nuclei release so much energy within such small central volumes. Only one explanation seems to fit: The energy comes from matter falling into a supermassive black hole. Gravity converts the potential energy of the infalling matter into kinetic energy. Collisions between infalling particles convert the kinetic energy into thermal energy, and photons carry this thermal energy away. As in X-ray binaries, we expect that the infalling matter swirls through an accretion disk before it disappears beneath the event horizon of the black hole. accretion into the black holes formed in supernovae, the light is coming not from the black hole itself but rather from the hot gas surrounding it. As discussed in the text, 10–40% of the mass-energy of matter falling into a black hole can be radiated away as energy. (The precise value for a particular black hole depends on its rotation rate: Faster rotation allows more energy to be released.) Suppose 10% of the mass-energy is radiated away. 16. Briefly explain how intergalactic clouds between a distant quasar and Earth leave distinctive marks in the quasar's spectrum. Along the way, these photons have passed through numerous intergalactic hydrogen clouds. The vast majority of these clouds are too diffuse and wispy ever to become galaxies, but a few have as much hydrogen as the disk of the Milky Way. The thickest of these clouds may well be protogalactic clouds in the process of becoming galaxies. Quasar spectra therefore contain valuable information about the properties of hydrogen clouds in the early universe. Because atoms tend to absorb light at very specific wavelengths, every time a light beam from a quasar passes through an intergalactic or protogalactic cloud some of the atoms in the cloud absorb photons from the beam, creating an absorption line. Studies of these absorption lines in quasar spectra can tell us what happened in protogalactic clouds during the epoch of galaxy formation and thus provide clues about how galaxies evolve. The extremely wide hydrogen absorption lines thought to be associated with newly forming galaxies are typically produced by the most distant clouds, indicating that the youngest galaxies are made mostly of gas. In fact, they contain about the same amount of mass in the form of hydrogen gas as older galaxies contain in the form of stars. Absorption lines from elements other than hydrogen corroborate this picture. The lines from these heavy elements are more prominent in the mature galaxies than in the youngest galaxies, implying that the mature galaxies have experienced more supernovae, which have added heavy elements to their interstellar gas. This overall pattern of gradual heavy-element enrichment accompanied by the gradual diminishing of interstellar hydrogen agrees well with what we know about the Milky Way. All across the universe, stars in the gaseous disks of galaxies appear to have been forming steadily for over 10 billion years. With every new study of a quasar spectrum, we learn more about the galaxies and intergalactic clouds that have left their mark on the light we observe from quasars. Perhaps someday soon these observations will help us fit together all the pieces of the galaxy evolution puzzle, and we at last will understand the whole glorious history of galaxy evolution in our universe. Until that time, we will keep peering deep into space and back into time, searching for the clues that will unlock the mysteries of cosmic evolution. Discussion Questions 1. The Case for Supermassive Black Holes. The evidence for supermassive black holes at the center of galaxies is strong. However, it is very difficult to prove absolutely that they exist because the black holes themselves emit no light. We can only infer their existence from their powerful gravitational influences on surrounding matter. How compelling do you find the evidence? Do you think astronomers have proved the case for black holes beyond a reasonable doubt? Defend your opinion. 2. Life in Colliding Galaxies. Suppose the Milky Way were currently undergoing a collision with another large spiral galaxy. Do you think this collision would affect life on Earth? Why or why not? How different would the night sky look if our galaxy was in the midst of such a collision? Problems True Statements? For problems 1–7, decide whether the statement is true and explain why it is or is not. 1. Galaxies that are more than 10 billion years old are too far away to see even with our most powerful telescopes. 2. Heavy elements ought to be much more common near the Milky Way's center than at its outskirts. 3. If the Andromeda Galaxy someday collides and merges with the Milky Way, then the resulting galaxy would probably be elliptical. 4. Starburst galaxies have been forming stars at the same furious pace ever since the universe was about a billion years old. 5. We know that some galaxies contain supermassive black holes because their centers are completely dark. 6. The black hole at the center of our own galaxy may once have powered an active galactic nucleus. 7. Analyses of quasar light can tell us about intergalactic clouds that might otherwise remain invisible. 8. Life Story of a Spiral. Imagine that you are a spiral galaxy. Describe your life history from birth to the present day. Your story should be detailed and scientifically consistent, but also creative. That is, it should be entertaining while at the same time incorporating current scientific ideas about the formation of spiral galaxies. 9. Life Story of an Elliptical. Imagine that you are an elliptical galaxy. Describe your life history from birth to the present. There are several possible scenarios for the formation of elliptical galaxies, so choose one and stick to it. Be creative while also incorporating scientific ideas that demonstrate your understanding. 10. Your Last Hurrah. Suppose you fell into an accretion disk that swept you into a supermassive black hole. Assume that, on your way down, the disk will radiate 10% of your mass energy, E = mc 2. (Hint: See Mathematical Insight 20.1.) 1. What is your mass in kilograms? (Hint: Use the conversion 1 kg = 2.2 pounds.) 2. Calculate how much radiative energy will be produced by the accretion disk as a result of your fall into the black hole. 3. Calculate approximately how long a 100-watt light bulb would have to burn to radiate this same amount of energy. 11. The Black Hole in NGC 4258. The molecular clouds circling the center of the active galaxy NGC 4258 orbit at a speed of about 1,000 km/s, with an orbital radius of 0.49 light-year = 4.8 X 1015 meters. Use the orbital velocity law (see Mathematical Insight 20.2) to calculate the mass of the central black hole. Give your answer both in kilograms and in solar masses (1M Sun = 2.0 X 1030 kg). Web Projects Find useful links for Web projects on the text Web site. 1. Future Missions. The subject of galaxy evolution is a very active area of research. Look for information on current and future NASA missions involved in investigating galaxy evolution (such as the Next Generation Space Telescope). How big are the planned telescopes? What wavelengths will they look at? When will they be launched? Write a short summary of a proposed mission. 2. Greatest Redshift. As of early 2001, the most distant quasar known has a redshift z = 5.8, meaning that the wavelengths of its light are 1 + 5.8 = 6.8 longer than normal. Find the current record holder for the largest redshift. Write a one-page report describing the object and its discovery. 3. The Quasar Controversy. For many years, some astronomers argued that quasars were not really as distant as Hubble's law indicates. Research the history of the discovery of quasars and the debates that followed. What evidence led some astronomers to think quasars might be nearer than Hubble's law suggested? Why did most astronomers eventually conclude that quasars really are far away? Write a one- to two-page report summarizing your findings. Chapter 21 Review Questions 1. In what sense is dark matter "dark"? It is so dark the dark matter cannot be seen. The majority of the matter in the universe, the stuff that binds galaxies together with the force of its own gravity, is too dark to see. We know that this matter exists because we can detect its gravitational influence on other things, is this so-called dark matter 2. What evidence suggests that the Milky Way contains dark matter? The evidence that the Milky Way contains dark matter qualifies as an interesting surprise on its own, but it is also a glimpse into a more profound mystery. If our suspicions about dark matter are correct, then the luminous part of the Milky Way's disk must be rather like the tip of an iceberg, marking only the center of a much larger clump of mass (Figure 21.1). A more detailed analysis involving the motions of nearby dwarf galaxies shows that the total mass of dark matter in the Milky Way might be 10 times greater than the mass of visible stars. Each galaxy in the universe is similar to our own in this respect, meaning that we probably cannot see most of the matter in the universe. This matter's darkness makes it challenging to study, but its overwhelming dominance of the universe makes it extremely important. Dark matter, by virtue of its mighty gravitational pull, seems to be the glue that holds galaxies and clusters of galaxies together. atomic hydrogen clouds lying farther from the galactic center than our Sun orbit the galaxy at unexpectedly high speeds. We concluded that much of our galaxy's mass must lie beyond the distance of the Sun's orbit around the galactic center, distributed throughout the galaxy's spherical halo. Yet most of the Milky Way's light comes from stars lying closer to the galaxy's center than does our Sun. Together, these facts imply that the halo contains large amounts of matter but this matter emits so little light that we cannot see it. we call it dark matter. the very fate of the universe hinges on the total amount of dark matter. 3. Briefly describe how we construct rotation curves for spiral galaxies and how these curves lead us to conclude that spiral galaxies contain dark matter. A rotation curve contains all the information we need to measure the mass contained within the orbits of the outermost gas clouds. (Because the Doppler effect tells us only about the velocity of material directly toward or away from us, we must also take into account the tilt of the galaxy before we construct the rotation curve.) The rotation curves of most spiral galaxies turn out to be remarkably flat as far out as we can see, which means that the orbital speeds of gas clouds remain roughly constant with increasing distance from the galactic center. our Milky Way's rotation curve remains more or less flat from well within the radius of the Sun's orbit (28,000 light-years) to beyond twice that radius. The rotation curves of some other spiral galaxies are flat to well beyond 150,000 light-years. Because the orbital speeds of gas clouds tell us the amount of mass contained within their orbital paths, the flat rotation curves imply that a great deal of matter lies far from the galactic center. In particular, if we imagine drawing bigger and bigger circles around a galaxy, the flat rotation curves imply that we must keep encircling more and more matter. The mass of a spiral galaxy with gas clouds orbiting at 200 km/s at a distance of 150,000 light-years from its center must be at least 500 billion (5 X 10 11) solar masses. 4. Briefly describe how we can infer the average orbital speeds of stars in an elliptical galaxy from the widths of its spectral lines and how this allows us to weigh elliptical glaxies. The motions of stars in an elliptical galaxy are disorganized, so we cannot assemble their velocities into a sensible rotation curve. Nevertheless, the velocity of each individual star still responds to the mass inside the star's orbit. At any particular distance from an elliptical galaxy's center, some stars are moving toward us and some are moving away from us. Thus, the spectral lines from the galaxy as a whole tend to be smeared out: Instead of a nice sharp line at a particular wavelength, we see a broadened line spanning a range of wavelengths reflecting the various Doppler shifts of the individual stars. The greater the broadening of the spectral line, the faster the stars must be moving. The broadening of absorption lines in an elliptical galaxy's spectrum tells us how fast its stars move relative to one another. When we compare spectral lines from different regions of an elliptical galaxy, we find that the speeds of the stars remain fairly constant as we look farther from the galactic center. 5. What is a mass-to-light ratio? Explain why higher mass-to-light ratios imply more dark matter. mass-to-light ratio is The mass of an object divided by its luminosity, usually stated in units of solar masses per solar luminosity. Objects with high mass-to-light ratios must contain substantial quantities of dark matter. We can determine how much dark matter a galaxy contains by comparing the galaxy's measured mass to its luminosity. For example, the Milky Way contains about 90 billion (9 X 10 10) solar masses of material within the Sun's orbit. However, the total luminosity of stars within this region is only about 15 billion (1.5 X 10 10) solar luminosities. on average, it takes 6 solar masses of matter to produce 1 solar luminosity of light in this region of the galaxy (15 billion X 6 = 90 billion). We therefore say that the Milky Way's mass-to-light ratio within the Sun's orbit is about 6 solar masses per solar luminosity. This fact tells us that most matter is dimmer than our Sun, which is not surprising since we know that most stars are smaller and dimmer than our Sun. We find similar mass-to-light ratios for the inner regions of most other spiral galaxies. 6. What are typical mass-to-light ratios for inner regions of spiral galaxies? For inner regions of elliptical galaxies? How do these mass-to-light ratios compare to the mass-to-light ratios we find when we look farther from a galaxy's center? What does this tell us about dark matter in galaxies? we know that most stars are smaller and dimmer than our Sun. We find similar mass-to-light ratios for the inner regions of most other spiral galaxies. Elliptical galaxies contain virtually no luminous high-mass stars, so their stars are less bright on average than the stars in a spiral galaxy. In the inner regions of elliptical galaxies, the orbits of stars indicate a mass-to-light ratio of about 10 solar masses per solar luminosity—nearly double the mass-to-light ratio in the central region of the Milky Way. This is not surprising given the fact that elliptical galaxies have dimmer stars. The surprise in mass-to-light ratios—and one of the key pieces of evidence for the existence of dark matter—comes when we look to the outer reaches of galaxies. As we look farther from a galaxy's center, we find a lot more mass but not much more light. The mass-to-light ratios for entire spiral galaxies can be as high as 50 solar masses per solar luminosity, and the overall ratios in some dwarf galaxies can be even higher. We are forced to conclude that stars alone cannot account for the amount of mass present in galaxies. For example, if a galaxy's overall mass-to-light ratio is 60 solar masses per solar luminosity and its stars account for only 6 solar masses per solar luminosity, then the remaining 90% of the galaxy's mass must be dark. 7. Briefly describe the three different ways of measuring the mass of a cluster of galaxies. Do the results from the different methods agree? What do they tell us about dark matter in galaxy clusters? We can now weigh clusters of galaxies in three different ways: by measuring the speeds of galaxies orbiting the center of the cluster, by studying the X-ray emission from hot gas between the cluster galaxies, and by observing how the clusters bend light as gravitational lenses [Section S3.5]. All three techniques indicate that clusters contain huge amounts of dark matter. Let's investigate each of these techniques more closely. Orbiting Galaxies Zwicky was one of the first astronomers to think of galaxy clusters as huge swarms of galaxies bound together by gravity. It seemed natural to him that galaxies clumped closely in space should all be orbiting one another, just like the stars in a star cluster. He therefore assumed that he could measure cluster masses by observing galaxy motions and applying the orbital velocity law. Armed with a spectrograph, Zwicky measured the redshifts of the galaxies in a particular cluster and used these redshifts to calculate the speeds at which the individual galaxies are moving away from us. He determined the velocity of the cluster as a whole by averaging the velocities of its individual galaxies. He then estimated the speed of a galaxy around the cluster—that is, its orbital speed—by subtracting this average velocity from the individual galaxy's velocity. Finally, he plugged these orbital speeds into an appropriate form of the orbital velocity law to estimate the cluster's mass and compared this mass to the luminosity of the cluster. clusters of galaxies have huge mass-to-light ratios: They contain hundreds of solar masses for each solar luminosity of radiation they emit. He concluded that most of the matter within these clusters must be almost entirely dark. 8. What is gravitational lensing? Why does it occur? How can we use it to estimate the masses of lensing objects? gravitational lensing is The magnification or distortion (into arcs, rings, or multiple images) of an image caused by light bending through a gravitational field, as predicted by Einstein's general theory of relativity. Because the light-bending angle of a gravitational lens depends on the mass of the object doing the bending, we can measure the masses of objects by observing how strongly they distort light paths. 9. Briefly explain what we mean by baryonic and nonbaryonic matter. Which type are you made of? baryonic matter Refers to ordinary matter made from atoms (because the nuclei of atoms contain protons and neutrons, which are both baryons). nonbaryonic matter Refers to exotic matter that is not part of the normal composition of atoms, such as neutrinos or the hypothetical WIMPs. I made of baryonic matter. 10. What do we mean by MACHOs? Describe several possibilities for the nature of MACHOs. Based on evidence from gravitational lensing events, can MACHOs explain all the dark matter in the Milky Way? Why or why not? MACHOs Stands for massive compact halo objects and represents one possible form of dark matter in which the dark objects are relatively large, like planets or brown dwarfs. Matter need not be extraordinary to be dark. In astronomy, "dark" merely means not as bright as a normal star and therefore not visible across vast distances of space. Your body is dark matter. Everything you own is dark matter. Earth and the planets are also dark matter. The process of star formation itself leaves behind dark matter in the form of brown dwarfs, those dim "failed stars" that are not quite massive enough to sustain nuclear fusion. We cannot see the MACHO itself, but the duration of the lensing event reveals its mass. Gravitational lensing events such as these are rare; they happen to about one star in a million each year. To detect MACHO lensing events, we therefore must monitor huge numbers of stars. Current large-scale monitoring projects now record numerous lensing events annually. These events demonstrate that MACHOs do indeed populate our galaxy's halo, but probably not in large enough numbers to account for all the Milky Way's dark matter. Something else lurks unseen in the outer reaches of our galaxy. Maybe it is also normal matter made from baryons, but maybe not. 11. Explain what we mean when we say that a neutrino is a weakly interacting particle. Why can't the dark matter in galaxies be made of neutrinos? A more exotic possibility is that most of the dark matter in galaxies and clusters of galaxies is not made of ordinary, baryonic matter at all. Let's begin to explore this possibility by taking another look at those nonbaryonic particles neutrinos. These unusual particles are dark by their very nature, because they have no electrical charge and cannot emit electromagnetic radiation of any kind. they are never bound together with charged particles in the way that neutrons are bound in atomic nuclei, so their presence cannot be revealed by associated light-emitting particles. In fact, particles like neutrinos interact with other forms of matter through only two of the four forces: gravity and the weak force. For this reason, they are said to be weakly interacting particles. If you recall that trillions of neutrinos from the Sun are passing through your body at this very moment without doing any damage, you'll see why the name weakly interacting fits well. The dark matter in galaxies cannot be made of neutrinos, because these tiny particles travel through the universe at enormous speeds and can easily escape a galaxy's gravitational pull. (However, as we'll discuss shortly, neutrinos might contribute to the amount of dark matter outside galaxies.) But what if other weakly interacting particles exist that are similar to neutrinos but considerably heavier? They too would evade direct detection, but they would move more slowly and could collect into galaxies, adding mass without adding light. 12. What do we mean by WIMPs? Why do many astronomers believe that dark matter consists largely of WIMPs? The dark matter in galaxies cannot be made of neutrinos, because these tiny particles travel through the universe at enormous speeds and can easily escape a galaxy's ravitational pull. WIMPs Stands for weakly interacting massiveparticles and represents a possible form of dark matter consisting of subatomic particles that are dark because they do not respond to the electromagnetic force. The dark matter in galaxies cannot be made of neutrinos, because these tiny particles travel through the universe at enormous speeds and can easily escape a galaxy's gravitational pull. (However, as we'll discuss shortly, neutrinos might contribute to the amount of dark matter outside galaxies.) But what if other weakly interacting particles exist that are similar to neutrinos but considerably heavier? They too would evade direct detection, but they would move more slowly and could collect into galaxies, adding mass without adding light. Such hypothetical particles are called WIMPs, for weakly interacting massive particles. (Weakly interacting particles that are slow-moving enough to collect into galaxies are sometimes called cold dark matter to set them apart from faster-moving hot dark matter particles such as neutrinos.) WIMPs could make up most of our galaxy's mass, but they would be completely invisible in all wavelengths of light. WIMPs could also explain why dark matter doesn't behave like the visible matter in galaxies. During the early stages of the Milky Way's formation, the ordinary (baryonic) matter settled toward our galaxy's center and then flattened into a disk. Meanwhile, the dark matter stayed where it was, out in the galaxy's halo. This resistance of the dark matter to settling is exactly what we would expect from weakly interacting particles. Because WIMPs do not emit electromagnetic radiation, they cannot radiate away their energy. They are therefore stuck orbiting out at large distances and cannot collapse with the rest of the protogalactic cloud. 13. What do we mean by gravitationally bound systems? How did such structures come to exist in an expanding universe? gravitationally bound system Any system of objects, such as a star system or a galaxy, that is held together by gravity. Stars, galaxies, and clusters of galaxies are all gravitationally bound systems, meaning that their gravity is strong enough to hold them together. In most of the gravitationally bound systems we have discussed so far, gravity has completely overwhelmed the expansion of the universe. That is, while the universe as a whole is expanding, space is not expanding within our solar system, our galaxy, or our Local Group of galaxies. the stronger gravity in regions of enhanced density gradually pulled in matter until these regions stopped expanding and became protogalactic clouds—even as the universe as a whole continued (and still continues) to expand. If dark matter is indeed the most common form of mass in galaxies, it must have provided most of the gravitational attraction responsible for creating the protogalactic clouds. 14. What are peculiar velocities? What causes them, and what do they tell us about the formation of clusters and superclusters? peculiar velocity (of a galaxy) The component of a galaxy's velocity relative to the Milky Way that deviates from the velocity expected by Hubble's law. Astronomers call this 400-km/s deviation from Hubble's law a peculiar velocity, but it's really not so peculiar. It is simply the effect of the gravitational attraction pulling us back toward Virgo against the flow of universal expansion. The overall effect is rather like that of swimming upstream against a strong current: You move "upstream" relative to other objects floating in the current, but you're still headed "downstream" relative to the shore because of the strong current. The speed of the current is like the speed of expansion of the universe, and your swimming speed "upstream" is your peculiar velocity. Just as the Earth's gravity slows a rising baseball and eventually turns it around and pulls it back toward the ground, the gravitational tug of the Virgo Cluster may eventually turn the galaxies of our Local Group around and pull them into the cluster. Similar processes are taking place on the outskirts of other large clusters of galaxies, where we see many galaxies with large peculiar velocities pointing in the direction of the cluster. Their peculiar velocities indicate that the cluster's gravity is pulling on them. Eventually, some or perhaps all of these galaxies will fall into the cluster. many clusters are still attracting galaxies, adding to the hundreds they already contain. On even larger scales, clusters themselves have surprisingly large peculiar velocities, hinting that they are parts of even bigger gravitationally bound systems, called superclusters, that are just beginning to form. 15. Briefly describe the appearance of the universe on the largest scales. What is the Great Wall of galaxies? already revealing large-scale structures much vaster than clusters of galaxies. One of the most famous depictions of large-scale structure is the "slice of the universe" pictured in Figure 21.14a. Many astronomers collaborated to measure the redshifts of all the galaxies they could find in this particular slice of the sky. This project dramatically revealed the complex structure of our corner of the universe. Each dot in such pictures represents an entire galaxy of stars. The arrangement of the dots reveals huge sheets of galaxies spanning many millions of light-years (Figure 21.14b,c). Clusters of galaxies are located at the intersections of these sheets. Between the sheets of galaxies lie giant empty regions called voids. large-scale structure (of the universe) Generally refers to structure of the universe on size scales larger than that of clusters of galaxies. Some of the structures we see in the universe are amazingly large. The so-called Great Wall of galaxies stretches across an expanse measuring some 180 million light-years side to side. Immense structures such as these apparently have not yet collapsed into randomly orbiting, gravitationally bound systems. They haven't had enough time. The universe may still be growing structures on ever larger scales even though it is billions of years old. Most astronomers believe that all these large-scale structures grew from slight density enhancements in the early universe, just as galaxies did. Galaxies, clusters, superclusters, and the Great Wall probably all started as mildly high-density regions of different sizes. The voids in the distribution of galaxies probably started as mildly low-density regions. If this picture of structure formation is correct, then the structures we see in today's universe mirror the original distribution of dark matter very early in time. Supercomputer models of structure formation in the universe can now simulate the growth of galaxies, clusters, and larger structures from tiny density enhancements as the universe evolves. 16. Explain how the total amount of dark matter in the universe holds the key to its final fate. According to current evidence about the amount of dark matter, what is the fate of the universe? Dark matter is dim too faint to see and depends on how much dark matter exists may depend on the fate of the universe. Dark matter remains enigmatic, but every year we are learning more about its role in the universe. Because galaxies and clusters of galaxies seem to contain much more dark matter than luminous matter, we believe that dark matter's gravitational pull must be the primary force holding these structures together. we strongly suspect that the gravitational attraction of dark matter is what pulled galaxies and clusters together in the first place. 17. Briefly describe the four possible patterns for the expansion of the universe. What is the fate of the universe in each case? How does the current age of the universe differ among the four cases? We now arrive at one of the ultimate questions in astronomy: How will the universe end? Edwin Hubble's work established that the galaxies in the universe are rapidly flying away from one another, but the gravitational pull of each galaxy on every other galaxy acts to slow the expansion. These facts suggest two possible fates for the universe. If gravity is strong enough, the expansion will someday halt and the universe will begin collapsing, eventually ending in a cataclysmic crunch. Alternatively, if the expansion can overcome the pull of gravity, the universe will continue to expand forever, growing ever colder as its galaxies grow ever farther apart. we do not yet know the overall strength of the universe's gravitational pull. The strength of this pull depends on the density of matter in the universe: The greater the density, the greater the overall strength of gravity and the higher the likelihood that gravity will someday halt the expansion. Precise calculations show that gravity can win out over expansion if the current density of the universe exceeds a seemingly minuscule 10–29 gram per cubic centimeter, which is roughly equivalent to a few hydrogen atoms in a volume the size of a closet. The precise density marking the dividing line between eternal expansion and eventual collapse is called the critical density. If large-scale structures really do contain a higher proportion of dark matter than do clusters, the influence of that extra dark matter should show up in the velocities of galaxies near those large-scale structures: Larger amounts of dark matter should cause greater deviations from Hubble's law. To date, studies of these galaxy velocities remain inconclusive. Some researchers claim to find evidence that large-scale structures have significantly higher mass-to-light ratios than do clusters of galaxies, in which case the universe's matter density could be close to the critical value. As of 2001, however, most studies hold the line near the value we infer from clusters, which is about 25% of the critical density required to reverse the expansion. If that is the case, the universe will continue to expand forever. Mysterious Acceleration In the past few years, observations of distant white dwarf supernovae have enabled us to probe the fate of the universe in an entirely new way. Because white dwarf supernovae are such good standard candles, we can use them to determine whether gravity has been slowing the universe's expansion, as it must if the universe is destined to end in a cataclysmic crunch. However, the astronomers who set out to measure gravity's influence over the universe by observing supernovae discovered something completely unexpected. Instead of slowing because of gravity, the expansion of the universe appears to be speeding up, suggesting that some mysterious repulsive force is pushing all the universe's galaxies apart. This discovery, if it holds up to further scrutiny, has far-reaching implications for both the fate of the universe and our understanding of the forces that govern its behavior on large scales. Before examining the evidence for an accelerating expansion, we must further explore the possible fates of the universe. Astronomers subdivide the two general possibilities for the fate of the universe, expanding forever or someday collapsing, into four broad categories, each representing a particular pattern of change in the future expansion rate. We will call these four possible expansion patterns recollapsing, critical, coasting, and accelerating. The first three possibilities assume that gravity is the only force that affects the expansion rate of the universe: If the matter density of the universe is larger than the critical density, the collective gravity of all its matter will eventually halt the universe's expansion and reverse it. The galaxies will come crashing back together, and the entire universe will end in a fiery "Big Crunch." If this is the fate of our universe, then we live in a recollapsing universe. (The overall geometry of a recollapsing universe closes upon itself like the surface of a sphere, which is why this type of universe is sometimes called a closed universe.) If the matter density of the universe equals the critical density, the collective gravity of all its matter is exactly the amount needed to balance the expansion. The universe will never collapse but will expand more and more slowly as time progresses. If this is the fate of our universe, then we live in a critical universe. (Mathematically speaking, a critical universe stops expanding after infinite time, and its overall geometry is flat like the surface of a table a critical universe is one example of what astronomers call a flat universe.) If the matter density of the universe is smaller than the critical density, the collective gravity of all its matter cannot halt the expansion. The universe will keep expanding forever, with little change in its rate of expansion. If this is the fate of our universe, then we live in a coasting universe. (A coasting universe is sometimes called an open universe, because its overall geometry is more like the open surface of a saddle than like the closed surface of a sphere. Because observations of distant supernovae suggest that a repulsive force opposes gravity on very large scales, astronomers are now seriously considering a fourth possibility: If a repulsive force causes the expansion of the universe to accelerate with time, then we live in an accelerating universe. Its galaxies will recede from one another increasingly faster, and it will become cold and dark more quickly than a coasting universe. (Depending on the strength of gravity relative to the repulsive force, the overall geometry of an accelerating universe could be flat, open, or closed; however, most astronomers favor a flat geometry for this case.) 18. Briefly describe the recent evidence suggesting that the expansion of the universe is accelerating. the average distance between galaxies changes with time for each possibility. The lines for the accelerating, coasting, and critical universes always continue upward as time increases, because in these cases the universe is always expanding; the steeper the slope, the faster the expansion. In the recollapsing case, the line begins on an upward slope but eventually turns around and declines as the universe contracts. All the lines pass through the same point and have the same slope at the moment labeled "now," because the current separation between galaxies and the current expansion rate in each case must agree with observations of the present-day universe. Note that the age for the universe that we infer from its expansion rate differs in each case. A recollapsing universe requires the least amount of time to arrive at the current separation between galaxies—the goes from zero separation to the current separation in only about 5 billion years. The cases for which gravity is less important require more time to achieve the current separation between galaxies. The ages we would infer are 10 billion years for a critical universe, 15 billion years for a coasting universe, and around 16 billion years for an accelerating universe. This relationship between the age of the universe and its expansion pattern enables us to determine the expansion pattern from supernova observations. To understand how, imagine observing a distant white dwarf supernova with spectral lines redshifted to twice their normal wavelengths. Recall that the expansion of the universe stretches light waves by the same amount that it increases the average distance between galaxies, so the light we are observing from that supernova must have left when the average distance between galaxies was only half its current value. Because white dwarf supernovae are such excellent standard candles, we can also determine the actual distance—and the lookback time to the supernova from its apparent brightness. In principle, knowing both the supernova's redshift and its lookback time enables us to determine the universe's past expansion rate. The horizontal dotted lines indicate the average distance between galaxies at the time of the supernova, and the vertical dotted lines indicate the corresponding lookback time for each of the illustrated expansion patterns. Note that the lookback times are smallest for models in which the universe grows most quickly to its present size. Thus, we expect a supernova with a given redshift to be somewhat closer, and therefore somewhat brighter, if the universe is recollapsing or critical than if it is coasting. Conversely, if the supernova turns out to be somewhat farther and dimmer than we would expect in a coasting universe, then we would conclude that the expansion is accelerating. In practice, observations of such distant supernovae are still very difficult, but the results to date favor an accelerating universe: White dwarf supernovae with large redshifts appear to be somewhat dimmer than we would expect if the universe were coasting. These observations are consistent with an accelerating universe and highly inconsistent with either a critical or a recollapsing universe. Exactly why the universe might be accelerating remains a deep mystery, because no known force would act to push the universe's galaxies apart. Some speculative ideas for what might generate such a force go by the names dark energy, quintessence, and cosmological constant. No matter what the mechanism turns out to be, it now seems likely that the universe is indeed doomed to expand forever, its galaxies receding ever more quickly into an icy, empty future. Discussion Questions 1. Dark Matter or Revised Gravity. One possible explanation for the large mass-to-light ratios we measure in galaxies and clusters is that we are currently using the wrong law of gravity to measure the masses of very large objects. If we really do misunderstand gravity, then many fundamental theories of physics, including Einstein's theory of general relativity, will need to be revised. Which explanation for these mass-to-light ratios do you find more appealing, dark matter or revised gravity? Explain why. Why do you suppose most astronomers find dark matter more appealing? 2. Our Fate. Scientists, philosophers, and poets alike have speculated on the fate of the universe. How would you prefer the universe as we know it to end, in a big crunch or through eternal expansion? Explain the reasons behind your preference. Problems True Statements? For problems 1–6, decide whether the statement is true and explain why it is or is not. 1. Astronomers now believe that most of any galaxy's mass lies beyond the portions of the galaxy that we can see. 2. If our galaxy had less dark matter, its mass-to-light ratio would be lower. 3. A cluster of galaxies is held together by the mutual gravitational attraction of all the stars in the cluster's galaxies. 4. We can estimate the total mass of a cluster of galaxies by studying the distorted images of galaxies whose light passes through the cluster. 5. Clusters of galaxies are the largest structures that we have so far detected in the universe. 6. There is no doubt remaining among astronomers that the fate of the universe is to expand forever. 7. Strange Repulsive Force. The idea that a strange repulsive force may be accelerating the universe's expansion is quite recent. What do we mean by an accelerating expansion, and what evidence suggests that such an acceleration may be occurring? If the acceleration is real, what is the fate of the universe? Explain. 8. Mass-to-Light Ratio. Suppose you discovered a galaxy with a mass-to-light ratio of 0.1 solar mass per solar luminosity. Would you be surprised? Explain why or why not. What would this measurement say about the nature of the stars in this galaxy? 9. Weighing a Spiral Galaxy. Figure 21.4 shows the rotation curve for a spiral galaxy called NGC 7541. 1. Use the orbital velocity law to determine the mass (in solar masses) of NGC 7541 enclosed within a radius of 30,000 light-years from its center. (Hint: 1 light-year = 9.461 1015 m.) 2. Use the orbital velocity law to determine the mass of NGC 7541 enclosed within a radius of 60,000 light-years from its center. 3. Based on your answers to parts (a) and (b), what can you conclude about the distribution of mass in this galaxy? 10. Weigh a Cluster of Galaxies. Suppose a cluster of galaxies has a radius of about 6.7 million light-years (6.2 X 1022 m) and an intracluster medium with a temperature of 8 X 107 K. Estimate the mass of the cluster. Give your answer in both kilograms and solar masses. 11. How Many MACHOs? Suppose the rotation of a highly simplified galaxy whose stars are all identical to the Sun (1 solar mass per solar luminosity) shows that its overall mass-to-light ratio is equal to 30 solar masses per solar luminosity. 1. What is the ratio of dark matter to luminous matter in this galaxy? 2. Suppose all the dark matter consists of MACHOs similar to Jupiter, each with a mass of 0.001 solar mass. How many of these MACHOs must the galaxy contain for each ordinary star? Explain. Web Projects Find useful links for Web projects on the text Web site. 1. Gravitational Lenses. Gravitational lensing occurs in numerous astronomical situations. Compile a catalog of examples from the Web. Try to find pictures of lensed stars, quasars, and galaxies. Supply a one-paragraph explanation of what is going on in each picture. 2. Accelerating Universe. Search for the most recent information about possible acceleration of the expansion of the universe. Write a one- to three-page report on your findings. 3. The Nature of Dark Matter. Find and study recent reports on new ideas about the possible nature of dark matter. Write a one- to three-page report that summarizes the latest ideas about what dark matter is made of. Chapter 22 Review Questions 1. Briefly explain why the early universe must have been much hotter and denser than the universe is today. the expanding universe is cooling and becoming less dense as it grows. Therefore, the universe must have been hotter and denser in the past. Calculating exactly how hot and dense the universe must have been when it was more compressed is similar to calculating the temperatures and densities in a car engine as the pistons compress the fuel mix, except that the conditions become much more extreme. Figure 22.1 shows just how hot the universe was during its earliest moments, according to such calculations. To understand these early moments, we need to know how matter and energy behave under such extraordinarily hot conditions. 2. What do we mean by the Big Bang theory? The Big Bang theory—the scientific theory of the universe's earliest moments—presumes that all we see today, from Earth to the cosmic horizon, began as an incredibly tiny, hot, and dense collection of matter and radiation. It describes how expansion and cooling of this unimaginably intense mixture of particles and photons could have led to the present universe of stars and galaxies, and it explains several aspects of today's universe with impressive accuracy. Our ideas about the earliest moments of the universe are quite speculative because they depend on aspects of physics that we do not yet fully comprehend. Big Bang The event that gave birth to the universe. 3. What is antimatter? How were particle–antiparticle pairs created in the early universe? How were they destroyed? antimatter Refers to any particle with the same mass as a particle of ordinary matter but whose other basic properties, such as electrical charge, are precisely opposite. One example of such a reaction is the creation or destruction of an electron–antielectron pair [Section S4.5]. When two photons collide with a total energy greater than twice the mass-energy of an electron (i.e., the electron's mass times c 2), they can create two brand-new particles: a negatively charged electron and its positively charged twin, the antielectron, also known as a positron (Figure 22.3). The electron is a particle of matter, and the antielectron is a particle of antimatter. The reaction that creates an electron–antielectron pair also runs in reverse: When an electron and an antielectron meet, they annihilate each other totally, transforming all their mass-energy back into photon energy. Similar reactions can produce or destroy any particle–antiparticle pair, such as a proton and antiproton or neutron and antineutron. The early universe was therefore filled with an extremely dynamic blend of photons, matter, and antimatter, converting furiously back and forth. Despite all these vigorous reactions, describing conditions in the early universe is straightforward, because we can calculate the proportions of the various forms of radiation and matter from the universe's temperature and density at any time. 4. Briefly summarize the characteristics marking each of the various eras shown in Figure 22.2. 5. What are the Planck era and the Planck time? Why can't our current theories describe the history of the universe during the Planck era? Planck era The era of the universe prior to the Planck time. Prior to the Planck time, in the Planck era, these random energy fluctuations were so large that our current theories are powerless to describe what might have been happening. The problem is that we do not yet have a theory that links quantum mechanics and general relativity. In a sense, quantum mechanics is our successful theory of the very small (subatomic particles), and general relativity is our successful theory of the very big (the large-scale structure of spacetime). Perhaps someday we will be able to merge these theories of the very small and the very big into a single "theory of everything." Until that happens, science cannot describe the universe before 6. What are grand unified theories? According to these theories, how many forces operated in the universe during the GUT era? Why? grand unified theory (GUT) A theory that unifies three of the four fundamental forces—the strong force, the weak force, and the electromagnetic force (but not gravity)—in a single model. Gravity dominates large-scale action, and electromagnetism dominates chemical and biological reactions. The strong and weak forces determine what happens within atomic nuclei: The strong force binds nuclei together, and the weak force mediates nuclear reactions such as fission or fusion. GUT era The era of the universe during which only two forces operated (gravity and the grand-unified-theory or GUT force), lasting from 10–43 second to 10–38 second after the Big Bang. 7. What do we mean by inflation? Briefly describe why inflation might have occurred at the end of the GUT era. inflation (of the universe) A sudden and dramatic expansion of the universe thought to have occurred at the end of the GUT era. Grand unified theories predict that the strong force froze out from the GUT force at this point, leaving three forces operating in the universe: gravity, the strong force, and the electroweak force. As we will discuss later, it now seems possible that this freezing out of the strong force released an enormous amount of energy. This energy release would have caused the universe to undergo a sudden and dramatic expansion that we call inflation. In the space of a mere 10–36 second, pieces of the universe the size of an atomic nucleus may have grown to the size of our solar system. Inflation sounds bizarre, but it might actually explain some puzzling features of today's universe. 8. What characterized the universe during the electroweak era? What evidence from particle accelerators supports the idea that the weak and electromagnetic forces were once unified as a single electroweak force? electroweak era The era of the universe during which only three forces operated (gravity, strong force, and electroweak force), lasting from 10–38 second to 10–10 second after the Big Bang. electroweak force The force that exists at high energies when the electromagnetic force and the weak force exist as a single force. The end of the GUT era marks the beginning of the electroweak era, so named because the electromagnetic and weak forces were still unified into the electroweak force. Intense radiation filled all of space, as it had since the Planck era, spontaneously producing matter and antimatter particles of many different sorts that immediately reverted back to energy. The universe continued to expand and cool throughout the electroweak era, dropping to a temperature of 1015 K when it reached an age of 10–10 second. This temperature is still 100 million times hotter than the temperature in the core of the Sun, but it was low enough for the electromagnetic and weak forces to freeze out from the electroweak force. After this instant (10–10 s), all four forces were forever distinct in the universe. 9. What characterized the universe during the particle era? What happened to the quarks that existed freely in the universe early in the particle era? particle era The era of the universe lasting from 10–10 second to 0.001 second after the Big Bang, during which subatomic particles were continually created and destroyed and ending when matter annihilated antimatter. quarks The building blocks of protons and neutrons, quarks are one of the two basic types of fermions (leptons are the other). Spontaneous creation and annihilation of particles continued throughout the next era, which we call the particle era because tiny particles of matter were as numerous as photons. These particles included electrons, neutrinos, and quarks-the building blocks of heavier particles such as protons, antiprotons, neutrons, and antineutrons. Near the end of the particle era, when the universe was about 0.0001 second old, the temperature grew too cool for quarks to exist on their own, and quarks combined in groups of three to form protons and neutrons. The particle era came to an end when the universe reached an age of 1 millisecond (0.001 s) and the temperature had fallen to 1012 K. At this point, it was no longer hot enough to spontaneously produce protons and antiprotons (or neutrons and antineutrons) from pure energy. 10. How long did the era of nucleosynthesis last? Why was this era so important in determining the chemical composition of the universe forever after? era of nucleosynthesis The era of the universe lasting from about 0.001 second to about 3 minutes after the Big Bang, by the end of which virtually all of the neutrons and about one-seventh of the protons in the universe had fused into helium The Era of Nucleosynthesis So far, everything we have discussed occurred within the first 0.001 second of the universe's existence—a time span shorter than the time it takes you to blink an eye. At this point, the protons and neutrons left over after the annihilation of antimatter attempted to fuse into heavier nuclei. However, the heat of the universe remained so high that most nuclei broke apart as fast as they formed. This dance of fusion and breakup marked the era of nucleosynthesis. The era of nucleosynthesis ended when the universe was about 3 minutes old. By this time, the density in the expanding universe had dropped so much that fusion no longer occurred, even though the temperature was still about a billion Kelvin (109 K)—much hotter than the temperature at the center of the Sun today. When fusion ceased, about 75% of the mass of the ordinary (baryonic) matter in the universe remained as individual protons, or hydrogen nuclei. The other 25% of this mass had fused into helium nuclei, with trace amounts of deuterium (hydrogen with a neutron) and lithium. Except for the relatively small amount of matter that stars later forged into heavier elements, the chemical composition of the universe remains unchanged today. 11. Briefly explain why radiation was trapped for 500,000 years during the era of nuclei and why the cosmic microwave background broke free at the end of this era. At the end of the era of nucleosynthesis, the universe consisted of a very hot plasma of hydrogen nuclei, helium nuclei, and free electrons. This basic picture held for about the next 500,000 years as the universe continued to expand and cool. The fully ionized nuclei moved independently of electrons during this period (rather than being bound with electrons in neutral atoms), which we call the era of nuclei. Throughout this era, photons bounced rapidly from one electron to the next, just as they do deep inside the Sun today, never managing to travel far between collisions. Any time a nucleus managed to capture an electron to form a complete atom, one of the photons quickly ionized it. The era of nuclei came to an end when the expanding universe was about 500,000 years old, at which point the temperature had fallen to about 3,000 K—roughly half the temperature of the Sun's surface today. Hydrogen and helium nuclei finally captured electrons for good, forming stable, neutral atoms for the first time. With electrons now bound into atoms, the universe suddenly became transparent. Photons, formerly trapped among the electrons, began to stream freely across the universe. 12. What do we mean by the era of atoms and the era of galaxies? What era do we live in? Explain. era of atoms The era of the universe lasting from about 500,000 years to about 1 billion years after the Big Bang, during which it was cool enough for neutral atoms to form. era of galaxies The present era of the universe, which began with the formation of galaxies when the universe was about 1 billion years old. We live in era of galaxies. The Era of Atoms and the Era of Galaxies We've already discussed the rest of the story in earlier chapters. The end of the era of nuclei marked the beginning of the era of atoms, when the universe consisted of a mixture of neutral atoms and plasma. Thanks to the slight density enhancements present in the universe at this time and the gravitational attraction of dark matter, the atoms and plasma slowly assembled into protogalactic clouds. Stars formed in these clouds, transforming the gas clouds into galaxies. The first full-fledged galaxies had formed by the time the universe was about 1 billion years old, beginning what we call the era of galaxies. The era of galaxies continues to this day. Generation after generation of star formation in galaxies steadily builds elements heavier than helium and incorporates them into new star systems. Some of these star systems develop planets, and on at least one of these planets life burst into being a few billion years ago. And here we are, thinking about it all. Describing both the follies and the achievements of the human race, Carl Sagan once said, "These are the things that hydrogen atoms do—given 15 billion years of cosmic evolution." 13. Briefly describe the two key pieces of evidence that support the Big Bang theory. Like any scientific theory, the Big Bang theory is a model designed to explain a set of facts. If it is close to the truth, it should be able to make predictions about the real universe that we can verify through observations or experiments. The Big Bang model has gained wide scientific acceptance for two key reasons: The Big Bang model predicts that the radiation that began to stream across the universe at the end of the era of nuclei should still be present today. Sure enough, we find that the universe is filled with what we call the cosmic microwave background. Its characteristics precisely match what we expect according to the Big Bang model. The Big Bang model predicts that some of the original hydrogen in the universe should have fused into helium during the era of nucleosynthesis. Observations of the actual helium content of the universe closely match the amount of helium predicted by the Big Bang model. Fusion of hydrogen to helium in stars could have produced only about 10% of the observed helium. The Cosmic Microwave Background The first major piece of evidence supporting the Big Bang theory arrived in 1965. Arno Penzias and Robert Wilson, two physicists working at Bell Laboratories in New Jersey, were calibrating a sensitive microwave antenna designed for satellite communications (Figure 22.5). (Microwaves fall within the radio portion of the electromagnetic spectrum.) Much to their chagrin, they kept finding unexpected "noise" in every measurement they made with the antenna. Fearing that they were doing something wrong, they worked frantically to discover and eliminate all possible sources of background noise. They even climbed up on their antenna to scrape off pigeon droppings, on the off-chance that these were somehow causing the noise. No matter what they did, the microwave noise wouldn't go away. The noise was the same no matter where they pointed their antenna, indicating that it came from all directions in the sky and ruling out the possibility that it came from any particular astronomical object or from any place on the Earth. 14. Briefly describe how the cosmic microwave background was discovered. cosmic microwave background The remnant radiation from the Big Bang, which we detect using radio telescopes sensitive to microwaves (which are short-wavelength radio waves). The first major piece of evidence supporting the Big Bang theory arrived in 1965. Arno Penzias and Robert Wilson, two physicists working at Bell Laboratories in New Jersey, were calibrating a sensitive microwave antenna designed for satellite communications (Figure 22.5). (Microwaves fall within the radio portion of the electromagnetic spectrum.) Much to their chagrin, they kept finding unexpected "noise" in every measurement they made with the antenna. Fearing that they were doing something wrong, they worked frantically to discover and eliminate all possible sources of background noise. They even climbed up on their antenna to scrape off pigeon droppings, on the off-chance that these were somehow causing the noise. No matter what they did, the microwave noise wouldn't go away. The noise was the same no matter where they pointed their antenna, indicating that it came from all directions in the sky and ruling out the possibility that it came from any particular astronomical object or from any place on the Earth. Embarrassed by their inability to explain the noise, Penzias and Wilson prepared to "bury" their discovery at the end of a long scientific paper about their antenna. The "noise" in the Bell Labs antenna was not an embarrassment after all. Instead, it was the cosmic microwave background—and the first strong evidence that the Big Bang had really happened. 15. Why does the Big Bang theory predict that the cosmic microwave background should have a perfect thermal radiation spectrum? How did the Cosmic Background Explorer (COBE) support this prediction of the Big Bang theory? What is the temperature of the cosmic microwave background? The cosmic microwave background came from the heat of the universe itself and therefore should have an essentially perfect thermal radiation spectrum. When this radiation first broke free 500,000 years after the Big Bang, the temperature of the universe was about 3,000 K, not too different from that of a red giant star's surface. the cosmic microwave background does indeed have a perfect thermal radiation spectrum, with a peak corresponding to a temperature of 2.73 K. In a very real sense, the temperature of the night sky is a frigid 3 degrees above absolute zero. 16. Briefly describe how theoretical calculations allow us to predict the fraction of ordinary matter in the universe that should consist of helium as opposed to hydrogen. A few reactions involving hydrogen-3 (also known as tritium) or helium-3 can create long-lasting nuclei. For example, fusing helium-4 and hydrogen-3 produces lithium-7. However, the contributions of these reactions to the overall composition of the universe were minor because hydrogen-3 and helium-3 were so rare. Models of element production in the early universe show that, before the cooling of the universe shut off fusion entirely, such reactions generated only trace amounts of lithium, the next lightest element after helium. aside from hydrogen, helium, and lithium, all other elements were forged much later in the nuclear furnaces of stars. (Beryllium and boron, which are heavier than lithium but lighter than carbon, were created later when high-energy particles broke apart heavier nuclei that formed in stars.) The Density of Ordinary Matter Calculations made with the Big Bang model allow scientists to estimate the density of ordinary (baryonic) matter in the universe from the observed amount of deuterium in the universe today. The fact that some deuterium nuclei still exist in the universe indicates that the fusing of neutrons into helium nuclei in the early universe was incomplete. The amount of deuterium—roughly one hydrogen atom in 100,000 contains a deuterium nucleus—tells us about the density of protons and neutrons (baryons) during the era of nucleosynthesis. If this density had been higher in the early universe, protons and neutrons would have fused more efficiently into helium, and less deuterium would have been left over. 17. How do measurements of the abundance of deuterium in today's universe allow us to estimate the density of ordinary matter during the era of nucleosynthesis? Explain why these measurements suggest that at least some of the dark matter in the universe must be extraordinary. Calculations made with the Big Bang model allow scientists to estimate the density of ordinary (baryonic) matter in the universe from the observed amount of deuterium in the universe today. The fact that some deuterium nuclei still exist in the universe indicates that the fusing of neutrons into helium nuclei in the early universe was incomplete. The amount of deuterium—roughly one hydrogen atom in 100,000 contains a deuterium nucleus—tells us about the density of protons and neutrons (baryons) during the era of nucleosynthesis. If this density had been higher in the early universe, protons and neutrons would have fused more efficiently into helium, and less deuterium would have been left over. The results of such calculations show that the density of ordinary (baryonic) matter in the universe is somewhere between 1% and 10% of the critical density. (Recall that the critical density is the density required if the expansion of the universe is to stop and reverse someday [Section 21.6].) Similar calculations based on the observed abundance of lithium lead to the same conclusion, adding to our confidence in the Big Bang model and implying something very interesting about the fate of the universe: Unless extraordinary (nonbaryonic) matter outweighs ordinary matter by at least a factor of 10, the universe cannot recollapse. 18. Why do we think that tiny quantum ripples should have been present in the early universe? How might inflation have caused these tiny ripples to become the seeds that later grew into galaxies? Not only is the slight lumpiness of the early universe a problem, but its large-scale smoothness is also a problem. Observations of the cosmic microwave background show that, overall, the density of the universe at the end of the era of nuclei varied from place to place by no more than about 0.01%. The standard Big Bang theory does not explain why distant reaches of the universe look so similar. the distribution of energy through space on very small scales is slightly irregular, even in a complete vacuum. These tiny quantum "ripples" can be characterized by a wavelength that corresponds roughly to their size. In principle, quantum ripples in the very early universe could have been the seeds for density enhancements that later grew into galaxies. However, the wavelengths of the original ripples were far too small to explain density enhancements like those we see imprinted on the cosmic microwave background. 19. How does inflation explain why the universe appears so uniform? Inflation would have dramatically altered these quantum fluctuations. The fantastic growth of the universe during the period of inflation would have stretched tiny ripples in space to enormous wavelengths. Ultimately, inflation could have caused these quantum ripples to grow large enough to become the density enhancements that later formed large structures in the universe. Amazingly, all the structure we see today in the universe may have started as tiny quantum fluctuations just before the period of inflation. Inflation goes a long way toward solving the structure problem. However, it is important to note that the models invoking inflation do not entirely solve the structure problem. Although these models make reasonable predictions for the wavelengths of the quantum ripples, they do not predict their amplitudes. This problem underscores the speculative nature of the idea of inflation. Many scientists are working hard to improve models of inflation in hopes that they will soon be able to make more definitive predictions that can be tested observationally. Radiation signals traveling at the speed of light would have had time to equalize all the temperatures and densities in this region. Inflation then pushed these equalized regions to much greater distances, far out of contact with one another. This explanation of why the universe appears so uniform at first appears paradoxical. It seems to require pieces of the observable universe to move faster than the speed of light during inflation. Yet we know that nothing can move faster than the speed of light. To understand why inflation does not violate this universal speed limit, remember that the expansion of the universe is really the expansion of space itself. Objects with large cosmological redshifts aren't moving at high speed so much as they are riding along with the expansion of the universe. 20. Briefly explain why the theory of inflation predicts that the universe ought to be flat. How is inflation being tested by astronomers? the effect of inflation on spacetime curvature is similar to the flattening of a balloon's surface when you blow into it. The flattening of space during the period of inflation would have been so enormous that it would virtually have eliminated any curvature the universe might have had previously. 21. What is Olbers' paradox? Explain how this simple paradox provides at least some support for the idea that the universe began in a Big Bang. Olbers' paradox Asks the question of how the night sky can be dark if the universe is infinite and full of stars. If the universe were infinite, unchanging, and everywhere the same, then the entire night sky would blaze as brightly as the Sun. Johannes Kepler was perhaps the first person to realize that the night sky in such a universe should be bright, but this realization is now called Olbers' paradox. To understand how Olbers' paradox comes about, imagine that you are in a dense forest on a flat plain. If you look in any given direction, you'll likely see a tree. If the forest is small, you might be able to see through some gaps in the trees to the open plains, but larger forests have fewer gaps (Figure 22.16). An infinite forest would have no gaps at all—a tree trunk would block your view along any direction. The universe is like a forest of stars in this respect. In an unchanging universe with an infinite number of stars, we would see a star in every direction, making every point in the sky as bright as the Sun's surface. Obscuring dust doesn't change this conclusion. The intense starlight would heat the dust over time until it too glowed like the Sun or evaporated away. Discussion Questions 1. The Moment of Creation. You've probably noticed that, in discussing the Big Bang theory, we never quite talk about the first instant. Even our most speculative theories at present take us back only to within 10–43 second of creation. Do you think it will ever be possible for science to consider the moment of creation itself? Will we ever be able to answer questions such as why the Big Bang happened? Defend your opinions. 2. The Big Bang. How convincing do you find the evidence for the Big Bang model of the universe's origin? What are the strengths of the theory? What does it fail to explain? Overall, do you think the Big Bang really happened? Defend your opinion. 3. The End of Time. According to our current understanding, the universe as we know it will eventually come to an end—either in a fiery Big Crunch or in a slow death as all the stars eventually die. However, some people speculate that the universe might then undergo some type of rebirth. In the case of a recollapsing universe, the rebirth might consist of a new Big Bang; some people even speculate that the universe might repeatedly oscillate through cycles of Big Bangs and Big Crunches. Discuss some ideas about how the universe might undergo rebirth if it continues to expand forever. (Note: You may wish to read Isaac Asimov's short story The Last Question, published in 1956.) 4. Forever. If you could live forever, would you choose to do so? Suppose the universe will keep expanding forever, as the bulk of observations currently suggest. How would you satisfy your energy needs as time goes on? How would you grow food? What would you do with all that time? Problems True Statements? For problems 1–8, decide whether the statement is true and explain why it is or is not. 1. According to the Big Bang theory, the universe's temperature was greater than 10 billion (1010) K when the universe was less than one ten-billionth (10–10) of a second old. 2. Although the universe today appears to be made mostly of matter and not antimatter, the Big Bang theory suggests that the early universe had nearly equal amounts of matter and antimatter. 3. According to the Big Bang theory, the cosmic microwave background was created when energetic photons ionized the neutral hydrogen atoms that originally filled the universe. 4. While the existence of the cosmic microwave background is consistent with the Big Bang theory, it is also easily explained by assuming that it comes from individual stars and galaxies. 5. According to the Big Bang theory, most of the helium in the universe was created by nuclear fusion in the cores of stars. 6. The theory of inflation suggests that the structure in the universe today may have originated as tiny quantum fluctuations. 7. Within the next decade, observations of the cosmic microwave background will prove definitively whether inflation really occurred in the early universe. 8. The fact that the night sky is dark tells us that the universe cannot be infinite, unchanging, and everywhere the same. 9. Life Story of a Proton. Tell the life story of a proton from its formation shortly after the Big Bang to its presence in the nucleus of an oxygen atom you have just inhaled. Your story should be creative and imaginative, but it also should demonstrate your scientific understanding of as many stages in the proton's life as possible. You can draw on material from the entire book, and your story should be three to five pages long. 10. The Cosmic Microwave Background. The cosmic microwave background first began to stream freely across the universe at the end of the era of nuclei, when the universe was 500,000 years old and its temperature was about 3,000 K. Since that time, the universe has expanded by a factor of about 1,000. 1. Using Wien's law (see Mathematical Insight 7.2), calculate the wavelength of maximum intensity for thermal radiation with a temperature of 3,000 K. 2. The observed temperature of the cosmic microwave background today is about 2.73 K. Use Wien's law to calculate the wavelength of maximum intensity for the cosmic microwave background today. 3. How much longer are the wavelengths of the cosmic microwave background today than they were at the time the radiation was first released? Is this change in wavelength consistent with the idea that the universe has expanded by a factor of about 1,000 since the end of the era of nuclei? Explain. (Hint: Look back at the discussion of cosmological redshifts in Chapter 19.) 11. 10100 Years. In the box Thinking About . . . The End of Time, we found that the final stage in the history of a critical, coasting, or accelerating universe will come about 10100 years from now. Such a large number is easy to write but difficult to understand. In this problem, we investigate some of the incredible properties of very large numbers. 1. The current age of the universe is around 1010 years. How much longer is a trillion years than this current age? How much longer is 1015 years? 1020 years? 2. Suppose protons decay with a half-life of 1032 years. When will the number of remaining protons be half the current amount? When will it be a quarter of its current amount? How many half-lives will have gone by when the universe reaches an age of 1034 years? What fraction of the original protons will remain at this time? Based on your answers, is it reasonable to conclude that all protons in today's universe will be gone by the time the universe is 1040 years old? Explain. 3. Suppose you were trying to write 10100 zeros on a piece of paper and could write microscopically, so that each zero (including the thickness of the pencil mark) occupied a volume of 1 cubic micrometer—about the size of a bacterium. Could 10100 zeros of this size fit in the observable universe? Explain. (Hints: Calculate the volume of the observable universe in cubic micrometers by assuming it is a sphere with a radius of 15 billion light-years. The volume of a sphere is 4/3 (radius)3; 1 light-year 1015 meters; 1 cubic meter = 1018 cubic micrometers.) Web Projects Find useful links for Web projects on the text Web site. 1. New Tests of the Big Bang Theory. The Cosmic Background Explorer (COBE) satellite provided striking confirmation of several predictions of the Big Bang theory. But new satellites are already being designed that will test the Big Bang theory further, primarily by observing the subtle variations in the cosmic microwave background with a much higher sensitivity than COBE. Use the Web to gather pictures and information about the COBE mission and its planned successors, such as MAP or Planck. Write a one- to two-page report about the strength of the evidence compiled by COBE and how much more we might learn from the upcoming missions. 2. Decay of the Proton. One of the most startling predictions of grand unified theories is that protons will eventually decay, albeit with a half-life of more than 1032 years. If this is true, it may be possible to observe an occasional proton decay, despite the extraordinarily long half-life. Several experiments to look for proton decay are under way or being planned. Find out about one or more of these experiments, and write a one- to two-page summary in which you describe the experiment(s), any results to date, and what these results (or potential results) mean to the grand unified theories. 3. New Ideas in Inflation. The idea of inflation solves many of the puzzles associated with the standard Big Bang theory, but we are still a long way from finding strong evidence that inflation really occurred. Find recent articles that discuss some of the latest ideas about inflation and how we might test these ideas. Write a two- to three-page summary of your findings.
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