ࡱ> y   !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~Root Entry F@dO-5WordDocument [CompObj^al sphere. The Foucault pendulum is a way to demon- of the month and concentrate on achieving the correct num- strate that the Earth rather than the sky is turning. ber of days in a year by using such conventions as the leap 3.2 Today, most of the world has adopted the Gregorian calendar established in 1582. The familiar cycle of the seasons results from the 23 year. tilt of the Earth's axis of rotation. At the summer solstice, the Sun is higher in the sky and its rays strike the Earth more di- rectly. The Sun is in the sky for more than half the day and can heat the Earth longer. At the winter solstice, the Sun is low in the sky and up for fewer than 12 hours. At the vernal and autumnal equinoxes, the Sun is on the celestial equator, and we get 12 hours of day and night. The seasons are dif- ferent at different latitudes. 3.3 The basic unit of astronomical time is the day (either the solar day or the sidereal day). Apparent solar time is based on the position of the Sun in the sky, and mean solar time is based on the average value of a solar day during the year. By international agreement, we define 24 time zones around the world, each with its own standard time. The con- SUMMARY 77 3.5 The Moon's monthly cycle of phases results from the changing angle of its illumination by the Sun. The full moon is visible in the sky only during the night; other phases are visible during the day. Because its period of revolution is the same as its period of rotation, the Moon always keeps the same face toward the Earth. 3.6 The twice-daily ocean tides are primarily the result of the Moon's differential gravitational force on the material of the Earth's crust and ocean. These tidal forces cause ocean water to flow into two tidal bulges on opposite sides of the Earth; each day the Earth rotates through these bulges. Ac- tual ocean tides are complicated by the additional effects of the Sun, and by the shape of the coasts and ocean basins. 3.7 The Sun and Moon have nearly the same angular size corona) comes into view. Solar eclipses take place rarely in (about 0.5). A solar eclipse occurs when the Moon moves any one location, but they are among the most spectacular between the Sun and the Earth, casting its shadow on a part sights in nature. A lunar eclipse takes place when the of the Earth's surface. If the eclipse is total, the observer is in Moon moves into the Earth's shadow; it is visible (weather the Moon's umbra, the light from the bright disk of the Sun permitting) from the entire night hemisphere of the Earth. is completely blocked, and the solar atmosphere (the  Have your group brainstorm about other ways (besides your astronomy midterm, either as a research assistant the Foucault Pendulum) that you could prove that it is or as a short-order cook!) Have your group discuss how our Earth that is turning once a day, and not the sky the days and nights will be different there and how these turning around us. (Hint: How does the spinning of the differences might affect you. Earth affect the oceans and the atmosphere?) Discuss with your group all the stories you have heard What would the seasons on Earth be like if the Earth's about the Moon and crazy behavior. Why do you think axis were not tilted? How many things about life on people associate crazy behavior with the full Moon? Earth can you think of that would be different in this What other legends besides vampire stories are con- case? nected with the phases of the Moon? After college and graduate training, members of your ,~ Your college town becomes the founding site for a group are asked to set up a school in New Zealand. De- strange new cult that worships the Moon. These true scribe some ways your school schedule in the Southern believers gather regularly around sunset and do a dance Hemisphere would have to differ from what we are used where they must extend their arms in the direction of to in the North. the Moon. Have your group discuss which way their arms will be pointing at sunset when the Moon is new, first quarter, full, and third quarter. Duܥe# t-[,Zl,ZlZZ Z (ZZZTZTnYTimes New Roman Symbol Arial TahomaTimes New Roman ArialLucida ConsoleTimes New RomanCourier NewArial Narrow Verdana Arial 0339716 054332 computing/uwnetid/password/ ralberg@u.washington.edu rob$rain https://myuw.washington.edu/servlet/myuw.mainpage.Mainpage?f=d&p=frp Textbook Information for ASTR C101 (CSN 3878) Franknoi, Andrew Voyages to the Stars and Galaxies 2nd Edition 2001 International Thomson Publishing Multiply the distance in pixels by your scale factor. Since your scale factor is in "kilometers per pixel," your answer will be in kilometers. For example, if your scale factor is "1 pixel = 10 kilometers" and the distance in pixels is 200, then the distance in kilometers is 2000. voyages Calendar Zone [wrobzone.com/] published eclipse calculations and guidebooks for many years, This rich, sometimes strange, but always enjoyable site has and his site contains a wealth of information on the details of everything you've ever wanted to ask or know about calendars lunar and solar eclipses, past and future, as well as observing and timekeeping-sometimes as part of the site, and some- and photography hints. times through links around the world. In addition to astronom- ical ideas, the site features the cultural and political aspects of ' The Sky Online Eclipse Page time systems as well as software for keeping track of time. [www.skypub.com/eelipses/eclipses.shtml] Sky dr Telescope magazine's sites for eclipses features good Calendars and Their History tourist information about eclipse tours, observing and photog- [astro.nmsu.edu/^Ihuber/leaphist.html] raphy hints, and lots of links. Good starting site for eclipse The late historian of astronomy Leroy Doggett wrote this intro- chasers or fans. duetion to calendars for The Explanatory Supplement to the Astronomical Almanac, and it still remains one of the best V Astronomical Data Services guides to different calendar systems and how they are based on [aa.usno.navy.mil/AA/data] the motions of celestial objects. Includes sections on the He- This rich site from the U.S. Naval Observatory allows you to ask brew, Islamic, Indian, and Chinese calendars. (Note that this is many questions about the Earth, Moon, and sky. Want to know just a plain text site, with no graphics or links.) when the full moon or new moon will fall in August of 2004? Or when the next lunar eclipse will occur? Or when the Moon or Sun will rise and set for any day of the year? It's all here and much more besides, in tables and as on-screen calculators. The Reasons for the Seasons [www.aspsky.org/html/tnll29/29.html] An issue of a newsletter for astronomy teachers that goes into more depth on what causes the seasons and how the different effects combine. ! Sundials on the Internet [www.sundials.co.uk/] Before modern clocks, shadows cast by the Sun were a primary way of telling time. This site, maintained by sun-dial devotees Eclipse Home Page has information about sundials around the world, the theory of [sunearth.gsfc.nasa.gov/eclipse/eclipse.html] sundials, references, and many links. Fred Espenak, of NASAs Goddard Space Flight Center, has SUMMARY  3.1 The terrestrial system of latitude and longitude makes vention of the international date line is necessary to rec- use of the great circles called meridians. An analogous ce- oncile times in different parts of the Earth. lestial coordinate system is called right ascension (RA) and 3.4 The fundamental problem of the calendar is to recon- declination, with the vernal equinox serving as reference cile the incommensurable lengths of the day, the month, and point (like the prime meridian at Greenwich on the Earth). the year. Most modern calendars, beginning with the Roman These coordinate systems help us locate any object on the (Julian) calendar of the 1st century s.c., neglect the problem celestiring the traditional U.S. Christmas vacation weeks, you are sent to the vicinity of the South Pole on a re-search expedition (depending on how well you did on Chapter 3 Review Questions 1. Discuss how latitude and longitude on Earth are similar to declination and right ascension in the sky? 2. What is the latitude of the North Pole? The South Pole? Why does longitude have no meaning at the North and South Poles? 3. Make a table showing each main phase of the Moon and roughly when the Moon rises and sets for each phase. During which phase can you see the Moon in the middle of the morn- ing? In the middle of the afternoon? 4. What are the advantages and disadvantages of apparent so lar time? How is the situation improved by introducing mean solar time and standard time? 5. What are the two ways that the tilt of the Earth's axis causes the summers in the United States to be warmer than the winters? During the summer when it is warmer the sun is closer to Earth. 6. Why is it difficult to construct a practical calendar based on the Moon's cycle of phases? 7. Explain why there are two high tides and two low tides every day Strictly speaking, should the period during which there are two high tides be 24 hours? If not, what should the interval be? When the Moon and the Sun are pulling at a 90 angle to each other, those are called Neap Tides. tides Rising and falling motion that bodies of water follow, exhibiting daily, monthly, and yearly cycles. Ocean tides on Earth are caused by the competing gravitational pull of the Moon and Sun on different regions of the Earth. the tides are high and where the Moon will be in the sky at that time. one on the near side and one on the far side. On the near side, we can explain the bulge by realizing that the water closest to the Moon is being pulled more strongly than any other water on the Earth, so it seems reasonable that a bulge should exist there. These tides pull on the oceans as well as the Earth itself (solid-body tides) the daily tides two low and two high in most places are being caused by the rotation of the Earth underneath these bulges pointing towards and away from the Moon. Similar much smaller bulges appear in the Earth itself as a result of the solid body tides. Rotating under these bulges or dragging them around the Earth if you look at it from the bulge's point of view tends to slow the Earth's rotation on its axis. This slowing amounts to a loss of angular momentum (something with mass is spinning slower than it was). Since we can mostly consider Earth & the Moon to be an isolated system, that angular momentum has to go somewhere, and there's nowhere left for it to go except into the Moon. Ocean tides are the result of gravitational interactions between the earth, moon, and sun and the waters of the earth. Earths gravity holds you and me and everything else on the earths surface in a firm grip. Although its a very small force, lunar gravity also acts on you and me and the earth itself. The reason we dont fall straight into the moon is that there is a separate force counteracting the lunar attractive force. The gravitational pull of the moon is responsible for tides on earth. Note that tides are created on the near-side and far-side of the earth with respect to the moon. This tidal action is also responsible for the orbital migration of the moon. Due to the slow-down in the earth's rotation rate, the orbital energy of the moon is increased - resulting in the moon getting farther away from us! This has been confirmed by laser radar ranging experiments carried out on the moon, as well as fossil records on the earth. Preliminary evidence suggests that 1 billion years ago, the moon only took 23 days to revolve around the earth. Further, the earth was rotating much faster -- with only 18 hours in a day! All of this complex orbital interplay could have had a significant impact on the origin and evolution of life on earth. Such tidal forces play an important role in the orbit of objects around one another. 8. What is the phase of the Moon during a total solar eclipse?- During a total lunar eclipse? THOUGHT QUESTIONS 9. Where are you on the Earth according to the following de- scriptions? (Refer back to Chapter 1 as well as this chapter.) a. The stars rise and set perpendicular to the horizon. b. The stars circle the sky parallel to the horizon. e. The celestial equator passes through the zenith. d. In the course of a year, all stars are visible. e. The Sun rises on September 23 and does not set until March 21 (ideally). I 0. In countries at far northern latitudes, the winter months tend to be so cloudy that astronomical observations are nearly impossible. Why can't good observations of the stars be made at those places during the summer months? 11, What is the phase of the Moon if it a. rises at 3:00 P.M.? b, is highest in the sky at 7:00 A.M.? c. sets at 10:00 A.M.? 78 CHAPTER 3 EARTH, MOON, AND SKY 12. A car accident occurs around midnight on the night of a full moon. The driver at fault claims he was blinded momentarily by . the Moon rising on the eastern horizon. Should the police be- lieve him? a. How often would the Sun rise? b. How often would the Earth set? c. During what fraction of the time would you be able to see the stars? 13. The secret recipe to the ever-popular veggie burgers in the college cafeteria is hidden in a drawer in the director's office. Two students decide to break in and get their hands on it, but they want to do it a few hours before dawn on a night when . there is no Moon, so they are less likely to be caught. What phases of the Moon would suit their plans? Crescent Moon The moon phases showing less light is good since it is harder to see at night. 14. Your granduncle, who often exaggerates events in his own life, tells you about a terrific adventure he had on February 29, 1900. Why would this story make you suspicious? I 5. One year, when money is no object, you enjoy your birth- day so much that you want to have another one right away. You get into your supersonic jet. Where should you and the people planet. You are given the task of coming up with a martian cal celebrating with you travel? From what direction should you endar for a new Mars colony. What might you do? approach? Explain. 16. Suppose you lived in the crater Copernicus on the side of the Moon facing the Earth 17. In a lunar eclipse, does the Moon enter the shadow of the Earth from the east or west side? Explain why PROBLEMS 18. Describe what an observer at the crater Copernicus would see while the Moon is eclipsed. What would the same observer see during what would be a total solar eclipse as viewed from the Earth? 19. The day on Mars is 1.026 Earth days long. The martian year lasts 686.98 Earth days. The two moons of Mars take 0.32 Earth days (for Phobos) and 1.26 Earth days (for Deimos) to circle the 20. a. If a star rises at 8:30 P.m. tonight, approximately what time will it rise two months from now? b. What is the altitude of the Sun at noon on December 22, as seen from a place on the Tropic of Cancer? analogous to leap year to make this calendar work? Can you also 21. Suppose the tilt of the Earth's axis were only 16. What, then, would be the difference in latitude between the Arctic Circle and the Tropic of Cancer? What would be the effect on of 23? 22. Consider a calendar based entirely on the day and the month (the Moon's period from full phase to full phase). How many days are there in a month? Can you figure out a scheme incorporate the idea of a week into your lunar calendar? 27 23. Show that the Gregorian calendar will be in error by one day in about 3300 years. the seasons compared with that produced by the actual tilt Aveni, A. Empires of Time: Calendars, Clocks, and Cultures. Kluepfel, C. "How Accurate Is the Gregorian Calendar?" in Sky 1989, Basic Books. e'1 Telescope, Nov. 1982, p. 417. Bartky I. and Harrison, E. "Standard and Daylight Saving Littmann, M. and Willcox, K. Totality. 1991, U. of Hawaii Press. Time" in Scientific American, May 1979. Fine introduction to science and lore of eclipses. Brown, H. Man and the Stars. 1978, Oxford U. Press. Contains Olson, D. and Doescher, R. "Lincoln and the Almanac Trial" in good sections on the history of astronomical timekeeping. Sky dr Telescope, Aug. 1990, p. 184. How he used the Coco, M. "Not Just Another Pretty Phase" in Astronomy, July Moon. 1994, p. 76. Moon phases explained. Pasachoff J. and Ressmeyer, R. "The Great Eclipse" in Na- DeVorkin, D. Practical Astronomy. 1986, Smithsonian Institu- tional Geographic, May 1992, p. 30. About the July 1991, tion Press. solar eclipse, with spectacular photographs. Gingerich, O. "Notes on the Gregorian Calendar Reform" in Rey, H. The Stars: A New Way to See Them. 1976, Houghton Sky dT Telescope, Dec. 1982, p. 530. Mifflin. Good introduction to time, the seasons, and celes- Harris, J. and Talcott, R. Chasing the Shadow: An Observer's tial coordinates by the author of the "Curious George" chil- Guide to Eclipses. 1994, Kalmbach. dren's stories.  SUGGESTIONS FOR FURTHER READING 79 along the line of sight, the formula for the Doppler shift of light is where ~ is the wavelength emitted by the source, 0~ is the difference between ~ and the wavelength measured by the observer, c is the speed of light, and v is the relative velo-city (speed) of the observer and the source in the line of sight. The variable v is counted as positive if the velocity is one of recession, and negative if it is one of approach. Solv-ing this equation for the velocity we find If a star approaches or recedes from us, the wave-lengths of light in its continuous spectrum appear short-ened or lengthened, respectively, as do those of the dark lines. However, unless its speed is tens of thousands of kilo-meters per second, the star does not appear noticeably bluer or redder than normal. The Doppler shift is thus not easily detected in a continuous spectrum and cannot be measured accurately in such a spectrum. On the other hand, the wavelengths of the absorption lines can be mea-sured accurately, and their Doppler shift is relatively sim-ple to detect. This may sound like a horrible note on which to end the chapter. If all the stars are moving and motion changes the wavelength of each spectral line, won't this be a disas ter for astronomers trying to figure out what elements are present in the stars? After all, it is the precise wavelength (or color) that tells astronomers which lines belong to which element. And we first measure these wavelengths in containers of gas in our laboratories, which are not moving. If every line in a star's spectrum is now shifted by its motion to a different wavelength (color), how can we be sure which lines and which elements we are looking at in a star whose speed we do not know? This situation sounds worse than it really is. As-tronomers rarely judge the presence of an element in an astronomical object by a single line. It is the pattern of lines unique to hydrogen or calcium that enables us to deter-mine that those elements are part of the star or galaxy we are observing. The Doppler effect does not change the pat-tern of lines from a given element-it only shifts the whole pattern slightly toward redder or bluer wavelengths. The shifted pattern is still quite easy to recognize. Best of all, when we do recognize a familiar element's pattern, we get a bonus: The amount the pattern is shifted now tells us the speed of the object in our line of sight. We hope you can see why the training of new as-tronomers includes so much work on learning to decode light (and other electromagnetic radiation). We have seen that a skillful "decoder" can learn the temperature of a star, its elemental composition, and even its speed in a direction toward us or away from us. That's really an impressive bit of decoding for a species that is likely to be looking at the stars from afar for some time to come. SURFING THE WEB SkyView [skyview.gsfc.nasa.gov/skyview.html] ~ Blackbody Radiation Demonstration This multiwavelength "virtual observatory" by Thomas McClynn [www-astro.phast.umass.edu/courseware/vrml/bb/] allows you to dial up any part of the sky and ask to see what it Astronomer Karen Strom has designed this site, which lets you looks like in various bands of the electromagnetic spectmm. You see blackbody curves for different temperatures and then goes can also find specific objects, such as the brightest stars. Don't on to explore some of the radiation laws we mention briefly in expect pictures as detailed as the ones in this book, but it's fun to this chapter. Can get technical in places. see what the sky would look like if you had radio or x-ray eyes. Tutorial on Temperature [www.unidata.ucar.edu/staff/blynds/tmp.html] An introduction to the idea and measurement of temperature, written by astronomer B. D. Lynds, with useful historical infor-mation and applications in the realms of astronomy. SUMMARY  4.1 James Clerk Maxwell showed that whenever charged a little packet of energy, called a photon. The apparent particles change their motion, as they do in every atom and brightness of a source of electromagnetic energy de- molecule, they give off waves of energy Light is one form of creases with increasing distance from that source in pro- this electromagnetic radiation. The wavelength of light portion to the square of the distance, a relationship known determines the color of visible radiation. Wavelength (A) is as the inverse-square law. related to frequency ( f) and the speed of light (c) by the equation c = ~f. Electromagnetic radiation sometimes be- 4.2 The electromagnetic spectrum consists of gamma haves like waves, but at other times it behaves as if it were rays, x rays, and ultravlolet radiadon (all forms of elec- $UMMARY 101 tromagnetic radiation with wavelengths shorter than that of 4.4 Atoms consist of a nucleus containing one or more visible light), visible light, and infrared, microwave, and positively charged protons. All atoms except hydrogen also longer-wave radio radiation (the last three with wavelengths contain one or more neutrons in the nucleus. Negatively longer than that of visible light). Many of these wavelengths charged electrons orbit the nucleus. The number of protons cannot penetrate the layers of the Earth's atmosphere and defines the element (hydrogen, helium, and so on) of the must be observed from space. The emission of electromag- atom. Nuclei with the same number of protons but different netic radiation is intimately connected to the temperature of numbers of neutrons are different isotopes of the same ele- the source. The higher the temperature of a blackbody (an ment. According to the Bohr model of the atom, when an idealized emitter of electromagnetic radiation), the shorter electron moves from one orbit to another closer to the is the wavelength at which the maximum amount of radia- atomic nucleus, a photon is emitted and a spectral emission tion is emitted. The mathematical equation describing this line is formed. Absorption lines are formed when an elec- relationship (Am;,~ = 3 X 106/T) is known as Wien's law. The tron moves to an orbit farther from the nucleus. Since each total energy emitted per square meter increases with atom has its own characteristic set of orbits, each is associ- increasing temperature. The relationship between emitted ated with a unique pattern of spectral lines. energy and temperature (E = 6T 4) is known as the Stefan- 4.5 An atom in its lowest energy level is said to be in the Boltzmann law. ground state. If an electron is in an orbit other than the 4.3 A spectrometer is a device that forms a spectrum, of- least energetic one possible, the atom is said to be excited. ten utilizing the optical phenomenon of dispersion. The If an atom has lost one or more electrons, it is called an ion light from an astronomical source can consist of a continu- and is said to be ionized. ous spectrum, a bright line or emission line spectrum, or 4.6 If an atom is moving toward us when an electron a dark line or absorption line spectrum. Because each el- ement leaves its spectral "signature" in the pattern of lines changes orbits and produces a spectral line, we see that line we observe, spectral analyses reveal the composition of the shifted slightly toward the blue of its normal wavelength in a Sun and stars. spectrum. If the atom is moving away we see the line shifted toward the red. This shift is known as the Doppler effect and can be used to measure the radial velocities of distant objects by the formula v = c(AA/1~).  1 NTER-ACT1 V 1TY Have your group make a list of all the electromagnetic wave technology that you use during the course of a typ-ical day. How many applications of the Doppler effect can your group think of in everyday life? For example, why would the highway patrol find it useful? Have members of your group go home and "read" the face of your radio set at home and then compare notes. What do all the words and symbols mean? What frequen-cies can your radio tune in on? What is the frequency of your favorite radio station? What is its wavelength? Suppose astronomers wanted to send a message to an alien civilization that is living on a planet with an atmosphere very similar to that of Earth's. This message must travel through space, make it through the other planet's atmosphere, and be noticeable by the residents of that planet. Have your group discuss what band of the electromagnetic spectrum might be best for this message and why. (Some people, including an earlier Congress, have warned scientists not to send such messages and reveal the presence of our civilization to a possible hostile cosmos. Do you agree with this concern?) electromagnetic spectrum The complete spectrum of light, including radio waves, infrared, visible light, ultraviolet light, X rays, and gamma rays. Chapter 4 REVIEW QUESTIONS 1. What distinguishes one type of electromagnetic radiation The electromagnetic spectrum consists of gamma rays, x rays, and ultravlolet radiadon. 2. What is a wave? Use the terms wavelength and frequency in give some familiar examples 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. The colors in a spectrum are pure forms of the basic colors red, orange, yellow, green, blue, and violet. 3. What is a blackbody? Is this textbook a blackbody? Why or effect? Explain why. Blackbody: An ideal object that is a perfect absorber of light the name since it would appear completely black if it were cold, and also a perfect emitter of light. Light is emitted by solid objects because those objects are composed of atoms and molecules which can emit and absorb light. They emit light because they are wiggling around due to their heat content (thermal energy). So a blackbody emits a certain spectrum of light that depends only on its temperature. The higher the temperature, the more light energy is emitted and the higher the frequency (shorter the wavelength) of the peak of the spectrum. Photosphere: The surface layer of the sun where the continuous blackbody-type spectrum is produced that we directly observe when we look at the Sun. the brightness of a blackbody decreases with increasing wavelength. The pulsar observations, along with the fact that the radiation is highly polarized, tell us that the pulsar's radiation is not caused by a black body but by something called synchrotron radiation, or non-thermal radiation. 4. Where in an atom would you expect to find electrons? Pro- atoms Consist of a nucleus made from protons and neutrons surrounded by a cloud of electrons. 5. Explain how emission lines and absorption lines are formed. from another? V~hat are the main categories (or bands) of the emission (of light) The process by which matter emits energy in the form of light. emission-line spectrum absorption (of light) The process by which matter absorbs radiative energy. absorption-line spectrum A spectrum that co In what sorts of cosmic objects would you expect to see each? electromagnetic spectrum? 6. Explain how the Doppler effect works for sound waves, and . your definition. the Doppler effect on sound; it is especially easy to notice when you stand near train tracks and listen to the whistle of a train. As the train approaches, its whistle is relatively high pitched; as it recedes, the sound is relatively low pitched. Just as the train passes by, you hear the dramatic change from high to low pitch-a sort of "weeeeeeee-oooooooooh" sound. You can visualize the Doppler effect by imagining that the train's sound waves are bunched up ahead of it, resulting in shorter wavelengths and the high pitch you hear as the train approaches. Behind the train, the sound waves are stretched out to longer wavelengths, resulting in the low pitch you hear as the train recedes. Doppler effect (shift) The effect that shifts the wavelengths of spectral features in objects that are moving toward or away from the observer. 7. What kind of motion for a star does not produce a Doppler why not? How about your little brother's head? How does the g, energy emitted by a blackbody depend on its temperature? Describe how Bohr's model used the work of Rutherford and Maxvvell. Why was Bohr's model considered a radical no factor determining the color of a star is its temperature. Which is hotter, a blue star or a red one? Explain. tion? tons? Neutrons? 102 CHAPTER 4 RADIATION AND SPECTRA  THOUGHT 'QUE'S'TIONS 9. Make a list of some of the many practical consequences of Maxwell's theory of electromagnetic waves (television would be one example). 14. Water faucets are often labeled with a red dot for hot water and a blue dot for cold. Given Wien's law, does this labeling make sense? 10. Suppose the Sun radiates like a blackbody. Explain how you would calculate the total amount of energy radiated into space by the Sun each second. What information about the Sun would you need to make this calculation? 11. What type of electromagnetic radiation is best suited to ob- serving a star with a temperature of 5800 K? 15. The planet Jupiter appears yellowish, and Mars is red. Does this mean that Mars is cooler than Jupiter? Explain your answer. 16. Suppose you are standing at the exact center of a park sur- a. rounded by a circular road. An ambulance drives completely b. a gas heated to a temperature of 1 million K? around this road, with siren blaring. How does the pitch of the c. a person on a dark night? siren change as it circles around you? 12. Why is it dangerous to be exposed to x rays but not (or at least much less) dangerous to be exposed to radio waves? 13. Go outside on a clear night and look carefully at the bright- est stars. Some should look red and others blue. The primary 17, How could you measure the Earth's orbital speed by pho- tographing the spectrum of a star at various times throughout the year? (Hint: Suppose the star lies in the plane of the Earth's orbit.) PROBLEMS  18. "Tidal waves," or tsunamis, are waves caused by earth- perature of 2900 K. Which is brighter? How much brighter is it? quakes that travel rapidly through the ocean. If tsunamis travel 21. If the emitted infrared radiation from Pluto has a wave- at the speed of 600 km/h and approach a shore at the rate of one length of maximum intensity at 50,000 nm (50 Rm), what is the wave crest every 15 min, what would be the distance between temperature of Pluto (assuming it behaves like a blackbody)? those wave crests at sea? 19. How many times brighter or fainter would a star appear if it were moved to a. twice its present distance? b. ten times its present distance? e. half its present distance? 22. What is the temperature of a star whose maximum light is emitted at a wavelength of 290 nm? 23. Suppose that a spectral line of some element, normally at 500 run, is observed in the spectrum of a star to be at 500.1 nm. How fast is the star moving toward or away from the Earth? 20. Two stars with identical diameters are the same distance away. One has a temperature of 5800 K; the other has a tem- Defense to carry out worldwide surveillance for possible space science, and the Russian space program, once the explosions of nuclear bombs, which emit gamma rays. ) The most ambitious of any nation, has been devastated by bud- Compton Gamma-Ray Observatory (Figure 5.24) has now getary problems. However, the spectacular success of cataloged thousands of the high-energy bursts or flashes HST and the other space observatories should assure that from all over the sky. astronomy will continue to have a place in space. The em- The worldwide reassessment of government priori- phasis is expected to be on smaller, cheaper satellites, but ties in the 1990s has had an impact on astronomy. Both the number of good ideas for astronomy space missions NASA and its European counterpart, the European Space continues to grow. Agency (ESA), have scaled back their commitments to SURFING THE WEB History of High-EnergyAstrophysics ground and in space are given in Tables 5.1 through 5.3. [heasarc.gsfc.nasa.gov/docs/heasarc/headates/ heahistory.html] Early Radio Astronomy The staff of the Laboratory for High-Energy Astrophysics at [www.nrao.edu/intro/ham.eonnection.html] NASAs Goddard Spaee Flight Center has assembled a good A brief summary of the history of radio astronomy with empha- chronology and set of web links detailing all major experiments sis on the connection with amateur (or "ham") radio. The rest of and space missions relevant to the study of gamma rays, x rays, the site, maintained by the National Radio Astronomy Observa- or ultraviolet waves from space. Find an instrument you are tory, also has some useful background information, along with looking for (including some that are not yet launched), and you more technical pages for astronomers who use the observatory's can go directly to its home page. facilities around the country (students can look for the button called Radio Astronomy Fundamentals). ~ Sites with Information on BuyingYour Own Telescope: Web sites for the major telescopes and observatories on the Whispers from the Cosmos [www.ncsa.uiuc.edu/Cyberia/Bima/BimaHome.html] This on-line "exhibit" about radio astronomy in general, and the Berkeley-Illinois-Maryland Association array of radio telescopes in particular, contains some useful background information about how radio observations can help us learn about a variety of cosmic objects and processes. Astronomy magazine: [www.kalmbach.com/astro/Hobby/ Beginner/firstscope/firstscope.html] Sky dT Telescope magazine: [www.skypub.eom/tips/ telescopes/telescopes.html] Frequently Asked Questions about Telescope Buying (by amateur astronomer Dennis Bishop): [www-personal. umich.edu/-dnash/saafaq/faq.html]  5. I The astronomical telescope collects light and forms an clear weather, dark skies, low water vapor, and excellent at- image, using a convex lens in a refractor or a concave mir- mospheric seeing (low atmospheric turbulence). A new ror in a reflector to bring it to a focus. The distance from generation of large instruments has been constructed in the the lens or mirror to the focus is called the focal length. 1990s, including the 10-m Keck telescopes at Mauna Kea The diameter, or aperture, of the telescope determines the and the four 8-m instruments that constitute the European brightness and resolution of the image. Resolution is usu- Very Large Telescope in Chile. ally expressed in units of arcseconds. 5.4 In the 1930s, radio astronomy was pioneered by Jansky 5.2 Optical (visible light) detectors include the eye, photo- and Reber. A radio telescope is basically a radio antenna (of- graphic film, and the charge-coupled device (CCD) de- ten a large curved dish) connected to a receiver. Significantly tector. Detectors sensitive to infrared radiation must be enhanced resolution can be obtained with interferometers, cooled to very low temperatures. A spectrometer disperses including interferometer arrays like the 27-element VLA. the light into a spectrum to be recorded for detailed analysis. Expanding to very long baseline interferometers, radio astronomers can achieve resolutions as good as 0.0001 arcsec. 5.3 Telescopes are housed in domes and controlled by Radar astronomy involves transmitting as well as receiving. computers. Observatory sites must be carefully chosen for The largest radar telescope is the 305-m bowl at Arecibo. Orbiting Astronomical Observatories [www.seds.orghspider/oaos/oaos.html] A good annotated list, with fine links, of the telescopes in Earth orbit. SUMMARY 125 5.5 Infrared observations are made with telescopes aboard largest aperture instrument in space is the Hubble Space aircraft and in space, as well as from ground-based facilities Telescope (HST). The Compton Gamma-Ray Observatory on dry mountain peaks. Ultraviolet, x-ray, and gamma-ray (GRO) is the most sophisticated instrument for observing observations must be made from above the atmosphere. high-energy gamma rays ever built. Many additional astro- Many orbiting observatories have been flown to observe in nomical satellites are planned, although most are smaller these bands of the spectrum in the last few decades. The (and less expensive) than HST. INTER-ACTIVITY Most large telescopes get many more proposals for ob- D Make a list of all the ways that an observing session at a serving projects than there is night observing time avail- large optical telescope and a large radio telescope might able in the course of a year. Suppose your group is the differ. (One hint: Bear in mind that because the Sun is not telescope time allocation committee reporting to an ob- especially bright at many radio wavelengths, observations servatory director. What criteria would you use in decid- with radio telescopes can often be done during the day.) ing how to give out time on the telescope? What steps E Another "environmental threat" to astronomy (besides could you take to make sure all your colleagues thought light pollution) comes from the encroachment of terres- the process was fair and people would still talk to you at trial communications into the "channels"-wavelengths future astronomy meetings? and frequencies-previously reserved for radio astron-omy. For example, the demand for cellular phones means that there could be more and more radio channels, used for this purpose. Thus the faint signals from cosmic radio sources will be drowned in a sea of earthly conversation (translated and sent as radio waves). Assume your group is a Congressional committee being lobbied by both radio astronomers who want to save some clear channels for doing astronomy and the companies that stand to make a lot of money from expanding cellular phone use. What ar-guments would sway you to each side? [For a real-world example of where this issue is being debated, see Science magazine, Nov. 28, 1997, p. 1569.] Your group is a committee of nervous astronomers, about to make a proposal to the government of a smaller Euro-pean country to chip in to build the world's largest telescope in the high dry desert of the Chilean Andes mountains. You expect the government ministers to be very skeptical about supporting this project. What argu-ments would you make to convince them to participate? The same government ministers we met in activity B ask you to draw up a list of the pros and cons of having the world's largest telescope in the mountains of Chile (in-stead of a mountain in Europe). What would your group list as a pro and as a con? Chapter 5 Review Questions I. Name the two spectral windows through which electromag- netic radiation reaches the surface of the Earth, and describe the largest aperture telescope currently in use for each window The apparent brightness of a star is called the apparent magnitude and that is what is measured by a telescope: how much energy does the star put into the telescope's collecting area per second. 6. Radio and radar observations are often made with the same antenna, but otherwise they are very different techniques. . Compare and contrast radio and radar astronomy in terms of the equipment needed, the methods used, and the kind of re- The 43-m telescope can achieve resolution of about 1' at a wavelength of 1 cm. The best angular resolution obtainable with a single radio telesscope is about 10" (for the largest instruments operating at millimeter wavelengths), at least 10 times coarser than the capabilities of the largest optical mirrors. 2. List the six bands into which we commonly divide the elec- tromagnetic spectrum, and list the largest-aperture telescope sults obtained. currently in use in each band. Types of Electromagnetic radiation Gamma rays X-rays Ultraviolet Visible Infraared Radio 700nm 600 nm 500 nm 400 nm electromagnetic spectrum The complete range of electromagnetic radiation, from radio waves to gamma rays, including the visible spectrum. All types of electromagnetic radiation are basically the same phenomenon, differing only by wavelength, and all move at the speed of light. 3. When astronomers discuss the apertures of their telescopes, they say bigger is better. Explain why. Soft X-ray Telescope X-ray images In a Newtonian telescope another type of a reflecting telescope. The light is intercepted by a flat secondary mirror before it reaches the prime focus and deflected 90, usually to an eyepiece at the side of the instrument. This is a popular design for smaller reflecting telescopes, such as those used by amateur astronomers. Each design of the four telescopes uses a primary mirror at the bottom of the telescope to capture radiation, which is then directed along different paths for analysis. Radio telescopes It also depends on the wavelength of the radiation. A very long wavelengths, like those of radio waves, im- ages become fuzzy because of the large diffraction fringes. As with an optical telescope the only way to improve the resolving power is to build a bigger tele- scope. Consequently radio telescopes must be quite large. Because there are two ways to focus light, there are two kinds of astronomical telescopes. Refracting telescopes use a large lens to gather and focus the light. Radio telescopes are built large in part because cosmic radio sources are extremely faint. Cosmic objects across the sky Can see and study a astronomical object like a Radio Galaxy. Visible image of the radio galaxy Centaurus A, with the radio emission from the region superimposed (in false color, with red indicating greatest radio intensity, blue the least). The resolution of the optical image is about 1", that of the radio map is 12". The angular resolution of ground-based optical telescopes is more seriously limited by Earth's turbulent atmosphere than by diffraction. Radio astronomers can sometimes overcome the problem of poor angular resolution by using a technique known as interferometry. This technique makes it possible to produce radio images of much higher angular resolution than can be achieved with even the best optical telescopes on Earth or in space. Optical Telescopes Astronomers build optical telescopes to gather light and focus it into sharp images. This requires sophisti- cated optical and mechanical designs, and it leads astronomers to build gigantic telescopes on the tops of high mountains. Radio Telescopes in deep valleys detect weak radio sources. 4. What are the properties of an image, and what factors deter- and how was it solved? mine each? the smaller the minimum separation, the more detail you can see when looking at Mars. Big telescopes are important because they allow us to resolve images that are really close together so detail can be better seen. However, the Earth's atmosphere blurs images because it is turbulent. in practice, the ability of a telescope to see detail is limited by the earth's atmosphere. This is why the Hubble Space Telescope is so important because it is above the atmosphere and is not affected by the distortion caused by it. Resolution is given by 4.56/D (inches) or 10/D(cm). The larger the objective, the better the telescope can resolve detail. This is the maximum resolution this objective can possibly give. For this reason, for telescopes larger than about 16-inches, it is not the limitations of the objective size but of the atmopshere that limits resolution. Only if a large telescope (size greater than about 16-inch) is above the atmosphere will the theoretically possible resolving power be met. Properties of Telescopes: Light Gather Power (LGP) measures the ability of the objective to gather light compared with the human eye. It is given by Area of objective / area of eye ; which is approximated by D2 / (1/5) 2 = 25D 2 if D is measured in inches. Diameter LGP 1-inch 25 6-inches 900 8-inches 1600 27-inches 18,225 200-inch (5-meter) 1,000,000 4-inch (10-meter in Hawaii) 4,000,000 big telescopes are important because they allow us to see very faint objects. Resolving Power (Resolution) 5. Compare the eye, photographic film, and CCDs as detectors resolution comparable to what astronomers working with vis- for light. What are the advantages and disadvantages of each? ible light can achieve. the advantages of a CCD over a photo- graphic plate Our eyes can see light with an angular resolution of about 1' equivalent to about a third of a millimeter at arm's length. The first advantage is CCD's are much more efficient than photographic plates, recording as many as 75 percent of the photons striking them, compared with less than five percent for photographic methods. This means that a CCD instrument can image objects 10 to 20 times fainter-or the same object 10 to 20 times faster-than can a photographic plate. The second advantage is CCDs produce a faithful representation of an image in a digital format that can be placed directly on magnetic tape or disk, or even sent across a computer network to an observer's home institution for analysis. the basic parts of a telescope Objective Lens Eyepiece Focus Knob a long tube Viewfinder Fine-Adjustment Knobs Lock Levers lens mirror radio astronomers can combine two or more radio telescopes to improve the resolving power. Such a linkup of radio telescopes is called a radio interferometer and has the resolving power of a radio telescope whose diameter equals the separation of the radio telescopes. For example the Very Large Array radio interferometer uses multiple radio dishes spread across the New Mexico-Arizona desert to simulate a single radio telescope with a diameter of 40 km. 25 miles. It can produce radio maps with a resolution better than 1 second of arc. 7. Why do astronomers place telescopes in Earth orbit? What are the advantages for different spectral regions? atmosphere turbulence and light pollution. the Earth's atmosphere absorbs X-rays, solar X-rays can only be studied from spacecraft above our atmosphere. the ability of a telescope to see detail is limited by the earth's atmosphere. This is why the Hubble Space Telescope is so important because it is above the atmosphere and is not affected by the distortion caused by it. Resolution is given by 4.56/D (inches) or 10/D(cm). The larger the objective, the better the telescope can resolve detail. This is the maximum resolution this objective can possibly give. 36 inch telescope to make infrared observations. Earth's atmosphere opaque to X-rays, so observations must be made from space. Light pollution on Earth effects viewing stars in outer space. 8. What was the problem with the Hubble Space Telescope? 9. Describe the techniques radio astronomers use to obtain a Radio telescopes are built large in part because cosmic radio sources are extremely faint. Cosmic objects across the sky Can see and study a astronomical object like a Radio Galaxy. Visible image of the radio galaxy Centaurus A, with the radio emission from the region superimposed (in false color, with red indicating greatest radio intensity, blue the least). The resolution of the optical image is about 1", that of the radio map is 12". The angular resolution of ground-based optical telescopes is more seriously limited by Earth's turbulent atmosphere than by diffraction. Radio astronomers can sometimes overcome the problem of poor angular resolution by using a technique known as interferometry. This technique makes it possible to produce radio images of much higher angular resolution than can be achieved with even the best optical telescopes on Earth or in space. Despite their unimpressive optical appearance, the large distances implied by quasar redshifts mean that these faint stars are in fact the brightest known objects in the universe! 3C 273, for example, has a luminosity of about 1040 W. try to make contact with extraterrestrials using electromagnetic radiation, the fastest known means of transferring information from one place to another. Because light and other short-wavelength radiation are heavily scattered while moving through dusty interstellar space, long-wavelength radio radiation seems to be the best choice. We do not attempt to broadcast to all nearby candidate stars, however-that would be far too expensive and inefficient. Instead, radio telescopes on Earth listen passively for radio signals emitted by other civilizations. Optical astronomers can observe only at night. Optical telescopes on Earth can see angular detail down to about 1" or few arc second. THOUGHT QUESTIONS 10. What happens to the image produced by a lens if the lens is 12. Fifty years ago, the astronomers on the staff of Mount Wil- l, down" with an iris diaphragm-a device that covers son and ~Palomar Observatories each received about 60 nights its periphery? per year for their observing programs. Today an astronomer 11. What would be the properties of an ideal astronomical de- feels fortunate to get 10 nights per year on a large telescope. tector? How closely do the actual properties of a CCD ap- Can you suggest some reasons for this change? proach this ideal? . 126 CHAPTER 5 ASTRONOMICAL INSTRUMENTS I 3. The largest observatory complex in the world is on Mauna Kea in Hawaii, at an altitude of 4.2 km. This is by no means the tallest mountain on Earth. What are some factors as- tronomers consider when selecting an observatory site? Don't forget practical ones. Should astronomers, for example, con- sider building an observatory on Mount McKinley (Denali) or short wavelengths? Mount Everest? 1 I 4. Another site recently developed for astronomy is the Antarctic plateau. Discuss its advantages and disadvantages. 15. Suppose you are looking for sites for an optical observatory, an infrared observatory and an x-ray observatory What are the main criteria of excellence for each? What sites are actually considered the best today? I6. Radio astronomy involves wavelengths much longer than those of visible light, and many orbiting observatories have probed the universe for radiation of very short wavelengths. What sorts of objects and physical conditions would you expect to be associated with radiation emissions of very long and very 17. The dean of a university located near the ocean proposes building an infrared telescope right on campus and operating it in a nice heated dome so that astronomers will be comfortable on cold winter nights. Criticize this proposal, giving your reasoning. PROBLEMS 18. The resolution of a radio interferometer is proportional to telescope? Per hour? Per minute? Can you think of any other the maximum spacing of the antennas. The VLA, with a maxi- activities that have such a high associated cost, in dollars per mum antenna separation of 36 km, achieves a resolution of hour? 1 arcsec at a wavcaength of 6 cm. 20. The HST cost about $1.7 billion for construction and $300 a. What is the resolution of a very long baseline interfer- million for its Shuttle launch, and it costs $250 million per year ometer at this wavelength if the antennas are separated to operate. If the telescope lasts a total of ten years, what is the by 3600 km? cost per year? Per day? If the telescope can be used just 30 per- b. What is the resolution of the VLBA, with antennas on cent of the time for actual observations, what is the cost per opposite sides of the Earth? hour and per minute for the astronomer's observing time on this 19. A typical large telescope today requires about $4 million instrument? per year to operate. What is the cost per night to use such a What it's like to use the telescope, and what work is being done with it. now being built or planned on the ground. $UGGESTIONS FOR FURTHER READING 127 SURFING THE WEB General Information Sites about the Sun: 12 Images of the Sun Today The Nine Planets Site: [seds.lpl.arizona.edu/niiieplanets/ [umbra.naseom.nasa.gov/images/latest.html] nineplanets/sol.html] Want to see what the Sun looks like today? This handy site col- Views of the Solar System Site: [wwv.hawastsoc.org/solar/ lects images from all over the Web in many wavelengths and has eng/sun.htm] handy links to the sites that store images of the Sun. Sites for Space Missions About the Sun The Stanford SOLAR Center [solar-center.stanford.edu/] An excellent place to begin your exploration of the Sun, with a treasure trove of solar information, including background, SOHO and other spacecraft results, images, links, activities, and even a section on solar folklore. Ulysses (flies over the Sun's poles): [ulysses.jpl.nasa.gov/ULSHOME.html] SOHO (an observatory with many instruments): [sohowww.nascom.nasa.gov/] TRACE (extreme-UV observations): [www.lmsal.com/TRACE/welcome.html] NASA Goddard Solar Flares Pages Yohkoh Soft X-ray Telescope: [hesperia.gsfc.nasa.govJsftheory/yohkoh.htm] [www.lmsal.com/SXT/homepage.html] An introduction to solar flares, whv we must study them using spacecraft, and what we learned from the Japanese Yohkoh (Sunbeam) mission.  SURFING THE WEB 147 - - rnnlax saa.z ap uoilhm maj r. jo sa.zn;e.ra uua; 'slea.% Z-( loj ;sel o; plus ualjo si unS ay; lo alo,6 .ti;ixyoe oyau q;LNN `EU010J )Ili n11r SUMMARY 6.1 The Sun, our star, is surrounded by a number of layers 6.3 The number of visible sunspots varies according to a that make up the solar atmosphere. In order of increasing sunspot cycle that averages 11 years in length. Spots fre- distance from the center of the Sun, they are the photos- quently occur in pairs. During a given 11-year cycle, all phere, with a temperature that ranges from 4500 K to leading spots in the northern hemisphere have the same about 6800 K; the chromosphere, with a typical tempera- magnetic polarity, while all leading spots in the southern ture of 104 K; the transition region, a zone that may be hemisphere have the opposite polarity. In the subsequent 11- only a few kilometers thick, where the temperature in- year cycle, the polarity reverses. For this reason, the mag- creases rapidly from 104 K to 106 K; and the corona, with netic activity cycle of the Sun is often said to last for 22 years. temperatures of a few million degrees Kelvin. Solar wind 6.4 Sunspots, solar flares, prominences, and bright re- particles stream out into the solar system through coronal gions, including plages, tend to occur in active regions-holes. Hydrogen and helium together make up 98 percent of the mass of the Sun, whose composition is much more characteristic of the universe at large than is a planet like the Earth. that is, in places on the Sun with the same latitude and longitude but at different heights in the atmosphere. These active regions are connected with the Sun's powerful mag-netic field. 6.2 The Sun's surface is mottled with upwelling currents seen as hot, bright granules. Sunspots are dark regions where the temperature is up to 1500 K cooler than in the surrounding photosphere. Their motion across the Sun's disk allows us to calculate how fast the Sun turns on its axis. The Sun rotates more rapidly at its equator, where the rota-tion period is about 25 days, than near the poles, where the period is slightly greater than 36 days. 6.5 Over long periods of time (100 years or more), there are changes in the level of solar activity and the number of sunspots seen at solar maximum. For example, the number of sunspots was unusually low from 1645 to 1715, a period now called the Maunder Minimum. There is strong histori-cal evidence that the Earth is cooler when the number of sunspots is unusually low for several decades. INTER-ACTIVITY Have your group make a list of all the ways the Sun af- either because of changes in the Sun or because of fects your life on Earth. How long a list can you come up greenhouse warming, one effect would be an increase in with? (Be sure you consider the everyday effects as well the rate of melting of the polar ice caps. How would this as the unusual effects due to solar activity) affect modern civilization? Long before the nature of the Sun was fully under- D Suppose we experience another Maunder Minimum on stood, astronomer (and planet discoverer) William Earth, with a drop in the average temperatures. Have Herschel (1738-1822) proposed that the hot Sun may ~ your group discuss how this would affect civilization and have a cool interior and may be inhabited. Have your international politics. Make a list of the most serious ef- group discuss this proposal and come up with modern fects you can think of. arguments against it. E Watching sunspots move across the disk of the Sun is In the text we discuss how the migration of Europeans one way to show that our star rotates on its axis. Can to North American was apparently affected by climate your group come up with other ways to show the Sun's change. If the Earth were to become significantly hotter, rotation? Chapter 6 REVIEW QUESTIONS I. Describe the main differences between the composition of the Earth and that of the Sun. 2. Make a sketch of the Sun's atmosphere showing the loca-tions of the photosphere, chromosphere, and corona. What is the approximate temperature of each of these regions? 3. Why do sunspots look dark? sunspots Blotches on the surface of the Sun that appear darker than surrounding regions. 4. What is the Zeeman effect, and what does it tell us about the Sun? 5. Describe three different types of solar activity. 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. sunspots Blotches on the surface of the Sun that appear darker than surrounding regions. solar prominences Vaulted loops of hot gas that rise above the Sun's surface and follow magnetic field lines. solar flares Huge and sudden releases of energy on the solar surface, probably caused when energy stored in magnetic fields is suddenly released. 6. How does activity on the Sun affect the Earth? Can effect telecommunications. solar wind A stream of charged particles ejected from the Sun. 7. Which aspects of the Sun's activity cycle have a period of about 11 years? Which vary during intervals of about 22 years? the number of sunspots gradually rises and falls in a sunspot cycle with a period of about 11 years the entire magnetic field of the Sun flip-flops every 11 years. These magnetic reversals hint that the sunspot cycle is related to the generation of magnetic fields on the Sun. They also tell us that the complete magnetic cycle of the Sun, called the solar cycle, really averages 22 years, since it takes two 11-year cycles before the magnetic field is back the way it started. 8. Summarize the evidence indicating that over several decades or more there have been variations in the level of solar activity. Chemical burning was ruled out because it cannot generate enough energy to account for the rate of radiation observed from the Sun's surface. A more plausible hypothesis of the late 1800s suggested that 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. weather Describes the ever-varying combination of winds, clouds, temperature, and pressure in a planet's troposphere. 148 CHAPTER 6 THE SUN: A GARDEN-VARIETY STAR THOUGHT QUESTIONS 9. Use the data in Table 6.1 to confirm that the density of the forms that extends from a latitude of 30 to a latitude of 40 Sun is 1.4 g/cm3. What kinds of materials have similar densities? along a fixed line of longitude. How will the appearance of that One such material is ice. How do you know that the Sun is not sunspot change as the Sun rotates? made of ice? 12. Suppose you live in northern Canada and an extremely 10. If the rotation period of the Sun is determined by observ- strong flare is reported on the Sun. What precautions might you ing the apparent motions of sunspots, must any correction be take? What could compensate you for your troubles? made for the orbital motion of the Earth? If so, explain what the 13, Give some reasons for why is it difficult to determine correction is and how it arises. If not, explain why the Earth's whether or not small changes in the amount of energy radiated orbital revolution does not affect the observations. by the Sun have an effect on the Earth's climate? 11. Suppose an (extremely hypothetical) elongated sunspot PROBLEMS 14. Suppose you observe a major solar flare while astronauts 17. Suppose an eruptive prominence rises at a speed of 150 km/s. are orbiting the Earth in the Shuttle. Use the data in Section 6.1 If it does not change speed, how far from the photosphere will to calculate how long it will be before the charged particles it extend after 3 hours? How does this distance compare with ejected from the Sun during the flare reach the Shuttle. the diameter of the Earth? I 5. Table 6.2 shows that 92 percent of the atoms in the Sun are 18. From the Doppler shifts of the spectral lines in the light hydrogen but only 73.4 percent of the mass of the Sun is made coming from the east and west edges of the Sun, it is found that up of hydrogen. Explain this difference. the radial velocities of the two edges differ by about 4 km/s. 16. Nearly all the light from the Sun emerges from a layer that Find the approximate period of rotation of the Sun. is only about 400 km thick. What fraction is this of the radius of the Sun? Suppose we could see light emerging directly from a 19. From the information in Figure 6.19, calculate the speed of the particles sent toward the spacecraft by this coronal mass layer that was 300,000 km thick. Would the Sun appear to have ejection. a sharp edge? Chapter 7 What the experiment showed was that the number of muon neutrinos coming up through the Earth to the de-tector was smaller than the number that reached it when the Sun was overhead. These data suggest that the muon neutrinos change to another type of neutrino on their way through the Earth. Those that travel only through the Earth's atmosphere don't have time to undergo this change. Since neutrinos can change type only if they have mass, this experiment is the first persuasive evidence that at least some kinds of neutrinos do have mass. Unfortunately this experiment does not tell us whether the electron neutrinos produced by the Sun have mass. The Japanese detector sees equal numbers of electron neutrinos in all directions. All this really tells us is that the electron neutrinos do not change from one type to another as they pass through the Earth. They still might change type on their long journey from the interior of the Sun through the vacuum of space to the Earth. To test this idea, scientists are now trying to determine whether the number of solar neutrinos arriving at the detector varies with the seasons. Remember that the Earth is about 3 percent closer to the Sun in winter than in summer, and this differ-ence may be enough to affect our neutrino counts. As you can see, ideas in science really do change as we are able to do better and better experiments. For decades, students were taught that the neutrino had no mass. When it was announced at a scientific conference in Japan in 1998 that the union neutrino apparently does have mass, the au-dience stood and cheered. New experiments over the next decade should help determine whether the other types of neutrinos also have mass and if so how much. And that, in turn, may help us solve the mystery of the missing solar neutrinos and understand even better just how the Sun produces its vast output of energy. SURFtNG THE WEB Albert Einstein Online U GONG Project Site [www.westegg.com/einstein /] [www.gong.noao.edu/index.html] S. Morgan Friedman of the University of Pennsylvania has as- The Global Oscillations Network Group (GONG) is an interna- sembled this very useful Web site that has a link to just about tional collaboration for helioseismology. Their Web site gives every other Web site about Einstein. Includes information about background information, news updates, images, movies, links, Einstein's life, books and papers he wrote, collections of quotes, etc. pictures, related science topics, and even Einstein T-shirts. The Super-Kamiokande Neutrino Detector Site Fusion: Physics of a Fundamental Energy Source [www.ps.uci.edu/-superk/sk-info.html] [fusedweb.pppl.gov/CPEP/Chart.html] Information about the detector in Japan that found that some This is a brief introductory Web-based "course" on fusion-in neutrinos may have mass, with pictures, background infor- the stars and on the Earth-with interesting images and mation, and many neutrino experiment links. (See also the site graphs. It is not for the real beginner, but will reward the seri- at the University of Washington: [www.phys.washington.edu/ ous reader with good information. -superk/]) Plasma Physics Laboratory Site [iPPexPPPIgov/ippex/] You can find a number of nontechnical pages about the quest for controlled fusion on Earth at this Princeton University site. SUMMARY 7.1 The Sun produces an enormous amount of energy 7.2 Solar energy is produced by interactions of elemen- every second. The Earth is 4.5 billion years old, so the Sun tary particles-that is, protons, neutrons, electrons, and must have been shining for at least that long. Neither chem- neutrinos. Specifically, the source of the Sun's energy is ical burning nor gravitational contraction can account for the the fusion of hydrogen to form helium. The series of reac- energy radiated by the Sun during all this time. tions required to convert hydrogen to helium is called the 166 CHAPTER 7 THE SUN: A NUCLEAR POWERHOUSE  proton-proton cycle. A helium atom is about 0.71 percent pressure, temperature, mass, and luminosity depend on dis- less massive than the four hydrogen atoms that combine to tance from the center of the Sun. form it, and that lost mass is converted to energy (with the ~.4 Studies of solar oscillations (solar seismology) and amount of energy given by the formula E = mc ). neutrinos can provide observational data about the Sun's in- 7.3 Even though we cannot see inside the Sun, it is possi- terior. The technique of solar seismology has so far shown ble to calculate what its interior must be like. As input for that the composition of the interior is much like that of the these calculations, we use what we know about the Sun. It is surface (except in the core, where some of the original hy- made entirely of hot gas. Apart from some very tiny changes, drogen has been converted to helium), and that the convec- the Sun is neither expanding nor contracting (it is in hydro- tion zone extends 30 percent of the way from the Sun's static equilibrium), but instead puts out energy at a con- surface to its center. Our solar models predict that we should stant rate. Fusion of hydrogen occurs in the center of the be able to detect more neutrinos than we do. This result may Sun, and the energy generated is carried to the surface by indicate that the mass of the neutrino is not exactly zero, and radiation and convection. A solar model describes the ongoing experiments are beginning to confirm this idea. structure of the Sun's interior. Specifically, it describes how INTER-ACTIVITY W sites are selected carefully, the Sun can be observed all but about 10 percent of the time with only six observing stations. What factors have to be taken into considera-tion in selecting the observing sites? Can you suggest six general geographic locations that would optimize the amount of time that the Sun can be observed? Check Solar astronomers can learn more about the Sun's inte- your answer by looking at the GONG Web site. rior if they can observe the oscillations 24 hours each f What would it be like if we actually manage to get con- day. That means that they cannot have their observa- trolled fusion on Earth to be economically feasible? If tions interrupted by the day/night cycle. Such an exper- the hydrogen in water becomes the fuel for releasing iment, called the GONG (Global Oscillation Network enormous amounts of energy, have your group discuss Group) project, has been set up. To save money this ex- how this would affect the world economy and interna- periment was designed to make use of the minimum tional politics. (Think of the role that oil and natural gas possible number of telescopes. It turns out that if the deposits now play on the world scene.) The text discusses that meteorites falling into the Sun could not be the source of the Sun's energy because the necessary increase in the mass of the Sun would lengthen the Earth's orbital period by 2 s per year. Have your group discuss what effects this would cause as the centuries went on. Chapter 7 REVIEW QUESTIONS 1 . How do we know the age of the Sun? 2. Explain how we know that the Sun's energy is not supplied either by chemical burning, as in fires here on Earth, or by grav- itational contraction (shrinking). The Sun generates energy by nuclear fusion, a source so efficient that the Sun can shine for about 10 billion years. Because the Sun is only 4.6 billion years old today. 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. 3. What is the ultimate source of energy that makes the Sun shine? 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. nuclear fusion. Hydrogen and Helium gas. 4. How is a neutrino different from a neutron? List all the ways you can think of. neutrino A type of fundamental particle that has extremely low mass and responds only to the weak force; neutrinos are leptons and come in three types-electron neutrinos, mu neutrinos, and tau neutrinos. neutrons Particles with no electrical charge found in atomic nuclei, built from three quarks. 5. Describe in your own words what is meant by the state- ment that the Sun is in hydrostatic equilibrium. 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. gravitational equilibrium Describes a state of balance in which the force of gravity pulling inward is precisely counteracted by pressure pushing outward. 6. Two astronomy students travel to South Dakota. One stands on the Earth's surface and enjoys some sunshine. At the same time, the other descends into a gold mine where neutri- nos are detected, arriving in time to measure the creation of a new radioactive argon nucleus. Although the photon at the sur- face and the neutrinos in the mine arrive at the same time, they have had very different histories. Describe the differences. ~, Why do measurements of the number of neutrinos emitted by the Sun tell us about conditions deep in the solar interior? the Homestake experiment detected only about one-third of the predicted number of neutrinos. 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. neutrinos come in three types: electron neutrinos, muon neutrinos, and tau neutrinos [Section S4.2]. Fusion reactions in the Sun produce only electron neutrinos, and most solar neutrino detectors can detect only electron neutrinos. g. Do neutrinos have mass? Describe the evidence for your answer. Yes. Neutrinos are small. Chapter 7 THOUGHT QUESTIONS 9. A friend who has not had the benefit of an astronomy course suggests that the Sun must be full of burning coal to shine as brightly as it does. List as many arguments as you can against this hypothesis. 10. Which of the following transformations is (are) fusion and which is (are) fission? (See Appendix 11 for a list of the ele- ments.) a. helium to carbon b. carbon to iron c. uranium to lead e. oxygen to neon 14. What mechanism transfers heat away from the surface of the Moon? If the Moon is losing energy in this way, why does it not simply become colder and colder? I 5. Suppose you are standing a few feet away from a bonfire on a cold fall evening. Your face begins to feel hot. What is the mechanism that transfers heat from the fire to your face? (Hint: Is the air between you and the fire hotter or cooler than your face?) 16. Give some everyday examples of the transport of heat by convection and by radiation. d. boron to carbon 17. Suppose the proton-proton cycle in the Sun were to slow down suddenly and generate energy at only 95 percent of its 1 I . Why is a higher temperature required to fuse hydrogen to current rate. Would an observer on the Earth see an immediate helium by means of the CNO cycle than is required by the decrease in the Sun's brightness? Would she immediately see a process that occurs in the Sun, which involves only isotopes of decrease in the number of neutrinos emitted by the Sun? hydrogen and helium? 18. Do you think that nuclear fusion takes place in the atmo- spheres of stars? Why or why not? I 2. The Earth s atmosphere is m hydrostatic eqmhbnum. What this means is that the pressure at any point in the atmosphere must be high enough to support the weight of air above it. How would you expect the pressure on Mt. Everest to differ from the pressure in your classroom? Explain why 20. Suppose a proton interacted with another proton an aver-age of once every 100 million years rather than once every 14 I 3. Explain what it means when we say that the Earth's oceans billion years. In general terms, how do you think the structure are in hydrostatic equilibrium. Now suppose you are a scuba of the Sun would change? (Hint: Think about what determines diver. Would you expect the pressure to increase or decrease as the pressure in the core of the Sun.) you dive below the surface to a depth of 200 ft? Why? PROBLEMS 21. According to the text, a contraction of the Sun by 40 m particular oscillation mode. What percent is this of the Sun's per year would be enough to account for its current output of total radius? energy Suppose you can measure the Sun's diameter with an 2q, Suppose you brought together a proton and an antiproton. accuracy of 1 percent. How long will you have to make mea- What would happen? How much energy would result? (Take surements in order to determine whether or not the Sun is con- the mass of a proton and antiproton to be 1.7 X 10-2~ kg each. ) tracting at this rate? 25. Now suppose you brought together a 100-kg linebacker 22. Verify that roughly 600 million tons of hydrogen must be from the National Football League and an antiproton (ignoring converted to helium in the Sun each second to explain its en- ~e air around them). What would happen? How much energy ergy output. (Hint: Recall Einstein's most famous formula, and ~,ould result? remember that for each kilogram of hydrogen, 0.0071 kg of mass is converted to energy ) 26. Every second, the Sun converts four million tons of matter to energy How long will it take the Sun to reduce its mass by 1 per-cent? 23. If an observed oscillation of the solar surface has a period Compare your answer with the lifetime of the Sun so far. of 10 min, and the average radial velocity is 1 m/s in and out, calculate the total displacement of the surface involved in this 168 CHAPTER 7 THE SUN:A NUCLEAR POWERHOUSE I 9. Why is fission not an important energy source in the Sun? 169 Measurements of the widths of spectral lines show spectroscopy, together with a rapidly maturing under- that many stars hotter than the Sun rotate in periods of standing of the ways atoms absorb and emit radiation, pro- only a day or two. The Sun, with its rotation period of about vided the tools to accomplish this "impossible" task. a month, rotates rather slowly. The rotation of most stars In this chapter we have seen that spectrum analysis cooler than the Sun is slower still, and often cannot be is an extremely powerful technique that allows the as measured with our present techniques. tronomer to learn all kinds of things about a star: its de-tailed chemical composition, as well as the temperature and pressure in its atmosphere. From the pressure, we get clues about its size. We can also measure its radial velocity and estimate its rotation. As we shall see in later chapters, In 1835 the French philosopher Auguste Comte wrote a spectroscopy helps us learn the same kinds of things about paper in which he asserted that it would never be possible galaxies, which are the most distant objects that we can ob- by any means to study the chemical composition of stars. serve. Without spectroscopy, we would know next to noth- Yet within a few decades the development of astronomical ing about the universe beyond the solar system. Spectroscopy:The Key to the Universe  SURFING THE WEB Speetral Classifieation the cataloging of infrared sources that led to the discovery of [zebu.uoregon.edu/~imamura/208/jan I 8/mk.html] the L type stars. Each site combines technical and nontechnical A brief tutorial on the spectral classification system, with information. graphic examples of what the spectra of different types of stars look like. Women in Astronomy Web Site [www.aspsky.org/html/astro/womenast bib.html] 2Mass Page [pegasus.phast.umass.edu OR This page brings together written and Web resources on the www.ipac.ealteeh.edu/2mass] contributions of women to astronomy, with general readings, These pages describe the work of the 2 Micron All Sky Survey, references about specific women, and links. SUMMARY 8. I The total energy emitted per second by a star is called 8.3 The differences in the spectra of stars are principally its luminosity. How bright a star looks to us is called its due to differences in temperature, not composition. The apparent brightness. For historical reasons, the apparent spectra of stars are described in terms of seven spectral brightnesses of stars are often expressed in terms of magni- classes. In order of decreasing temperature, these spectral tudes. If one star is five magnitudes brighter than another, it classes are O, B, A, F, G, K, and M. Recently, some as- emits 100 times more energy. Since the apparent brightness tronomers have suggested adding a type L, for stars whose of a star depends on its luminosity and distance, determina- spectra indicate that they are very cool and very low in mass. tion of apparent brightness and measurement of the dis- Spectra of stars of the same temperature but different at- tance to a star provide enough information to calculate its mospheric pressure have subtle differences, so spectra can luminosity. . be used to determine whether a star has a large radius and low atmospheric pressure (a giant star), or a small radius 8.2 Stars have different colors, and these are indicators of and high atmospheric pressure. Stellar spectra can also be temperature. The color index of a star is the difference in used to determine the chemical composition of stars; hydro- the magnitudes measured at any two different wavelengths. gen and helium make up most of the mass of all stars (just as The difference between blue and visual magnitudes, B - V, they do in the Sun). Measurements of line shifts produced is one frequently used color index; redder, cooler stars have by the Doppler effect indicate the radial velocity of a star. more positive values of B - V Broadening of spectral lines by the Doppler effect is a mea-sure of rotational velocity 182 CHAPTER 8 ANALYZING $TARLIGHT  Voyagers in Astronomy on Annie Cannon discusses # Suppose you could observe a star that has only one spec- some of the difficulties women who wanted to do as- tral line. Can you tell what element that spectral line tronomy faced in the first half of the 20th century. How comes from? Make a list of reasons with your group does your group think the situation is today? Do men about why you answered yes or no. and women have an equal chance to become scien- ~ A very wealth y alumnus of your colle g give e decides to tists? In your experience, were boys and girls equally fifty million dollars to the astronomy department to encouraged to do science and math where you went to build a world-class observatory for learning more about school? the characteristics of stars. Have your group discuss After you have done activity A, here is a little minidrama what kind of equipment they would put in the observa- your group can try. One member of the group plays a tory. Where should this observatory be located? Justify well-known woman astronomer, who has some observ- your answers. (You may want to refer back to the chap- ing time on a large telescope (scheduled 8 months ago) ter on telescopes and to revisit this question as you learn and has to fly there with her graduate students tomor- more about the stars in future chapters.) row. Her husband works in a large corporation and has .~ , Forsome astronomers introducing a new spectral type an important meetin g with a client tomorrow. They have for the stars (like the type L discussed in the text) is sim- two children, ages 4 and 10. The grandparents do not ilar to introducing a new area code for telephone calls in live near them. The person who helps them with child care has just called in sick for tomorrow. The two par- an urban area. Have your group make a list of why as- care are having a discussion about what they should do. tronomers would be reluctant to have a new spectral If v~ou prefer, all the people in the group can take the ~e for classifying stars. two roles in turn. Chapter 8 REVIEW QUESTIONS I . What two factors determine how bright a star appears to be in the sky? 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. luminosity-distance formula. Example: What is the apparent brightness of sunlight as seen from the Earth Solution: The Sun's luminosity is L Sun = 3.8 X 1026 watts, and the Earth's distance from the Sun is d = 1.5 X 1011 meters. Before the twentieth century, humans classified stars primarily by their brightness and location in our sky. The brightest stars within each constellation still bear Greek letters designating their order of brightness. For example, the brightest star in the constellation Centaurus is Alpha Centauri, the second brightest is Beta Centauri, the third brightest is Gamma Centauri, and so on. However, a star's brightness and membership in a constellation tell us little about its true nature. A star that appears bright could be either extremely powerful or unusually close, and two stars that appear right next to each other in our sky might not be true neighbors if they lie at significantly different distances from Earth. 2. Explain why color is a measure of a star's temperature. Measuring a star's surface temperature is somewhat easier than measuring its luminosity because the measurement is not affected by the star's distance. Instead, we determine surface temperature directly from the star's color or spectrum. One note of caution: We can measure only a star's surface temperature, not its interior temperature. (Interior temperatures are calculated with theoretical models [Section 14.3].) When astronomers speak of the "temperature" of a star, they usually mean the surface temperature unless they say otherwise. A star's surface temperature determines the color of light it emits. A red star is cooler than a yellow star, which in turn is cooler than a blue star. The naked eye can distinguish colors only for the brightest stars, but colors become more evident when we view stars through binoculars or a telescope. Astronomers can determine the "color" of a star more precisely by comparing its apparent brightness as viewed through two different filters. For example, a cool star such as Betelgeuse, with a surface temperature of about 3,400 K, emits more red light than blue light and therefore looks much brighter when viewed through a red filter than when viewed through a blue filter. In contrast, a hotter star such as Sirius, with a surface temperature of about 9,400 K, emits more blue light than red light and looks much brighter through a blue filter than through a red filter. The hottest stars, with the bluest colors, are called spectral type O, followed in order of declining surface temperature by spectral types B, A, F, G, K, and M. The time-honored mnemonic for remembering this sequence, OBAFGKMEach spectral type is subdivided into numbered subcategories (e.g., 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. determine a star's luminosity, surface temperature, and mass. 3. What is the main reason that the spectra of stars are not all 4. What elements are stars made of? How do we know this? Helium Gas, Hydrogen Gas, Deuterum. 5. What did Annie Cannon contribute to the understanding of stellar spectra? As more stellar spectra were obtained and spectra were studied in greater detail, it became clear that the classification scheme based solely on hydrogen lines was inadequate. Ultimately, 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. 6. Name at least three characteristics of a star that can be de-termined by measuring its spectrum. Explain how you would use a spectrum to determine these characteristics. identical? Explain. THOUGHT QUESTIONS 7. If the star Sirius emits 23 times more energy than the Sun, 10. Suppose you are given the task of measuring the colors of why does the Sun appear brighter in the sky? the stars in Appendix 9 through three filters. The first transmits blue light, the second transmits yellow light, and the third trans- 8. Draw a picture showing how two stars of equal intrinsic lu- mits red light. The way colors are defined, if you observe the minosity, one of which is blue and the other red, would appear star Vega, it will appear equally bright through each of the three on two images, one taken through a filter that passes mainly filters. (This is because Vega has a temperature very close to blue light, and the other through a filter that transmits mainly 10,000 K and the B - V color of a 10,000 K star is defined to be zero.) Which stars will appear brighter through the blue filter than through the red filter? Which stars will appear brighter through the red filter? Which star is likely to have colors most nearly like that of Vega? red light. 9. Table 8.1 lists the temperature ranges that correspond to various spectral types. What part of the star do these tempera-tures refer to? THOUGHT QUESTIONS 183 I I . Star A has lines of ionized helium in its spectrum, and star 14. Look at Appendix 11. Can you identify any relationship be- B has bands of titanium oxide. Which is hotter? Why? The tween the abundance of an element and its atomic weight? Are spectrum of another star shows lines of ionized helium and also there any obvious exceptions to this relationship? molecular bands of titanium oxide. What is strange about this spectrum? Can you suggest an explanation? ~ 5 Appendix 8 lists the nearest stars. Are most of these stars hotter or cooler than the Sun? Do any of them emit more en- I 2. The spectrum of the Sun has hundreds of strong lines of ergy than the Sun? If so, which ones? non-ionized iron but only a few, very weak, lines of helium. A star of spectral type B has very strong lines of helium but very ~ 6 Look at Appendix 8. Which stars are the hottest? Which are weak iron lines. Do these differences mean that the Sun con- the brightest? Are they the same? tains more iron and less helium than the B star? Explain. ~ 7, What is the brightest star in the sky? The second brightest? I 3. What are the approximate spectral classes of stars with the What color is Betelgeuse? Use Appendix 9 to find the answers. following characteristics? I8. Suppose primitive people of 1,000,000 years ago had left a. Balmer lines of hydrogen are very strong; some lines of behind maps of the night sky. Would these maps represent ac- ionized metals are present. curately the sky that we see today? Why or why not? b. The strongest lines are those of ionized helium. ~ q, Why can only a lower limit to the rate of stellar rotation be e. Lines of ionized calcium are the strongest in the spec- determined from rotational broadening, rather than the actual trum; hydrogen lines show with only moderate strength; rotation rate? (Refer to Figure 8.9.) lines of neutral and ionized metals are present. d. The strongest lines are those of neutral metals and bands of titanium oxide. PROBLEMS  20. A fifth-magnitude star is about the faintest that can be seen d. 1200 nm without optical aid unless you have access to a very dark, unpol- e. 1500 nm luted sky How much fainter is it than a zero-magnitude star? A good pair of binoculars can reveal tenth-magnitude stars. How 24. The following equation describes the duantitative relation- much fainter are these than stars of zero magnitude? ship between the magnitudes and light flux received from two stars. If ~nl and m2 are the magnitudes corresponding to stars 21. As seen from the Earth, the Sun has an apparent magni- from which we receive light flux in the amounts h and l2, the tude of about -26. What is the apparent magnitude of the Sun difference between ml and m2 is defined by as seen from Saturn, about 10 AU away? (Remember that 1 AU is the distance from the Earth to the Sun.) ml - m2 = 2.51og (l2/h) 22. If a star has a color index of B - V = 2.5, how many times brighter does it appear in visual light than in blue light, relative to a standard star with B - V = 0? 23. What are the approximate spectral classes for stars whose wavelengths of maximum light have the following values? (See Section 4.2.) a. 290 nm b. 50 nm c. 600 nm Use this equation to calculate the following: a. The difference in magnitudes of two stars that differ in light flux received at the Earth by a factor of ten. b. The difference in light flux received from two stars that differ by ten magnitudes. c. The difference in magnitudes of two identical stars, one of which is ten times farther away than the other. 25. Appendix 9 lists the 20 brightest stars. How much more luminous is the brightest of these stars than the faintest? 1 84 CHAPTER 8 ANALYZING $TARLIGHT  SUGGESTIONS FOR FURTHER READINd Berman, B. "Magnitude Cum Laude" in Astronomy, Dec. Kaler, J. Stars and Their Spectra. 1989, Cambridge U. Press. A 1998, p. 92. On how we measure apparent brightnesses detailed introduction to the field of spectroscopy and what of stars. it can tell us about the stars. Fraknoi, A. and Freitag, R. "Women in Astronomy: A Resource Kidwell, P. "Three Women of American Astronomy" in Ameri- Guide" in Mercury, Jan./Feb. 1992, p. 27. Part of an issue can Scientists, May/June 1990, p. 244. Focuses on Annie devoted to a discussion of women in astronomy. Cannon and Cecilia Payne. Hearnshaw, J. "Origins of the Stellar Magnitude Scale" in Sky dT Sneden, C. "Reading the Colors of the Stars" in Astronomy, Apr. Telescope, Nov. 1992, p. 494. A good history of how we 1989, p. 36. Discusses what we learn from spectroscopy. have come to have this cumbersome system. Steffey, P. "The Truth about Star Colors" in Sky e'r Telescope, Hearnshaw, J. The Analysis of Starlight. 1986, Cambridge U. Sept. 1992, p. 266. About the color index, and how the eye Press. A history of spectroscopy in astronomy. and film "see" colors. Hirshfeld, A. "The Absolute Magnitude of Stars" in Sky dr Tele- Tomldns, J. "Once and Future Celestial Kings" in Sky e'r Tele- scope, Sept. 1994, p. 35. scope, Apr. 1998, p. 59. Calculating the motion of stars Kaler, J. "Origins of the Spectral Sequence" in Sky dr Telescope, through space and determining which stars were, are, and Feb. 1986, p. 129. will be brightest in the sky. Kaler, J. Stars. 1992, Scientific American Library/W. H. Free- Welther, B. "Annie J. Cannon: Classifier of the Stars" in Mer- man. Good modern review of our understanding of stars. cury, Jan./Feb. 1984, p. 28. SUGGESTIONS FOR FURTHER READING 185 Dog Star-being located in the constellation of Canis matter in Chapter 14. For now, we should just note that Major, the big dog-Sirius B is sometimes nicknamed the white dwarfs are dying stars, reaching the end of their pro- Pup.) ductive lives and ready for their stories to be over. We have now found hundreds of white dwarfs. A good The British astrophysicist (and science popularizer) example of a typical white dwarf is the nearby star 40 Eri- Arthur Eddington described the first known white dwarf dani B. Its surface temperature is a relatively hot 12,000 K, this way: "The message of the companion of Sirius, when but its luminosity is only 1/275 Lsn. Calculations show that decoded, ran: `I am composed of material three thousand its radius is only 1.4 percent of the Sun's, or about the same times denser than anything you've ever come across. A ton as that of the Earth, and its volume is 2.5 X 10-6 that of the of my material would be a little nugget you could put in a Sun. Its mass, however, is 0.43 times the Sun's mass, just a matchbox.' What reply could one make to something like little less than half. To fit such a substantial mass into so that? Well, the reply most of us made in 1914 was, `Shut up; tiny a volume, the star's density must be about 170,000 don't talk nonsense."' Today, however, astronomers not only times the density of the Sun, or more than 200,000 g/cm3. accept that stars as dense as white dwarfs exist, but-as we A teaspoonful of this material would have a mass of some will see-have found even denser objects in their quest to 50 tons! At such densities, matter cannot exist in its usual understand the evolution of different types of stars. state; we will examine the peculiar behavior of this type of SURFING THE WEB Stars of the Week Site ~2 How Big IsThat StarActivity [www.astro.uiuc.edu/~kaler/sowlist.html] [imagine.gsfc.nasa.gov/docs/teachers/lessons/star size/ Astronomer and prolific author James Kaler hosts this site, star size cover.html] which features "biographical summaries" of famous stars-not An elementary activity on using actual eclipsing binary star data the Hollywood type, but ones in the real sky You can learn more (in x rays) to measure star diameters. about each star's place in ancient legends, its characteristics, companions, etc. Not an elegant site, but an informative one. ~ Henry Norris Russell's Work [mondrian.princeton.edu/cgi-bin/mfs/05/Gompanion/ Hubble Observations Relevant to this Chapter: russell henry.html] A Very Massive, Luminous Star (nicknamed the "Pistol Star") A brief summary of Russell's career is part of this site devoted to [oposite.stsci.edu/pubinfo/pr/97/33.htm1] Princeton University history. Image and Characteristics of Gliese 229B (Now Confirmed as Brown Dwarf) [oposite.stsci.edu/pubinfo/pr/95/48.htm1] ~ EcIiPsing Binary Stars Site [www.physics.sfasu.edu/astro/binstar.html] Dan Bruton at S. F. Austin State U. has put a series of anima-tions, articles, and links here showing how astronomers use eclipsing binary light curves. The Widest One Hundred Visual Binaries [www.cyburban.comhmrflc.htm] Michael Feltz lists the binary star systems that are easiest for beginners and gives observing advice and links for those who want to find them. SUMMARY 9.1 To understand the properties of stars, we must make scopic binary only the spectrum reveals the presence of wide-ranging surveys. We find the stars that appear brightest two stars. Stellar masses range from about 1/12 to (rarely) to our eyes are bright primarily because they are intrinsically more than 100 times the mass of the Sun. Objects having very luminous, not because they are the closest to us. Most less mass than stars do are called brown dwarfs and plan- of the nearest stars are intrinsically so faint that they can be ets. New instruments and techniques have recently allowed seen only with the aid of a telescope. The luminosity of stars us to discover a number of nearby brown dwarfs. The most ranges from about 10-4 Lsn to more than 106 Lst,. Stars massive stars are, in most cases, also the most luminous, and with low luminosity are much more common than stars with this correlation is known as the mass-luminosity relation. high luminosity. 9.3 The diameters of stars can be determined by mea- 9.2 The masses of stars can be determined by analysis of suring the time it takes an object (the Moon, a planet, or a the orbits of binary stars. In visual binaries the two stars companion star) to pass in front of it and block its light. Di- can be seen separately in a telescope, while in a spectro- ameters of members of eclipsing binary systems (where 204 CHAPTER 9 THE STARS: A CELESTIAL CENSUS the stars pass in front of each other) can be determined The position of a star along the main sequence is deter through analysis of their orbital motions. mined by its mass: High-mass stars emit more energy and are hotter than low-mass stars on the main sequence. Main-9.4 The Hertzsprung-Russell diagram, or H-R diagram, sequence stars derive their energy from the fusion of hy- is a plot of stellar luminosity as a function of surface temper- drogen to helium. About 90 percent of the stars in the solar ature. Most stars lie on the main sequence, which extends neighborhood lie on the main sequence. Only 10 percent diagonally across the H-R diagram from high temperature of the stars are white dwarfs, and fewer than 1 percent are and high luminosity to low temperature and low luminosity. giants or supergiants. INTER-ACTIVITY Two stars are seen close together in the sky, and your information about 5 main-sequence stars that are typical group is given the task of determining whether they are of the stars closest to us. Where would these stars be on a visual binary or whether they just happen to be seen the H-R diagram and why? in nearly the same direction. What types of measure- ments would you make to determine whether they orbit each other? A very wealthy (but eccentric) alumnus of your college donates a lot of money for a fund that will help in the search for more brown dwarfs. Your group is the com-mittee in charge of this fund. How would you spend the money? (Be as specific as you can, listing instruments and observing programs.) Your group is given information about 5 main-sequence stars that are among the brightest appearing stars in the sky, and yet pretty far away. Where would these stars be on the H-R diagram and why? Next your group is given Chapter 8 REVIEW QUESTIONS 1. How does the intrinsic luminosity of the Sun compare with 2. Name and describe the three types of binary systems. 3. Describe two ways of determining the diameter of a star. Luminosity of brightness of star. 4. What are the largest and smallest known values of the mass, luminosity, surface temperature, and diameter of stars (roughly)? 5. You are able to take spectra of both stars in an eclipsing bi- nary system. List all properties of the stars that can be mea- sured from their spectra and light curves. that of the 30 brightest stars? With that of the stars within 15 LY? Refer to Appendices 8 and 9. 6. Sketch an H-R diagram. Label the axes. Show where cool supergiants, white dwarfs, the Sun, and main-sequence stars are found. THOUGHT QUESTIONS `  7. Is the Sun an average star? Why or why not? number eclipsing binaries. Why? Which is easier to observe at 8. Suppose you want to determine the average educational large distances-a spectroscopic binary or a visual binary? level of people throughout the nation. Since it would be a great 12. The eclipsing binary Algol drops from maximum to minimum deal of work to survey every citizen, you decide to make your brightness in about 4 hours, remains at minimum brightness for task easier by asking only the people on campus. Will you get 20 min, and then takes another 4 hours to return to maximum the right answer? Will your survey be distorted by a selection brightness. Assume that we view this system exactly edge-on, so effect? Explain. that one star crosses directly in front of the other. Is one star 9. Why do most known visual binaries have relatively long pe- much larger than the other, or are they fairly similar in size? riods, and most spectroscopic binaries relatively short periods? (Hint: Refer to the diagrams of eclipsing binary light curves.) 10. Figure 9.12 shows the light curve of a hypothetical eclips- 13 Consider the following data on five stars: ing binary star in which the light of one star is completely blocked by another. What would the light curve look like for a system in which the light of the smaller star is only partially blocked by the larger one? Assume the smaller star is the hotter one. Sketch the relative positions of the two stars that corre-spond to various portions of the light curve. Star Apparent Magnitude Spectrum I 12 G, main sequence 2 8 K, giant 3 12 K, main sequence 4 15 O, main sequence 5 5 M, main sequence 11. There are fewer eclipsing binaries than spectroscopic bina-ries. Explain why. Within 50 LY of the Sun, visual binaries out-  THOUGHT QUESTIONS 205 a. Which is the hottest? 17. Approximately 6000 stars are bright enough to be seen b. Coolest? without a telescope. Are anv of these white dwarfs? Use the in- c. Most luminous? formation given in this chapter, and explain your reasoning. d. Least luminous? 18. Use the data in Appenduc 9 to plot an H-R diagram for the e. Nearest? brightest stars. Use the data from Table 9.2 to show where the ^ Most distant? main sequence lies. Do 90 percent of the brightest stars lie on In each case, give your reasoning. (Recall that apparent magni- or near the main sequence? Can you explain why or why not? tude is a measure of apparent brightness, where the larger the ~ q, Use the diagram you have drawn for Question 18 to answer number, the dimmer the star appears to us.) the following questions. ~~~hich star is more massive-Sirius or 14. W'hich changes by the largest factor along the main sequence Alpha Centauri? Rigel and Regulus have nearly the same spec- from spectral types O to M-mass, luminosity, or radius? tral type. Which is larger? Rigel and Betelgeuse have nearly the 15. Suppose you want to search for main-sequence stars with same luminosity. Which is larger? Which is redder? very low mass using a space telescope. Will you design your 20. Use the data in Appendix 8 to plot an H-R diagram for the telescope to detect light in the ultraviolet or the infrared part of nearest stars. How does this plot differ from the one for the the spectrum. Why? brightest stars (Question 18)? Why? 16. An astronomer discovers a type-M star with a large lumi-nosity How is this possible? What kind of star is it? PROBLEM  21. Plot a diagram like Figure 9.2 for the nearest stars (see Ap- the density of Ross 614B, the red supergiant described in Sec- pendix 8) and for the 20 brightest stars (Appendix 9). Explain tion 9.4, which has 50 times the mass and 400 times the radius how and why these two diagrams differ. of the Sun. The outer parts of such a star would constitute an 22. Find the combined mass of two stars in a binary system excellent laboratory vacuum. whose period of mutual revolution is two years, and for which 26. Suppose you weigh 70 kg on the Earth. How much would you weigh on the surface of a white dwarf star the same size as 23. We view a binary star exactly edge-on and observe eclipses, the Earth but having a mass 300,000 times larger (nearly the The star being eclipsed has an orbital velocity of 100 km/s. The mass of the Sun)? the semimajor axis of the relative orbit is 2 AU. time interval from first to second contact is 2 hr 30 min. The 27. One more way to estimate the radius of a star relies on the time from second to third contact is 10 hr, and from third to Stefan-Boltzmann law (Chapter 4), according to which the to- fourth contact, 2 hr 30 min, again. What are the diameters of the tal energy emitted per second per square meter is given by the two stars? How do these compare with the diameter of the Sun? equation E = QT4. To calculate the total energy emitted by a 24. In Figure 9.7, is Star A or Star B more massive? Assume the star, we must multiply the energy emitted per square meter by orbit is viewed edge-on. What is the diameter of each star's or- the surface area of the star, which is equal to 4irR . The star bit? If both stars are main-sequence stars, which is more lumi- Betel~euse has a temperature of about 3000K and a luminosity nous? Which is hotter? of 10' Ls. Calculate the radius of Betelgeuse relative to the radius of the Sun. 25. Verify that a red dwarf with 1/12 the mass and 1/10 the ra-dius of the Sun has a density 80 times that of the Sun. Calculate 206 CHAPTER 9 THE STARS: A CELESTIAL CENSUS  the stars pass in front of each other) can be determined The position of a star along the main sequence is deter through analysis of their orbital motions. mined by its mass: High-mass stars emit more energy and are hotter than low-mass stars on the main sequence. Main-9.4 The Hertzsprung-Russell diagram, or H-R diagram, sequence stars derive their energy from the fusion of hy- is a plot of stellar luminosity as a function of surface temper- drogen to helium. About 90 percent of the stars in the solar ature. Most stars lie on the main sequence, which extends neighborhood lie on the main sequence. Only 10 percent diagonally across the H-R diagram from high temperature of the stars are white dwarfs, and fewer than 1 percent are and high luminosity to low temperature and low luminosity. giants or supergiants. INTER-ACTIVITY Two stars are seen close together in the sky, and your information about 5 main-sequence stars that are typical group is given the task of determining whether they are of the stars closest to us. Where would these stars be on a visual binary or whether they just happen to be seen the H-R diagram and why? in nearly the same direction. What types of measure- ments would you make to determine whether they orbit each other? A very wealthy (but eccentric) alumnus of your college donates a lot of money for a fund that will help in the search for more brown dwarfs. Your group is the com-mittee in charge of this fund. How would you spend the money? (Be as specific as you can, listing instruments and observing programs.) Your group is given information about 5 main-sequence stars that are among the brightest appearing stars in the sky, and yet pretty far away. Where would these stars be on the H-R diagram and why? Next your group is given Chapter 9 REVIEW QUESTIONS  How does the intrinsic luminosity of the Sun compare with 5. You are able to take spectra of both stars in an eclipsing bi- that of the 30 brightest stars? With that of the stars within nary system. List all properties of the stars that can be mea- 15 LY? Refer to Appendices 8 and 9. sured from their spectra and light curves. 2. Name and describe the three types of binary systems. 6. Sketch an H-R diagram. Label the axes. Show where cool 3. Describe two ways of determining the diameter of a star. supergiants, white dwarfs, the Sun, and main-sequence stars are found. 4. What are the largest and smallest known values of the mass, luminosity, surface temperature, and diameter of stars (roughly)? THOUGHT QUESTIONS `  7. Is the Sun an average star? Why or why not? number eclipsing binaries. Why? Which is easier to observe at 8. Suppose you want to determine the average educational large distances-a spectroscopic binary or a visual binary? level of people throughout the nation. Since it would be a great 12. The eclipsing binary Algol drops from maximum to minimum deal of work to survey every citizen, you decide to make your brightness in about 4 hours, remains at minimum brightness for task easier by asking only the people on campus. Will you get 20 min, and then takes another 4 hours to return to maximum the right answer? Will your survey be distorted by a selection brightness. Assume that we view this system exactly edge-on, so effect? Explain. that one star crosses directly in front of the other. Is one star 9. Why do most known visual binaries have relatively long pe- much larger than the other, or are they fairly similar in size? riods, and most spectroscopic binaries relatively short periods? (Hint: Refer to the diagrams of eclipsing binary light curves.) 10. Figure 9.12 shows the light curve of a hypothetical eclips- 13 consider the following data on five stars: ing binary star in which the light of one star is completely blocked by another. What would the light curve look like for a system in which the light of the smaller star is only partially blocked by the larger one? Assume the smaller star is the hotter one. Sketch the relative positions of the two stars that corre-spond to various portions of the light curve. Star Apparent Magnitude Spectrum I 12 G, main sequence 2 8 K, giant 3 12 K, main sequence 4 15 O, main sequence 5 5 M, main sequence 11. There are fewer eclipsing binaries than spectroscopic bina-ries. Explain why. Within 50 LY of the Sun, visual binaries out- THOUGHT QUESTIONS 205 SUGGESTIONS FOR FURTHER READW "The Grand Illusion: What We See Is Not Neces- McAllister, H. "Twenty Years of Seeing Double" in Sky e'T Telescope. Diameter of the Moon 29 Exploring the Moon -- A Teacher's Guide with Activities, NASA EG-1997-10-116-HQ Purpose To calculate the diameter of the Moon using proportions. Background The diameter of the Moon is proportional to the diameter of a cardboard disk, given that you know the distance to the Moon and the distance to the cardboard disk. The relationship is: d D l L so that: D = L(d/l) where D = diameter of Moon d = diameter of cardboard disk L = distance to Moon l = distance to cardboard disk In this activity, students will measure d and l. They will be given L. They will calculate D. The diameter of the Moon (D) is 3,476 km. Preparation Review and prepare materials listed on the student sheet. Choose a day and location for this activity which is best for viewing a full Moon. A cardboard disk of 2 cm diameter works well. Better accuracy may be achieved by using a larger disk, thus a greater distance l. However, if obtaining or cutting cardboard is difficult, then this activity can also be done with dimes. A dime held out at arm's length will cover the Moon. The distance from Earth to the Moon for a given date can be obtained by asking a local planetarium staff, Or for this activity, students may use an average value of 382,500 km. Diameter of the Moon 30 Teacher Page Exploring the Moon -- A Teacher's Guide with Activities, NASA EG-1997-10-116-HQ In Class If students work in pairs, then one student can use the string to measure distance from their partner's eye to the disk. The same units do not have to be used on both sides of the equation, but d and l have to be the same units. The D will be the same unit as L. Wrap-Up To compute the density of the Moon use the diameter to compute volume and use the mass value of 7.35 x 1022 kg. Density of the Moon is 3.34 grams/cubic cm. Diameter of the Moon 31 Exploring the Moon -- A Teacher's Guide with Activities, NASA EG-1997-10-116-HQ 1. On a day when you can see the Moon: place a cardboard disk on top of a stake or on a window sill so that it exactly covers the Moon from your point of view behind the cardboard disk. 2. Have a friend measure the distance from your eye to the cardboard disk. Call this distance l and write the value here: l = 3. The distance from Earth to the Moon varies between 360,000 km and 405,000 km. Find the distance for todays date or use an average value for your calculations of 382,500 km. Write the value that you are going to use here: L = 4. What is the diameter of the cardboard disk? d = 5. The diameter of the Moon is proportional to the diameter of your cardboard disk by this equation: d D l L so that, D = L(d/l) where: D = diameter of Moon d = diameter of cardboard disk L = distance to Moon l = distance to cardboard disk Procedure Key Words proportional Materials Purpose To calculate the diameter of the Moon using proportions. 2-cm wide cardboard disk wooden stake (optional) meter stick calculator string Diameter of the Moon 32 Exploring the Moon -- A Teacher's Guide with Activities, NASA EG-1997-10-116-HQ Results 1. By your calculations, the diameter of the Moon is: D = 2. Compare your result with the accepted diameter of the Moon. How close did you get? 3. How many times smaller is the diameter of the Moon than the diameter of Earth? 4. When you calculated the diameter of the Moon, did you have to use the same units on both sides of the equation? 5. How and where could you find the value for the distance to the Moon for today's date? 6. 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