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Astro Raven

University of Washington
Astronomy Department

Introductory Astronomy Clearinghouse

The Sky
Short Questions about the Sky
Sky Matching Exercise Intro Larson This one's hard! A matching activity of locations on the Earth and things that happen in those locations.
How big is big? Intro Balick  
Sun Days Intro Balick  
Suntanning Intro Balick Notes for Teachers
Solar System
Short Questions about the Solar System
Solar System Scale Intro Balick  
Sizes of Astronomical Objects Intro ?  
Global Warming Intro    
Europa Essay Intro Larson  
Short Questions about the Stars
Spectra Problem Set Intro ?  
The Lifetime of the Sun Intro ?  
Solar Power Intro Agueros Modification of above.
Properties of Sun and Stars Intro ?  
Cepheid Yardstick Intro ?  
Stellar Evolution
Short Questions about Stellar Evolution
H-R diagram Intro ? This exercise has some serious inconsistencies and graphing problems. Improvements are currently underway, but we recommend you do not use this exercise until this message disappears. -- AML
Black Holes Intro Palen  
Short Questions about Galaxies
Distance to the Center of the Milky Way Intro Larson  
Short Questions about Cosmology
Expansion of the Universe Intro Balick  
Short Questions about Miscellaneous Topics
Physical Principles Intro ?  
Marbles in a Beaker Intro ?  

Activities Labs Main Page Movies Lecture Resources Links of Interest Exams Feedback

Short Questions about the Sky skyquest.html

Short Questions about the Sky


  1. What is the main reason naked eye astronomy was easier in the past?

    Less city light pollution.
  2. What are two ancient uses of Astronomy?

  3. Why do we have seasons (summer and winter for example)?

    In the summer the sun is closer to Earth. In the winter the sun is farther away from Earth.
  4. Why is it that the positions of the stars in the sky are different at the same time of night in different seasons?

  5. What is the chief difference between Ptolemy's and Copernicus' ideas for the arrangement of the solar system?

    Ptolemy's Cosmological System. Each planet orbits around a small circle called a epicycle. The system is not exactly centered on the Earth but on a point called the equant. The Greeks needed all this complexity to explain the motions in the sky because they believed the Earth was stationary. Copernicus In the early to mid 1500's, Copernicus, who was familiar with Aristarchus' idea of a Sun-centered universe, began to try to fit the heliocentric model to the observed behavior of the sky. The heliocentric universe explained many observations more simply than the geocentric model. The planets could now be put in order by distance from the Sun, and that information both explained planetary regression and provided a constant increase in sidereal period with distance. The problem with the Copernican theory was inability to abandon the idea that planets could move in anything other than perfect circles. This idea had persisted since Ptolemy, and by keeping it, Copernicus had to add epicycles and deferents to his model to explain existing planetary observations. The new model needed even more epicycles than the Ptolemaic model. The general principle in science (called Occam's razor) is that the simplest explanation that fits the facts is the correct one. More epicycles made this theory more complicated. The theory was published in Latin, a language known only among the educated, in general. Ptolemaic model Geocentric solar system model, developed by the second century astronomer Claudius Ptolemy. It predicted with great accuracy the positions of the then known planets.
  6. For what scientific reason did the ancient Greeks favour Ptolemy's idea?

    It predicted with great accuracy the positions of the then known planets. During the Middle Ages (approx. 500 AD to approx. 1500 AD), Western science didn't make much progress. Middle Eastern astronomers kept Ptolemy's work alive and it remained the dominant theory of how the universe worked for over a thousand years. The contributions to astronomy.
  7. What is the chief difference between Copernicus' and Kepler's ideas for the arrangement of the solar system?

    Copernicus said the appearance that the Earth is stationary and that the Sun and planets move about the Earth is illusory. Pine points out that solid matter is known to be 99.9% empty space (the authorities he quotes would object, 99.9999999999% would be closer) - the solidity of matter is shown to be illusory also. Kepler's first and second laws of planetary motion. The first law: The orbits of the planets are ellipses with the sun at one focus. The second law: A line extending from the sun to a planet sweeps out equal areas in equal times. These laws give a precise description of planetary motion, accounting for the details of non-uniform speed in orbit, the changing size of the moon, the unequal length of the seasons-everything that was observable at that time. This made possible accurate predictions of planetary positions without the cumbersome, ad hoc patchwork of epicycles. The simplification was more than impressive; it was, of course, revolutionary.
  8. What was the key factor that allowed Kepler to be confident in his new ideas, compared to those of Ptolemy for example?

    Kepler's achievements seem to have little connection with his goals, the abundance of mystical detail has been discarded and only the general ideas were retained and confirmed. The shapes and sizes of orbits and the speeds of orbiting bodies are all related mathematically. The key to planetary motion lies in the influence of the central sun. Such a brief summary of a lifetime of work, and particularly poignant when compared with Kepler's own assessment Ptolemy, to provide a very satisfying precise representation of the motion of all the planets, sun and moon. This was another great triumph of geometry, which even Ptolemy considered the noblest accomplishment of the Greek mind.
  9. Discuss in a few sentences what the church objected to in Galileo's ideas.
    (I am not looking for a specific answer here but your response must fit what we know about Galileo, his ideas and the church of the time).

    Galileo Galilei 1564-1642 Italian astronomer and physicist. The first to use a telescope to study the stars. Discoverer of the first moons of an extraterrestrial body (see above). Galileo was an outspoken supporter of Copernicus's heliocentric theory. In reaction to Galileo, the Church declared it heresy to teach that the Earth moved and silenced him. The Church clung to this position for 350 years; Galileo was not formally exonerated until 1992. (16k gif; 136k jpg) (See also the Galileo exhibit at Institute and Museum of History of Science, Florence ITALY; The Galileo Project from Rice and APOD 980913) gegenschein a round or elongated spot of light in the sky at a point 180 degrees from the Sun. Also called counterglow. George III 1738-1820 King of Great Britain and Ireland (1760-1820). His government's policies fed American colonial discontent, leading to revolution in 1776. geosynchronous orbit a direct, circular, low inclination orbit in which the satellite's orbital velocity is matched to the rotational velocity of the planet; a spacecraft appears to hang motionless above one position of the planet's surface. Galileo's experiments on motion and inertia. Controversy followed Galileo’s support for the heliocentric model of the cosmos, as it was in direct conflict with the religious teaching of that time. For the church, the question was who had the authority to interpret scripture? As Galileo found out, the 17th Century church was very capable of handling questions of authority. It is interesting that Galileo's ridicule of medieval physics, ideas about motion, etc., was phrased in terms of terrestrial experiments. He did not apply these new ideas to the heavens. There is perhaps a limit to how much can be stripped away by a single individual. Even for Galileo, it seemed only right, that celestial bodies should follow uniform, circular motion.
  10. Newtons law of Gravity is more general when compared to Kepler's laws of motion."
    Discuss in a few sentences what I mean by general in the above sentence. In science a theory that is more general is usually considered better.
    Include an example of when Kepler's laws cannot be used but Newton's law can. (hint: Something simple and everyday will do.)

Newton’s law of gravity states that the gravitational force between two objects depends on the gravity of their masses and inversely on the gravitational force of their separation. There is no question about Kepler's three laws being crucial clues; however, they had to be extracted from long passages of mystical causes, harmonies, symmetries, references to magnetism and other distractions. Aristotle the boundary between heaven and earth lay just this side of the moon; it was the closest celestial body and appears to be under the influence of the earth. The moon played a crucial role for Newton too. If he could explain its motion in terrestrial terms, then that might provide a stepping stone to the solar system if not the Universe. In retrospect, his hopes were verified; gravity is our fundamental principle of the universe This is Newton's formulation of his classic law of Universal Gravitation, whereby one explains then moon's orbit by reasoning from the motion of a falling apple by measuring how far it falls in one second. This scenario is not meant to represent historically the manner in which Newton came to various conclusions, but he did use the cannonball thought-experiment to illustrate a line of reasoning much like that given here. The same ideas can then be applied to the planetary orbits about the sun. Newton was able to show that his law of gravity, together with his laws of motion implied (from fundamental principles) Kepler's elliptical orbits for orbiting bodies with circular orbits as a special case. Further more he noted that since the two bodies are subject to equal but opposite gravitational forces, they accelerate toward each other in inverse proportion to their masses (a=F/M) and orbit a common center, the so-called center of mass of a system. For two bodies of very unequal mass, the center of mass is very close to the center of the more massive body. The solar system, the earth does not (in the strict sense) orbit the Sun, but rather the center of mass of the earth-sun system which is very close to but not at the center of the sun. Copernicus thought first to put the sun at the center, then has to move it a bit off. Then Kepler put it back at the center by placing it exactly at the foci of his ellipses. But then Newton came along and had to move it off a bit. Newton's fundamental and more precise formulation of planetary orbits in fact led to a correlation of Kepler's third law. Rather than the orbital period depending solely on the major axis of the orbit, showed that it also depends on the mass of the planet relative to the mass of the sun.


  1. List the qualities astronomers look for in an observing site. What are the pros and cons of space-based telescopes?

  2. Astronomers often choose very faint objects in the sky to study.
    In fact, "cutting edge" observational astronomy usually means studying the faintest objects.
    What is it that telescopes do that is really useful for studying faint objects?
    This particular advantage exists even if you are just looking through the telescope with your eyes.

Motions of the Sky

  1. Which declinations can be observed from the North Pole? the South Pole? the Equator? our latitude (47.6 degrees North)?
    Which right ascensions can be seen from the above locations each day?

  2. What is the latitude of the North Pole? Why is it impossible to give the longitude?

  3. How many "hands" would be needed to measure completely around the horizon?

  4. What range of azimuth would include all the locations on the horizon at which a star can rise? Would this question make sense at the North and South poles?

  5. How would the length of the solar day change if the Earth rotated in the opposite direction? (A diagram of the solar vs. sidereal day will be useful to you!)

  6. Suppose that the ecliptic and the celestial equator were not tilted with respect to each other. How would the azimuth of sunrise vary throughout the year? How would the length of day and night vary throughout the year?

Sun-Earth-Moon System

  1. You are an astronaut on the moon. You look into the sky, and see the Earth in its Full phase. What lunar phase is observed by people on Earth? What if you saw a first quarter Earth? New Earth? third quarter Earth? (A diagram of the lunar phases will help with this!)

  2. The speed of light is 300,000 kilometres per second. This number isn't easy to get a feel for but it's good it's so fast because it allows us to see things instantly on Earth without waiting for the light to arrive.
    The Sun is far enough away that light takes an appreciable time to travel to us. Assuming the sun is 150,000,000 kilometres away, how long would it take us to realize if the sun suddenly stopped shining?


  1. Assume that the Moon has oceans. What will the tides be like? How many high and low tides will occur in the course of a day?
Sky Matching Exercise matching.html Sky Matching Exercise

At right is a pictogram of the Earth, with the labels of various locations on the Earth listed. Match up the locations with the descriptions of the sky from that location. More than one location may apply to each description.
Location Description of Sky
a. North Pole _________1. The Sun can be seen at the zenith twice during the year.
b. North of the Arctic Circle _________2. North circumpolar stars are seen.
c. Arctic Circle 66.5 deg N latitude _________3. The Sun can be seen at the zenith only once during the year.
d. South of the Arctic Circle _________4. North celestial pole seen at the zenith.
e. North of the Tropic of Cancer _________5. All stars rise and set.
f. Tropic of Cancer _________6. All northern stars are circumpolar.
g. South of the Tropic of Cancer _________7. Celestial poles are seen on the horizon.
h. North of the Equator _________8. South celestial pole is seen at the zenith.
i. Equator _________9. All southern stars are circumpolar.
j. South of the Equator _________10. The ecliptic can be seen directly overhead at local noon on June 21.
k. North of the Tropic of Capricorn _________11. The ecliptic can be seen directly overhead at local midnight on December 21.
l. Tropic of Capricorn _________12. The Sun is at the zenith on March 21.
m. South of the Tropic of Capricorn _________13. The Sun fails to rise above the horizon between March 21 and September 21.
n. North of the Antarctic Circle _________14. Only place on Earth where Pisces and Virgo can be seen at the zenith.
o. Antarctic Circle 66.5 deg S latitude _________15. Location that is closest to the Sun at winter solstice.
p. South of the Antarctic Circle  
q. South Pole  

How Big is Big? bigisbig.html How Big is Big?


In this homework, you will learn the types of objects in the Universe, develop an idea of the sizes of objects and the typical distances between them. You will also recall how to express very large numbers using powers of ten notation. A scientific calculator will help you.

Background and Theory

Suppose someone asks you how far it is from Seattle to Vancouver, B.C. You might reply "Oh, about three hours." Obviously, what you mean is that a car traveling at about 50 mph can drive the distance in three hours. So the distance is "three car hours".

We can launch rockets that travel at about 25,000 mph, or 40,000 km/hr. Such rockets can orbit the Earth in just over an hour. The circumference of the Earth is "one spaceship-hour". Similarly, the Moon is about 1/2 a spaceship-day away.

  1. The names of various objects are listed in the first column of the table below. Please describe the sizes of these objects using "standard" Earth units (kilometers), and spaceship travel time. The sizes of the objects can be found by browsing through the textbook. For reference, the diameter of the Earth is about 13,000 km, and the diameter of the Sun is 1,400,000 km (1.4X106 km), a bit more than 100 times the size of the Earth. Spaceship travel times should be described in hours, days, years, centuries; whichever allows the most comfortable numbers---between 1 and 1000 if possible.

    Object Diameter (km) Diameter (spaceship travel-time)
    Moon  my answer The diameter of the Moon (D) is 3,476 km.  
    Earth 13,000 km  
    Sun 1.4X106  
    Solar System    
    Milky Way Galaxy    
    Virgo Cluster 1.67X1019 km  

  2. Suppose that during your lifetime, technology improves, and space travel of 100,000 km/hr becomes feasible. At this speed, how long would it take humans to reach Pluto from Earth?
  3. Suppose someone asks you how far it is from the Earth to the Sun. You could answer "93 million miles", or you could say "8 light minutes". If you know how fast light travels (186,000 miles per second or 300,000 km/s), then the second answer replaces an uncomfortably large number with a more reasonable one.

    Distances in the astronomical realm are huge. Using miles or kilometers becomes silly when you are consistently talking about "four hundred million trillion miles". It makes sense to switch to much more reasonable units. The normal choice is the light travel time. Fill in the blanks in the table. Light travel times can be given in light-hours, light-days, or light-years; whichever allows the use of the most comfortable numbers.

    Object Distance (km or A.U.) Distance (light travel time)
    Sun 1 A.U.=1.5X108km  
    Pluto 38 A.U.  
    Nearest Star (not the Sun)    
    Nearest Large Galaxy (M31)   2 Mly = 2 million light years
    Nearest Cluster of Galaxys    
    Sun Days sundays.html Sun Days


    As we have seen in the planetarium, the sky appears to revolve once per day. We can use the sky's rotation to tell time. The questions below are all related to timekeeping and rotations.


    Assume that the Earth is round and that it rotates around its axis every day. Also, assume that the moon moves in a circular orbit around the Earth every four weeks and that the Earth orbits the Sun once per year. (By the way, we all claim to know these facts, but I challenge you to prove them experimentally!) Assume the Sun is very far away.

    Feel free to use figures (sketches or graphs) to make your answers clearer and shorter.

    1. (1/2 page maximum including figures) The definition of a day is ambiguous. Let's say that we use object A in the sky to keep time. To define the length of a day we would start a stopwatch when object A crosses the meridian - your longitude line projected onto the sky. The length of a day is the reading on the stopwatch the next time object A crosses the meridian.

      The solar day is measured with respect to the Sun, and is 24h 00m in length on average. The sidereal day is measured with respect to the stars, and is 23h 56m. The lunar day is measured with respect to the moon, and is about 24h 48m long.

      Explain why the length of the day depends on whether you use a star, the Sun, or the Moon to measure it. Also account qualitatively for the fact that the lunar day is the longest, the sidereal day is the shortest, and the solar day is in between. If it helps to do so, pretend that all stars are visible in the daytime (this would be true if the Earth didn't have an atmosphere). Then you can treat the stars as a reference system against which the locations of the Sun and Moon can be monitored.

      You can see the moon or Sun moving slowly from the eastern sky to the western sky. The Sun is always rising and setting about the same times each day each year. The sun can be centerally located centered position in the sky directly above or sort of at 12 p.m. solar day The period of time between the instant when the Sun is directly overhead (i.e. at noon) to the next time it is directly overhead. sidereal day The time needed for a star on the celestial sphere to make one complete rotation in the sky. For example, for Earth, we have D = 1 solar day and P = 365.25 solar days, so we can solve for R and get (1/1) + (1/365.25) = 1/R, so 1/R = 1.002737 and R = 0.9973 days. That works out to 23 hours, 56 minutes, just as we saw earlier. The weird part about Venus' rotation is that it is retrograde (backwards relative to just about everything else in the solar system). This means its sidereal day should be negative in the formula above. There are no seasons on Venus because of this slow rate of rotation, combined with the thick cloud cover and the small axial tilt of 3°. Also, Venus moves so slowly that we don't expect a strong magnetic field. In the late 1970's, the Pioneer series sent probes down through the atmosphere of Venus, where they transmitted information until the incredible pressure, heat (about 700K or about 800 F), and corrosive atmosphere (which includes sulfuric & hydrofluoric acid) destroyed them. A decade later, Magellan was sent to Venus to map it using cloud-penetrating radar. Both observation and theory suggest that the constant high temperatures on Venus give the surface a putty-like quality that tends to round off mountains as they gradually flow back down to the lower levels of the planet. This plasticity in the rocks may also explain the lack of plate tectonic activity on Venus.
    2. (2 pages maximum including figures) Outside the lab room, on the southwest wall facing the Burke-Gilman trail, you will find a sundial. (The sundial was designed in 1994 by Prof. Woody Sullivan of the Astronomy Dept. for the new building.) Sketch the sundial and turn the sketch in. Note the time when you observed the sundial.

      If the sun is out, then be sure to include the shadow of the gnomon (stick) and its ball in your sketch. (If the Sun isn't out then guess where their shadows would fall and draw this.) Also indicate the expected direction of the shadow's motion over the next few hours.

      Be sure to carefully read the explanatory plaque below the sundial. Then answer these questions:
      1. From an astronomical point of view, how does this (and every other) sundial work?
      2. Why can't this particular sundial be used very early in the morning?
        EXTRA CREDIT (A few sentences only)
      3. It is easy to read the season of the year using the sundial - but only if you know whether the current date lies between Dec. 21 and June 21, or between June 21 and Dec. 21. Why?

    3. (1 page maximum including figures) Explain how you could use the noon shadow of a stick of known length to measure your latitude on March or September 21 (that is, at the spring and autumnal equinox).

    Suntanning suntan.html Suntanning


    In this lab you and your lab partner will be assigned a month of the year. You're going for a virtual all-expense-paid, one-weekend trip (Friday evening to Sunday evening) to get a great suntan in your appointed month. Where will you go? How do you select the perfect place?

    My report is I go to San Diego since it is not too hot for those unwanted sun burns while getting a tan. More damage to skin could come if went to Valparaiso since the temperatures are in the low 70s and upper 60s. Not a lot of sunshine in Seattle or Barrow. Colder. More likely to get skin cancer in San Diego then in Seattle or Barrow. More sun rays of sun light in San Diego. Mean Monthly Temperatures at Five Locations Avg Daily Temps (oF) Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Valparaiso (33oS) 72 72 70 67 64 60 62 63 64 66 68 71 Quito (0oS) 59* 59* 59* 58* 58* 58* 58* 59* 59* 59* 59* 59* San Diego (33oN) 55 56 57 59 62 64 68 69 67 64 61 57 Assignment

    The heart of this lab is sorting through your options, which are many and complex. This is where your discussions with your lab partner are of central importance.

    Be sure to write up and submit your recommendation independently. There is no right answer, only a reasonable one. We want to see how you added structure to an ambiguous problem in formulating a decision.

    In a few short paragraphs, state where you would go and why you selected that location. The quality of your answer is much more important than the quantity. Your grade depends on the strength, clarity and conciseness of your arguments. Insofar as your grade is concerned, we're looking for a strong astronomical rationale. This is an astronomy class after all. So state very clearly all of the astronomical criteria you considered, and whether you treated them as primary or secondary in importance.

    But that isn't all there is to this problem. The non-astronomical considerations are also germane. Mention three issues which you considered. How did these issues affect your decision? (Please be specific as well as brief.)

    There are many challenges in identifying the best place to suntan. So before you proceed much further think carefully about what they are. Consider the relevance of such things as the duration of daylight, the height of the Sun, etc. Weather is another issue. And don't forget about skin cancer. Finally, if you select a very remote beach, keep in mind that you'll have to squander a lot of time getting to and from it by helicopter.

    To make your job a lot easier, here are some average temperatures for cities along the west coast of the Americas at various latitudes.

    Mean Monthly Temperatures at Five Locations
    Avg Daily Temps (oF) Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
    Valparaiso (33oS) 72727067646062 6364666871
    Quito (0oS) 59*59*59*58*58*58* 58*59*59*59*59*59*
    San Diego (33oN) 55565759626468 6967646157
    Seattle (48oN) 41434651566163 6460534642
    Barrow (71oN) -16-18-150193440 4131171-10
    * Quito is cool owing to its altitude of 12,000 feet. Add 30 degrees for the temperatures at sea level at this latitude.

    Below, you'll find a table with some useful astronomical data for these same cities. If you need it, there's quite a bit of additional data on these cities in various atlases in Suzallo or public libraries. Feel free to use Redshift in Suzallo or the Computer Lab in A214 (first check with your T.A. for access).


    Location: Barrow Latitude: 71o N
    Date    Rise Time   Set Time         Noon Altitude          Rise Azimuth           Set Azimuth          Day Length
    1/22       --         --         nevero above hor'zn             --                     --              00:00 hr:m
    2/22     9:37 AM     5:47 PM       9o above S hor'zn    120o=30o S of E(ESE)   240o=30o S of W (WSW)
    3/22     6:18 AM     6:24 PM      20o above S hor'zn     85o             (E)   275o              (W)
    4/22     4:34 AM    10:22 PM      31o above S hor'zn     45o=45o N of E (NE)   315o=45o N of W  (NW)
    5/22       --         --          39o above S hor'zn             --                     --              24:00
    6/22       --         --          42o above S hor'zn             --                     --              24:00
    7/22       --         --          39o above S hor'zn             --                     --              24:00
    8/22     4:44 AM    10:12 PM      30o above S hor'zn     47o=43o N of E  (NE)  312o=42o N of W  (NW)
    9/22     7:06 AM     7:32 PM      19o above S hor'zn     87o= 3o N of E   (E)  273o= 3o N of W   (W)
    10/22    9:20 AM     5:02 PM       8o above S hor'zn    124o=34o S of E (ESE)  236o=34o S of W (WSW)
    11/22      --          --        nevero above hor'zn             --                     --              00:00
    12/22      --          --        nevero above hor'zn             --                     --              00:00
    Location: Seattle Latitude: 48o N
    Date    Rise Time   Set Time         Noon Altitude          Rise Azimuth           Set Azimuth          Day Length
    1/22     7:48 AM     4:55 PM      23o above S hor'zn    119o=29o S of E(ESE)   241o=29o S of W (WSW)       hr:m
    2/22     7:03 AM     5:43 PM      32o above S hor'zn    104o=14o S of E  (E)   256o=14o S of W   (W)
    3/22     6:09 AM     6:25 PM      43o above S hor'zn     88o         (due E)   272o          (due W)
    4/22     5:08 AM     7:09 PM      54o above S hor'zn     71o=19o N of E  (E)   289o=19o N of W   (W)
    5/22     4:24 AM     7:48 PM      63o above S hor'zn     57o=33o N of E(ENE)   302o=32o N of W (WNW)
    6/22     4:11 AM     8:11 PM      66o above S hor'zn     52o=38o N of E(ENE)   307o=37o N of W (WNW)
    7/22     4:34 AM     7:57 PM      63o above S hor'zn     58o=32o N of E(ENE)   302o=32o N of W (WNW)
    8/22     5:14 AM     7:10 PM      54o above S hor'zn     71o=19o N of E  (E)   288o=18o N of W   (W)
    9/22     5:56 AM     6:08 PM      43o above S hor'zn     88o         (due E)   271o          (due W)
    10/22    6:38 AM     5:09 PM      31o above S hor'zn    105o=15o S of E  (E)   254o=16o S of W   (W)
    11/22    7:24 AM     4:26 PM      22o above S hor'zn    120o=30o S of E(ESE)   240o=30o S of W (WSW)
    12/22    7:55 AM     4:20 PM      19o above S hor'zn    125o=35o S of E(ESE)   235o=35o S of W (WSW)
    Location: San Diego Latitude: 33o N
    Date    Rise Time   Set Time         Noon Altitude          Rise Azimuth           Set Azimuth          Day Length
    1/22     6:49 AM     5:11 PM      38o above S hor'zn    113o=23o S of E(ESE)   247o=23o S of W (WSW)       hr:m
    2/22     6:24 AM     5:40 PM      47o above S hor'zn    102o=12o S of E  (E)   259o=11o S of W   (W)
    3/22     5:50 AM     6:01 PM      58o above S hor'zn     89o         (due E)   271o          (due W)
    4/22     5:11 AM     6:23 PM      69o above S hor'zn     75o=15o N of E  (E)   285o=15o N of W   (W)
    5/22     4:45 AM     6:45 PM      78o above S hor'zn     65o=25o N of E(ENE)   295o=25o N of W (WNW)
    6/22     4:41 AM     7:00 PM      81o above S hor'zn     61o=29o N of E(ENE)   299o=29o N of W (WNW)
    7/22     4:55 AM     6:54 PM      77o above S hor'zn     65o=25o N of E(ENE)   295o=25o N of W (WNW)
    8/22     5:16 AM     6:26 PM      69o above S hor'zn     75o=15o N of E  (E)   284o=14o N of W   (W)
    9/22     5:36 AM     5:45 PM      57o above S hor'zn     89o         (due E)   271o          (due W)
    10/22    5:58 AM     5:08 PM      46o above S hor'zn    103o=13o S of E  (E)   257o=13o S of W   (W)
    11/22    6:25 AM     4:44 PM      37o above S hor'zn    114o=24o S of E(ESE)   246o=24o S of W (WSW)
    12/22    6:47 AM     4:47 PM      34o above S hor'zn    118o=28o S of E(ESE)   242o=28o S of W (WSW)
    Location: Quito Latitude: 0o S (note: alt=12,000 feet)
    Date    Rise Time   Set Time         Noon Altitude          Rise Azimuth           Set Azimuth          Day Length
    1/22     6:22 AM     6:29 PM      71o above S hor'zn    110o=20o S of E(ESE)   250o=20o S of W (WSW)    12:07 hr:m
    2/22     6:24 AM     6:31 PM      80o above S hor'zn    100o=10o S of E  (E)   260o=10o S of W   (W)    12:07
    3/22     6:18 AM     6:24 PM      90o=overhead           89o         (due E)   271o          (due W)    12:06
    4/22     6:09 AM     6:16 PM      78o above N hor'zn     78o=12o N of E  (E)   282o=12o N of W   (W)    12:07
    5/22     6:07 AM     6:14 PM      69o above N hor'zn     70o=20o N of E(ENE)   290o=20o N of W (WNW)    12:07
    6/22     6:13 AM     6:19 PM      66o above N hor'zn     66o=24o N of E(ENE)   294o=24o N of W (WNW)    12:06
    7/22     6:17 AM     6:24 PM      69o above N hor'zn     70o=20o N of E(ENE)   290o=20o N of W (WNW)
    8/22     6:14 AM     6:20 PM      78o above N hor'zn     78o=12o N of E  (E)   282o=12o N of W   (W)
    9/22     6:04 AM     6:10 PM      90o=overhead           89o         (due E)   270o          (due W)
    10/22    5:55 AM     6:02 PM      79o above S hor'zn    101o=11o S of E  (E)   259o=11o S of W   (W)
    11/22    5:56 AM     6:04 PM      70o above S hor'zn    110o=20o S of E(ESE)   250o=20o S of W (WSW)
    12/22    6:08 AM     6:17 PM      67o above S hor'zn    113o=23o S of E(ESE)   247o=23o S of W (WSW)
    Location: Valparaiso Latitude: 33o S (note: on Pacific Coast due West of Santiago)
    Date    Rise Time   Set Time         Noon Altitude          Rise Azimuth           Set Azimuth          Day Length
    1/22     6:01 AM     7:59 PM      76o above N hor'zn    114o=24o S of E(ESE)   246o=24o S of W (WSW)      hr:m
    2/22     6:31 AM     7:53 PM      67o above N hor'zn    103o=13o S of E  (E)   257o=13o S of W   (W)
    3/22     6:53 AM     6:58 PM      56o above N hor'zn     90o         (due E)   270o          (due W)
    4/22     7:16 AM     6:18 PM      44o above N hor'zn     76o=14o N of E  (E)   284o=14o N of W   (W)
    5/22     7:37 AM     5:53 PM      36o above N hor'zn     66o=24o N of E(ENE)   294o=24o N of W (WNW)
    6/22     7:52 AM     5:49 PM      33o above N hor'zn     62o=28o N of E(ENE)   298o=28o N of W (WNW)
    7/22     7:47 AM     6:03 PM      36o above N hor'zn     66o=24o N of E(ENE)   294o=24o N of W (WNW)
    8/22     7:19 AM     6:24 PM      45o above N hor'zn     76o=14o N of E  (E)   284o=14o N of W   (W)
    9/22     6:39 AM     6:45 PM      56o above N hor'zn     90o         (due E)   270o          (due W)
    10/22    6:00 AM     7:07 PM      68o above N hor'zn    104o=14o S of E  (E)   256o=14o S of W   (W)
    11/22    5:34 AM     7:35 PM      76o above N hor'zn    115o=25o S of E(ESE)   256o=26o S of W (WSW)
    12/22    5:36 AM     7:58 PM      80o above N hor'zn    119o=29o S of E(ESE)   241o=29o S of W (WSW)

    Short Questions about the Solar System

    Short Questions about the Solar System ssquest.html

    1. The solar system rotates quite fast with all the planets going around the sun on time scales of years. The clouds of gas and dust we see in the galaxy that are probably going to form new solar systems are rotating so slowly we can barely detect it but we are sure they are rotating a little bit. Describe how the change to fast rotation probably occurred as our solar system was being formed. You may wish to use the analogy of a spinning figure skater or a child moving on a roundabout.

      Some pulsars have been observed having extremely short periods, such as 0.003 seconds. These are the millisecond pulsars. These rotate rapidly because, it is thought, material falling onto the neutron star spins it up, just like a ball rotating on your fingertip will speed up if you periodically strike it in the appropriate manner. Most stars form in giant moleeular clouds that have star masses as large as 106 times the mass of the Sun and typical diameters of 50 to 200 LY. The best-studied molecular cloud is Orion, where star formation began about 12 million years star formation to our view in Orion. The formation of a star inside a molecular cloud begins with a dense core of mater- ial, which accretes matter and collapses due to gravity The accumulation of material halts when the protostar develops a strong stellar wind. A turbulent cloud will form a rotating planet. with an equatorial disk of material. The wind tends to emerge more easily in the direction of a protostar's poles,
    2. There appears to be little in the way of junk left in the solar system within the orbits of the giant gas planets except the asteroid belt. By junk I mean other asteroids, mini-planets or mountainous chunks of ice similar to comets. From the craters on the moon and elsewhere we think that there was probably a lot of junk around in the early solar system. Describe what we think happened to any junk that didn't hit something directly.

      Most likely the junk continued on out of the solar system.
    3. Historically astronomy was limited to visible light; meaning light we can see with our eyes.
      Visible light is still particularly important for astronomers on the ground even though we have electronics that can detect all sorts of other wavelengths of light we cannot see with our eyes.
      What is it about Earth's atmosphere that makes visible light more useful than most other wavelengths of light for astronomers on the ground?
      Note: The answer you give should have nothing to do with whether we can see particular type of light using our eyes.

      Unlike stars, which are fueled by nuclear reactions, planets faintly reflect light and emit thermal infrared radiation. In our solar system, the sun outshines its planets about one billion times in visible light and one million times in the infrared. Because of the distant planets' faintness, astronomers have had to devise special methods to locate them. The Doppler planet-detection technique, which involves analyzing wobbles in a star's motion. Ultraviolet Light, Infrared, Gamma Rays.
    4. Brightness and Radar measurements. Suppose we have a radar dish that generates a strong signal that travels out to hit an asteroid 109 kilometres away.
      (a) How would the brightness of the radar signal arriving at the asteroid change if the asteroid was moved twice as far away?
      The asteroid would become 20 18 kilometres away. The asteroid would be dimmer. (b) How would the brightness of a signal originating at the asteroid and detected back on Earth vary if the asteroid was moved twice as far away?
      The brightness of a signal would become dimmer more fainter to see. (c) In the radar experiment the asteroid reflects that part of radar signal that arrives at it back in all directions. In this way it is behaving like a weak source of radar signals. The part of the signal comes back to the original radar has a brightness of 81. The lowest signal we can detect has a brightness of 1. Determine the way the strength of the detected signal varies with the distance that the asteroid is away from the radar dish. What is the furthest an asteroid of the same size and other characteristics could be away from us before we could no longer use this radar equipment to measure the distance to it?

      The asteroid would be a brightness of 1.

    5. Examine the table. Which planets would float if you dropped them in the Sun? Which would float if you dropped them in water? Which would sink fastest?

    6. How many sets of planets would you need to create the mass of the Sun?

    7. What do the orbits of the planets and satellites tell us about the rotation of the cloud that formed the solar system?

    8. The speed of light is 300,000 kilometres per second. This number isn't easy to get a feel for but it's good it's so fast because it allows us to see things instantly on Earth without waiting for the light to arrive.
      The Sun is far enough away that light takes an appreciable time to travel to us. Assuming the sun is 150,000,000 kilometres away, how long would it take us to realize if the sun suddenly stopped shining?

      8 minutes.

    A Scale Model of the Solar System scale.html
    A Scale Model of the Solar System


    For this homework, we want you to describe an astronomical scale model.


    The distances and numbers we will discuss in this class are so large that they are often hard to relate to. One way of making these numbers more comprehensible is to shrink it down - to make a scale model. Architects and engineers will often make scale models to see what their project will look like before building it; model railroads and doll houses are other examples of scaled down versions of the real objects. The basic idea behind all of these is to ``scale'' the real thing down - make everything the same fraction of its real size.


    Design a scale model of the solar system and its nearest neighbor. Your model should include the following:

    My model is *Sun *Earth *Moon *Mars *Jupiter *Pluto * Alpha Centauri Object Distance (km) Angular size (") Sun 1.5 X 10 8 1800 Mars distance from the sun is 1.5237 a.u. 2.279 x 10 8 km. Jupiter 5.2028 a.u. 7.783 x 10 8 km. Pluto 6.3 x 10 9 0.06 All of the relevant numbers for the sizes and distances for these objects can be found in the appendices (1) of the text book. To convert them to your scale, simply divide them by your chosen scale factor. For example: If you choose to make a 1/10th scale model, you would then make the Earth (with a real radius of 6378 km) have a radius of 637.8 km in your model. Obviously, picking the correct scale is important. Making a 1/10th scale model of the Earth isn't very useful, but making a 1/1000th scale model of a doll house isn't going to be much good either. So choosing the right scale to display your information is important. If you are having trouble choosing a scale (or with any other part of this assignment) talk to your TA.

    What to turn in:

    (1) - The Appendices: The back of astronomy textbooks are full of data tables of useful information. For this project, the most useful parts are unit conversions, the information on the sun, and the information on the planets. The semi-major axis is the average distance from the planet to the sun. Alpha-Centauri is just like the sun in size.
    The Sizes of Everything sizes.html The Sizes of Everything

    The goal of this exercise is to identify objects spanning a full range of physical sizes. A secondary goal is to reacquaint you with power-of-ten notation. Get help quickly if you need it.

    The exercise is much harder than it looks. You may work with a partner, but everyone must turn in their own version.


    Sizes will be measured in light-seconds, light-hours, light-years, etc. A light-unit is the distance travelled by light in the indicated time. For example, since light travels at a speed of 300,000 km/sec, a light-second is 300,000 km. A light year (l-y) is the distance travelled by light in one year, or:

    300,000 km/sec x 60 sec/min x 60min/hr x 24hr/day x 365.26 days/yr = 1013 km.

    Your job is to fill the empty parts of the table below with examples of objects or distances of the appropriate size. You may not be able to fill all of the entries (feel free to leave any two boxes empty). Your entries in the table should follow the examples shown below. The words "distance" or "size" should appear in each entry along with a corresponding number rounded to the nearest power of 10.

    Be as complete as you can. You may need to browse through the entire text to find the answers. Even better is the videotape "Powers of 10" available at the media center of the Oedegaard undergraduate library (mezzanine level). For faster service mention Astronomy 101 when requesting the tape.

    There is no value in being highly precise in your answers. That's why the range of powers of ten is shown in each box. We're just looking for scale sizes. Its like saying that people are larger than rain drops (a few millimeters) and smaller than cars (a few meters).

    Approx Size Example of object size or distance from Earth
    10-18 - 10-15 l-s size of atom = about 10-19 light-sec
    10-15 - 10-12 l-s  
    10-12 - 10-9 l-s  
    10-9 - 10-6 l-s size of person = few x 10-9 light-sec
    10-6 - 10-3 l-s  
    10-3 - 100 l-s  
    100 - 103 l-s distance to Moon = about 1 light-sec
    103 -106 l-s  
    106 - 109 l-s
    note: 107.5 l-s = 1 l-y
    distance to nearest stars = a few light years
    (Switch to the more reasonable units of light years hereafter...)
    103 - 106 l-y  
    106 - 109 l-y  
    109 - 1012 l-y  
    1012 - 1015 l-y  

    Global Warming warming.html
    Global Warming


    This is a little exercise on "global warming". You will be given a month of the year. For your month you are to go and look up the year which had the highest high temperature and the lowest low temperature on EACH day of that month. You can find this information by looking up old local newspapers (the weather page should have the information you need) or in an almanac.

    Then you should plot two histograms of the distribution of "hot" years and "cold" years, and comment on what you find. Do you see a trend? Is it significant? What does this data suggest about the possibility of global warming? Are there problems with the data?

    Comment briefly (1-2 paragraph), on your results. Also, mention where you got your information from, the name of the almanac or newspaper. You may work in pairs to collect your data, but you must each turn in your own write-up.

    Life on Europa? europa.html

    Life on Europa?


    Given information about life living under extreme conditions on Earth and the evidence for a liquid ocean on Europa, the students will summarize their position in the "Life on Europa" debate and judge whether or not further exploration is warranted.


    This is a web-research activity. Your first goal is to find and read enough information to be able to present, in a few paragraphs, the arguments for and against the possibility of primitive life in the liquid oceans underlying Europa's icy surface. Your second goal is to judge whether or not we should be funding future probes to Europa.

    Because this is an essay and not a lab, some initial guidance is definitely warranted. First, because we are looking for life that can live under hostile and exceptional conditions, we need to formally define some terms. As you review the following "definitions," be sure to read the supporting links for needed information.


    Type up your responses for the following topics. Your essay should be in narrative form, having good paper structure, and not simply rote answering of the questions. Put in a good opening paragraph that will let the reader know what is to follow. You do not need to go into great detail in any of the areas, but you must show you have read the material and are "qualified" to enter into the scientific debate. Nicely constructed two-three paragraphs for each should do. Be sure to bring in information from the above readings and what you have learned during this quarter.

    My Europa essay is Europa's icy surface is only lightly cratered. Europa Liquid Water Locked in Ice Europa is covered by an ocean of liquid water whose surface layers are frozen. Europa, have thick rocky mantles, possibly similar to the crusts of the terrestrial planets, surrounding iron/iron sulfide cores. Europa has a thin water/ice outer shell about 150 km thick. has relatively few craters on its surface, suggesting geologic youth, perhaps just a few million years. Recent activity must have erased the scars of ancient meteoritic impacts. Europa's surface displays a vast network of lines crisscrossing bright, clear fields of water ice. Some of these linear "bands," or fractures, appear to extend halfway around the satellite and resemble in some ways the pressure ridges that develop in ice floes on Earth's polar oceans. Figure 11.19 The second Galilean moon is Europa. Its icy surface is only lightly cratered, indicating that some ongoing process must be obliterating impact craters soon after they are formed. The origin of the cracks crisscrossing the surface is uncertain. The resolution of the Voyager 2 mosaic in (a) is about 5 km. The two images below it (b and c) display even finer detail. (d) At 20-m resolution-the width of a typical house-this image from the Galileo spacecraft shows a smooth yet tangled surface resembling the huge ice flows that cover Earth's polar regions. Jupiter’s Moon Europa Before Galileo's arrival, some researchers had theorized that Europa is completely covered by an ocean of liquid water whose top is frozen at the low temperatures that prevail so far from the Sun. In this view, the cracks in the surface are attributed to the tidal influence of Jupiter and the gravitational pulls of the other Galilean satellites, although these forces are considerably weaker than those powering Io's violent volcanic activity. However, other planetary scientists had contended that Europa's fractured surface was instead related to some form of tectonic activity, one involving ice rather than rock. High-resolution Galileo observations now appear to support the former idea. Figure 11.19(d) is a Galileo image of this weird moon, showing what look like "icebergs -flat chunks of ice that have been broken apart and reassembled, perhaps by the action of water currents below. Mission scientists speculate that Europa's ice may be several kilometers thick and that there may be a 100-km-deep ocean below it. If Europa does have an ocean of liquid water below its surface ice, it opens up many interesting avenues of speculation about the possible development of life there. In the rest of the solar system, only Earth has liquid water on or near its surface, and most scientists agree that water played a key role in the appearance of life here (see Chapter 28). However, bear in mind that the existence of water does not necessarily imply the emergence of life. Europa is a very hostile environment compared with Earth. The surface temperature on Europa is just 130 K, and the atmospheric pressure is only a billionth the pressure on our planet. Nevertheless, the possibility, however remote, of life on Europa was an important motivating factor in the decision to extend the Galileo mission for two more years.
    The total essay should be about 2-3 pages long (12 pt, space-and-a-half, 1" margins -- or single spaced with double spaces between paragraphs). Your essay will be graded upon the clarity of your writing, indication that you have reviewed the material, and overall good writing techniques.

    Other sites of interest

    So, now you want to become an astrobiologist. You can, you know. Study hard and then apply to become a graduate student in the first astrobiology PhD program in the States. Check out the University of Washington Astrobiology Program, a cross-disciplinary study in the possibility of life beyond Earth.

    catalog of Europan links

    A different approach to the debate of liquid water and life on Europa

    Europa Web Sites

    Extremophiles Scientific American, April 1997.

    Some very serious considerations about Preventing the Forward Contamination of Europa from The National Academies.

    Last updated on: Short Questions about Stars starquest.html

    Short Questions about Stars

    1. Sunlight is composed of a mix of colours: effectively all of the colours our eyes can appreciate. Anything that produces fairly similar amountsof all kinds of visible light appears white to our eyes.
      When sunlight bounces off a blue shirt, the shirt doesn't look white.
      What is happenning to blue light that comes from the sun and strikes the shirt?
      What happens to light of other colours?

    2. Parallax. Two people are sitting in a car driving along a road towards the sun at sunset so that the sun is level with the car in the vertical direction. Each person sitting in his or her seat is 1 metre to either side of the centre of the car and there is a traffic light 100 metres directly ahead of the centre of the car.

      a. What is the angle between the traffic light and the sun for the driver?
      You may wish to draw a diagram to help you visualize this. I will also describe the situation if asked.
      b. Will the angle between the traffic light and the sun increase or decrease as the car moves closer to the light?

    3. Parallax and proper motion are both movements of stars in the sky. Describe an experiment which will "untangle" the two effects.

    4. What can be said about a star's radial velocity if its spectrum shows no Doppler shift?

    5. Which of the following pairs of quantities can be plotted against each other to produce an H-R diagram?
      a) Temperature and Distance
      b) Temperature and Spectral Class
      c) Luminosity and Spectral Class
      d) Luminosity and Temperature
      e) Luminosity and distance
      f) distance and spectral class

    6. Why are most stars in the H-R diagram on the main sequence?

    7. How does the brightness of a giant star compare with the brightness of a main sequence star of the same spectral class?

    8. Describe what happens to a blackbody's brightness and color as the temperature increases.

    9. What evidence do we have that stars form in the "clumps" of Giant Molecular Clouds?

    10. Why is it impossible for a gas with all its atoms in the ground (lowest-energy) state to produce emission lines?

    11. The photosphere is where most of the light we see coming from the sun originates.

      Briefly describe the physical processes involved in setting a depth for the photosphere. Think in terms of a specific photon moving outward at some depth within the sun.

    12. The solar cycle lasts 22 years.

      (a) Describe the way that the sun changes as the solar cycle approaches a maximum.
      (b) Explain why there are solar maxima every 11 years.

    13. What is the principle difference between stars that determines the observed colour of the star? This difference is apparent in the photosphere of the star.

    14. A rough guide to the apparent brightness of a star is as follows:
      Brightness = constant x Area of surface x (Temperature4)
      This assumes that the star is close to a blackbody emitter of light.

    15. Stars are brighter when they are larger because there is a greater area of star emitting light.
      What other property of massive stars contributes to the greater amount of light energy being emitted by them compared to less massive stars?

    16. A Red giant star is an old star that has expanded in size. It is much brighter than the original star.
      a. If the radius of the star has increased by a factor of 1000 (engulfing the inner planets) how would you expect the brightness to change?
      b. How could you explain it if the brightness increased by a factor of 500,000 when the star became a red giant? Assume that the radius of the star was still increased by a factor of 1000. Please give a numerical estimate of the change.

    17. Stars are hot and produce light before they start to burn Hydrogen into Helium using fusion. What is the early source of energy?

    18. (a) Why is it that converting Hydrogen into Helium produces energy?
      (b) For which elements does the process of converting those elements into heavier elements using fusion not produce energy?

    19. What is the difference between an optical double and a true binary star system?

    20. What property of each individual star can we attempt to measure when the star is a member of a binary star system that we can't measure for single stars? (Hint: using Newton's Law of Gravity)

    21. Variable Stars result from an instability in the way the shells where fusion is occuring in the star burn. State a way a variable star might change periodically that results in greater and lesser amounts of light coming from the star.

    22. (a) What is required for a star to be able to burn heavier elements than Hydrogen (what condition must the star achieve in its core?)
      (b) What happens to a star when is starts to run out of the current element it is burning in its core? (hint: This will happen to the sun in 4-5 billion years when it has exhausted all the Hydrogen in its core)
      (c) What property of a star determines the heaviest element it can burn?
      For example, how can we tell if a star will eventually burn Carbon into heavier elements?

    23. Why is it that we saw neutrinos before we saw the light from Supernova 1987a?

    24. Degenerate Electron pressure holds up white dwarf stars. Explain how this makes the star stable and not prone to the dramatic expansion and collapse phases that it underwent when it was still using fusion to produce energy. (hint: consider what held the star up before)

    25. Neutron stars are the size of mountains and weigh as much as a star. Why do neutron stars spin so fast?

    26. For a very large black hole of the type thought to occupy the centres of galaxies the tides near the event horizon are too weak to harm a space traveller.
      Could you tell when you passed through the event horizon of such a black hole?

    27. Why would no pulses be observed from a rotating neutron star if its magnetic axis and spin axis were aligned?

    28. What does angular momentum have to do with the rapid rotation of neutron stars?

    29. Describe the main difference between the mass-radius relationship for main sequence stars and the mass-radius relationship for white dwarfs.

    Spectra Homework spectra.html Spectra

    I. Thermal Radiation

    Solids and dense gases give off a continuous spectrum of electromagnetic radiation simply due to the thermal motion of the atoms and molecules jostling each other about. For example, a chunk of lead is heated to 1,000 degrees Kelvin, then 2,000 degrees Kelvin, then 3,000 degrees Kelvin. The amount of electromagnetic radiation given off at each wavelength of the spectrum is measured, using a light meter. The following results are obtained:

    at 1,000 K at 2,000 K at 3,000 K
    4,000 8.7 X 10-7 56 23,000
    5,000 3.8 X 10-4 675 82,000
    6,000 0.018 2986 162,000
    7,000 0.26 7660 236,000
    8,000 1.8 14,000 285,000
    10,000 21 28,000 312,000
    15,000 336 41,000 210,000
    20,000 879 33,000 117,000
    30,000 1283 15,000 39,000
    40,000 1030 7249 16,000

    a) Graph the amount of EM radiation emitted versus wavelength for each temperature all on one plot. (So you should have 3 curves, one for each temperature, on your graph. Put wavelengths on the horizontal axis (from 4,000 to 40,000 angstroms), and amount of radiation emitted on the vertical axis (from 0 to 350,000 ergs/cm2/s/angstrom).

    b) Referring to Figure 4-3 on p. 48 of your text, label the type of electromagnetic radiation that corresponds with the wavelengths on your horizontal axis (for example, "x-rays", "blue visible light", "radio").

    c) The peak of the curve shows the wavelength at which most of the radiation is being emitted. At which temperature would you most likely be able to see radiation with your naked eye? Explain your answer.

    d) From the three curves you plotted, at which temperature does the lead give off the most radiation at ALL wavelengths?

    e) Describe how your graph would be different if a chunk of aluminum were heated instead of a chunk of lead. Note that aluminum has 13 protons and lead has 82 protons.

    II. Line Radiation

    a) The above section described radiation from a solid chunk of material. The spectrum of a thin gas (many examples of which are in the spectroscopy lab) is very different from the thermal radiation spectrum of a solid or dense gas. How is the spectrum different?

    [Atom image] b) Describe how a photon would interact with the atom drawn at right to create:

    i) an absorption line
    ii) an emission line

    c) The above hydrogen atom absorbs a photon which has just the right amount of energy to kick the electron from the 2nd energy level to the 3rd. When this energized atom relaxes, how will the wavelength of the emitted photon compare with the wavelength of the photon which was absorbed?

    d) The spectrum from a star has continuous thermal radiation with absorption lines. Explain how this could be (a drawing may be helpful).

    III. Stars

    a) Suppose you observe three stars with both a red and a blue filter. Star A is brighter in the blue than in the red. Star B is brighter in the red than in the blue and Star C is equally bright in both the red and the blue. With this information, put the three stars in order of increasing temperature. Explain briefly how you got your answer.

    b) Suppose you see two stars with the same color--the peak of the thermal radiation curve is at the same wavelength. Yet one star appears 100 times brighter than the other. What can you conclude?

    Lifetime of the Sun lifetime.html The Lifetime of the Sun

    The sun gives off energy all of the time. This is the energy that all life uses to grow and live; whether directly (as photosynthesis by plants) or indirectly (as herbivores and carnivores that consume the energy stored in living things). Without that energy source, the Earth would be a dark, cold, lifeless place. So, it is certainly of interest to ask "Will the Sun be there tomorrow?", or, more usefully, to ask when the sun will stop shining. In other words, how long will the sun last?
    The goal of this homework assignment is to answer that question. The Sun formed from a spinning cloud of gas through gravitational collapse. The planets formed at the same time. So the ages of the planets provide a good estimate of the age of the Sun: 4.5 billion years. The Sun has been shining brightly, at almost exactly the same rate (a constant luminosity), for 4.5 billion years. This implies that it has been producing energy at a constant rate for those 4.5 billion years.

    1. Why can we say that the rate at which the sun gives off energy at the surface (the luminosity) must be equal to the rate at which it produces energy deep down in the core? (Hint: What would happen to the temperature of the sun if the two rates werent the same?)

      So, measuring the luminosity of the sun is equivalent to measuring the rate at which the nuclear reactions produce energy in the core of the sun. But we think we know exactly how those reactions work:

      4 H atoms -> 1 He atom + energy

      where the energy is released because some of the mass of the Hydrogen atoms is converted to energy.

      Mass of 1 Hydrogen atom:       1.673 x 10-24 grams
      Mass of 1 Helium atom:         6.644 x 10-24 grams
    2. This nuclear reaction has an input (4 H atoms) and two outputs : 1 He atom and energy. Since the He atom has less mass than 4 H atoms, that difference in mass must have been converted to energy. If the energy is produced via E=mc2, how much energy is produced by producing one He atom from 4 H atoms? (see also the units notes at the bottom). (Hint: How much mass is converted into energy?)

      So, for every 4 hydrogen atoms fused, we get the amount of energy you calculated above. But we know how fast the sun has produced energy (the luminosity, according to #1), so we know how fast the hydrogen fuel in the core of the sun is being used up.

    3. If the sun gives off 3.89 x 1033 ergs every second, how many hydrogen atoms are being destroyed every second?

      The sun will remain a main sequence star until it runs out of hydrogen fuel in the core of the star. The core of the sun contains about 10% of the total mass of the star.

    4. Why are these reactions confined to the core?

    5. The total mass of the sun is 2x1033 gm. How long will it take until the sun has used up all the hydrogen atoms in the core (the central 10%)? That is, what is the main-sequence lifetime of the sun?

    6. Compare the lifetime of the sun to the current age. How soon will the sun running out of fuel be a problem?

    Units Notes:
    Luminosity - energy per second; usually the total energy given off by an object per second.
    1 Watt = 107 ergs/sec
    1 Solar Luminosity = 3.89 x 1033 ergs/sec

    Energy - Bah. Try and define that. Usually measured in ergs; an erg is about the energy of one flea jump.
    1 erg = 1 gm*cm2/sec2 = 10-7 joules
    [if you use E=mc2 with the mass in grams, the speed in cm/sec, then you get E in gm*(cm/sec)2, which is gm*cm2/sec2 = ergs]

    Mass - the amount of matter. Usually measured in grams, or solar masses.
    1 solar mass = 1.989 x 1033 gm
    1 hydrogen atom = 1 proton = 1.67352 x 10-24 gm

    Speed - velocity; distance traveled per time unit. Measured in lots of units; We'll use cm/sec because of the definition energy in ergs
    Speed of light = c = 3.00 x 1010 cm/sec = 300,000 km/sec

    Time - measured in seconds, days, months, years.
    1 year = 3.15 x 107 seconds

    No Title sun.html

    The Sun

    The Sun is a Main Sequence star and therefore derives its energy from the fusion of Hydrogen nuclei into Helium. This process, known as the p-p cycle, starts with four Hydrogen nuclei and produces one Helium nucleus, and energetic positrons, neutrinos, and gamma rays.

    Four Hydrogen nuclei have a combined mass of M4H=6.693X10-27 kg, and one Helium nucleus has a mass of MHe=6.645X10-27 kg. The difference in the initial and final total mass in each fusion process, tex2html_wrap_inline87M = M4H - MHe = 0.048X10-27 kg, is converted into energy (and the Sun "loses" this mass). This is the famous tex2html_wrap_inline95, where m in this case is the difference in the masses tex2html_wrap_inline87M and c is the speed of light. The amount of energy released every time this takes place is tex2html_wrap_inline87Mc2=4.3X10-12 Joules.

    Star bright: Powering the Sun

    The Sun's total luminosity, 4X1026 Watts (or Joules/second)1, is ultimately derived from the energy released by many fusion reactions each second.

    1. How many fusion reactions per second are required to sustain the Sun's luminosity of 4X1026 Watts?

    Your answer should be roughly 100,000,000,000,000,000,000,000,000,000,000,000,000 (1038)!!

    2. The Sun is losing mass each time a fusion reaction occurs. What is the rate at which the Sun's mass is decreasing (in kilograms per second)?

    Your answer should be about several billion (109) kg / s. Since one ton is 103 kg, express this in millions (106) of tons per second. If one car weighs about 2 tons, how many millions of cars per second is this?

    3. How many years does it take for the Sun to lose the equivalent of the Earth's mass, M =6X1024 kg? Express this number in years (there are approximately 3X107 seconds in a year).

    That's a mighty long time: Lifetime of the Sun

    1. Here are pretty good assumptions about the Sun:

    1. The Sun was initially composed only of pure Hydrogen;

    2. The Sun's luminosity does not change over time;

    3. The Sun will use about 10% of its initial mass in fusion reactions2;

    4. . The Sun's total mass is approximately 2X1030 kg, which hasn't changed much since the Sun formed.

    Use this information to estimate how long the Sun can fuse Hydrogen into Helium.

    2. We can't directly measure the age of the Sun. However, the oldest rocks found on the surfaces of the Earth and the Moon are about 4.5X109 years old. What does this tell us about the current age of the Sun? How much longer will the Sun remain on the Main Sequence?


    3. Look at Table 1. The Sun is a G2 star. You might expect that stars more massive than the Sun will live longer than the Sun because the massive stars have more fuel available to burn: for example, a 15 Mtex2html_wrap_inline159 star should last 15 times longer than the Sun, or 150X109 years. But according to this table a 15 Mtex2html_wrap_inline159 star lasts a mere 11X106 years. Why?

    4. The age of the Universe is believed to be close to 14X109 years. Which classes of stars have never left the Main Sequence? Explain.

    Wed Feb 20 14:20:07 PST 2002
    The Sun, and General Properties of Stars sunstars.html
    The Sun and General Properties of Stars

    Answer the following questions on your own paper. Please show all work and answer each question completely.

    It was once thought that the source of the Sun's energy was gravitational contraction, a process that we know generates heat even today (that's how protostars initially ignite their nuclear fuel). We know that the Sun must generate energy as fast as it releases it. The total energy released by the Sun per second is about 4 x 1033 ergs. So if we can just find out how much energy the Sun can release over its whole lifetime (in ergs), we can determine how long it will live.

    A similar process can be used for a car. Say a car uses up 2 gallons of gas per hour. If we figure out how much fuel the car can hold (say, 20 gallons), then we know the car's lifetime of burning 2 gallons of fuel every hour will be 10 hours.

    (1) If we assume the Sun gets all of its energy from gravitational contraction, we find that the Sun has 4 x 1048 ergs of available "fuel''. How long can the Sun live (in years) with gravity as its only source of energy?
    This result was widely known and accepted around the turn of the century, until geologists using radioactive dating determined that the age of the Earth was about 5x109 years (5 billion years) old, much older than the apparent age for the Sun estimated in (1)! In fact, this was used as a creationist argument, supporting the fact that the Earth is indeed the oldest object in the Universe and hence must have been created.

    Much later, when the theory of nuclear fusion was being developed, scientists applied their theory to stellar energy generation and the Sun. Einstein's famous E = mc2 equation doesn't quite work here, since the reaction involved only converts a small fraction of the mass involved into useful energy. Still, there's a lot of energy involved.
    (2) Assuming that 10% of the Sun's mass is available for nuclear energy generation during its main sequence lifetime (only the Hydrogen close to the core, for reasons we will get into in class), and assuming that the mass is converted into energy with an efficiency of only 0.7%

    E = 0.1*0.007*MSunc2,

    calculate the total energy (in ergs) of the Sun. The mass of the Sun is 2 x 1033 grams and the speed of light is 3 x 1010 cm/sec.

    (3) Now estimate the lifetime of the Sun in years as in (1) with nuclear fusion as the power source. Your answer should be more in line (in order of magnitude at least) with the estimated age of the Earth.

    (4) We said in problem (2) that only the Hydrogen close to the core of the Sun or any other star will participate in the nuclear energy generation of the star during its main sequence lifetime. Explain why this is true.

    Atomic reactors (and weapons) produce large amounts of energy. Below you will compare this energy to the energy that a star gives off when it explodes as a supernova. (We will discuss supernova later in the quarter, for now it is sufficient to know that stars more massive than our Sun end their fusion lifetimes with a supernova event.)

    (5) When it first ignites, a rough estimate for the luminosity of a supernova is 1051 ergs/sec (about 1018 or a billion billion times more luminous than the Sun). We are located at about 1013 cm from the Sun. Imagine a supernova explodes at the center of the Solar System. We want to compare the amount of energy we receive from a supernova explosion to the energy we receive (remember the inverse square goes as 1/r2) at a distance of about 1 km from an atomic blast (1 km = 105) cm). A modern atomic weapon is rated at 50 Megatons (that's the amount of energy it can release), which is roughly 1024) ergs released per second. What is the ratio of the energy received from a supernova explosion on the Earth from the Sun to the ratio of energy we'd receive viewing a nuclear explosion from 1 km away?
    The questions below will help you understand parallax, and absolute versus apparent brightness.
    (6) There is a certain class of star called r-Lisam and all of these type of stars have the same luminosity (absolute brightness) = 3 x 1033) ergs/sec. One example of this type of star (Star A) has a parallax of 1/50 arcsecs. How far (in parsecs) is this star from Earth?

    (7) There is a another r-Lisam star (Star B) that has a parallax of 1/50 arcsecs as seen from SATURN. How far (in parsecs) is this star from Saturn? (Useful information: Saturn is 10 AU from the Sun.) About how far (in parsecs) is this star from Earth?

    (8) The apparent brightness of Star A (as measured in those funny units again) is 6x1032 ergs/sec/cm-2. What is the apparent brightness of Star B as seen from Earth? What would be the absolute brightness of Star B as observed from Neptune?

    The Cepheid Yardstick cepheid.html The Cepheid Yardstick


    At the age of nineteen, John Goodricke, an eighteenth century English astronomer observed that the star delta-Cephei brightened and dimmed in approximately 5-day cycles.

    When you spend a few days in a dark place with clear skies, you can observe the same cycles that Goodricke did in 1784. delta-Cephei is a star in the constellation Cepheus, near the north star. By keeping a careful record of its brightness relative to nearby stars over the course of a few nights, you can trace out a curve like the one shown in the figure.

    Since Goodricke's time, astronomers have discovered and catalogued thousands of stars whose brightness, or luminosity, like delta-Cephei's, undergoes cycles with periods of a few days. Such stars, called Cepheid variables, play an important role in determining the distances to nearby galaxies. This is because of a relationship, first noted by the American astronomer Henrietta Leavitt in 1912, between a Cepheid's period and its intrinsic brightness. If we know how much light a Cepheid in a distant galaxy gives off, we can calculate how far away it must be for it to appear as faint to us as it does. This lab explores this relationship and its application in detail.

    We cannot directly measure the distances to stars, and stars in other galaxies are much too far away for parallax measurements. We can, however, measure the periods of any Cepheid variable stars we can find in them. By assuming that these Cepheids obey the same period - absolute luminosity relation that their friends nearby have been observed to follow, we can compute how far away a galaxy must be in order that its Cepheids have their observed apparent luminosities. The distances to galaxies as far away as several million light years have been measured in this fashion.

    Cepheids in the SMC

    In 1522, a rag-tag crew of 21 sailed into the Spanish harbour of Seville. They were all that remained of Ferdinand Magellan's crew of 270 that had set sail from that same port three years before. Magellan and most of his crew hadn't survived the voyage, but those who had had sailed 'round the world. Among the stories they brought back to Europe was one of two fuzzy patches of starlight visible in the southern hemisphere's sky, which came to be known as the large and small Magellanic clouds.

    1. Today we know the Magellanic ``clouds'' to be nearby galaxies. Some of the stars in them are Cepheid variables whose periods and apparent luminosities have been measured. The data for nine Cepheids in the Small Magellanic Cloud or SMC are collected in the accompanying table.

      Star Period (days) App. Mag. log(Period)
      HV1871 1.2413 17.21 0.0934
      HV1907 1.6433 16.96 0.216
      HV11114 2.7120 16.54 0.433
      HV2015 2.8742 16.47 0.459
      HV1906 3.0655 16.31 0.486
      HV11216 3.1148 16.31 0.493
      HV11113 3.2139 16.56 0.507
      HV212 3.9014 15.89 0.591
      HV11112 6.6931 15.69 0.826

      Make a graph of apparent magnitude vs. log(Period) on a piece of graph paper. Draw a line through the data which represents approximately the period-luminosity relationship you observe.

    2. What, qualitatively, is the relationship between a Cepheid variable's period and its luminosity?

    3. Since all these Cepheids are the same distance away from us, their relative apparent magnitudes are the same as their relative absolute magnitudes. For this reason, when Henrietta Leavitt first made this plot, she realized that it suggested an approximate relationship between a Cepheid's period and its absolute magnitudes, and conjectured that this approximate relationship holds for all Cepheids. Suppose, for example, there were a Cepheid in the SMC with the same period as delta-Cephei, 5.3663 days (log(5.3663)=0.730). Read off from your graph what you would expect its apparent magnitude to be. You may indicate a range of reasonable values by including an uncertainty (i.e, +/-) in your answer.

              m(SMC-Ceph) = 

    4. The observed apparent magnitude of delta-Cephei is

              m(delta-Ceph) = 4.0

      much brighter than the apparent magnitudes of Cepheids in the SMC. This suggests that the SMC is much farther away than delta-Cephei. The distance to delta-Cephei has been determined using a variety of independent methods to be about

      	D(delta-Ceph) = 850 +/- 80 ly = 265 +/- 25 pc

      Using the Magnitude equation:

      	M = m + 5 - 5log(d)

      where d is in parsecs, compute the absolute magnitude(M) of delta-Cephei.

              M(delta-Ceph) = 

    5. The period-luminosity relation tells us that this is also the absolute magnitude of the (fictitious) SMC Cepheid with the same period as delta-Cephei, whose apparent magnitude you already estimated. Using the magnitude equation again, in this form:


      compute the distance to the SMC.
               Distance to SMC = 

      Give your answer in parsecs and in light-years (1 parsec=3.2 light years). The SMC is the second CLOSEST galaxy to the Milky Way (just slightly farther away than the Large Magellanic Cloud).

    6. The accepted distance to the SMC is 0.06 Mpc. Discuss briefly the possible source of errors in your calculated distance.

    Short Questions about Stellar Evolution evolquest.html

    Short Questions about Stellar Evolution

    1. Why does chemical composition change most rapidly in the center of a star?

    2. Why do nuclei of elements other than hydrogen require higher temperatures to fuse?

    3. Suppose 2 stars form at the same time. They have the same masses and compositions. What can be said about the evolution of the two stars from that point forward?

    4. Why does the process of creating neutrons from protons and electrons reduce the ability of a Giant star to support the weight of the star? In other words, why does gravity have a bigger advantage once the protons and electrons fuse into neutrons?

    5. Main sequence stars of 5 MSun are though to evolve into 1 MSun white dwarfs. What happened to the other 4 MSun?

    6. Why would no pulses be observed from a rotating neutron star if its magnetic axis and spin axis were aligned?

    7. What does angular momentum have to do with the rapid rotation of neutron stars?

    8. Which of the following pairs of quantities can be plotted against each other to produce an H-R diagram?
      a) Temperature and Distance
      b) Temperature and Spectral Class
      c) Luminosity and Spectral Class
      d) Luminosity and Temperature
      e) Luminosity and distance
      f) distance and spectral class

    9. Why are most stars in the H-R diagram on the main sequence?

    10. How does the brightness of a giant star compare with the brightness of a main sequence star of the same spectral class?

    11. What evidence do we have that stars form in the "clumps" of Giant Molecular Clouds?

    HR Diagram hrdiagram.html

    The H-R Diagram


    In the early part of this century, two astronomers, one Danish and one American, invented a diagram showing the basic characteristics of stars. The color-magnitude diagram, often called the Hertzsprung-Russell (HR) diagram in their honor, has proved to be the Rosetta Stone of stellar astronomy. The purpose of this homework is to give you some familiarity with the diagram. In addition, you will be asked to investigate the types of biases in mesurement used to construct this diagram. Biases are especially important in understanding astronomical data. Unlike laboratory sciences, astronomical experiments must be conducted under the conditions the Universe gives us. Since the astronomer has no direct control over the experiment, it is imperative that he or she understand the prejudices introduced into the data by the human perspective.

    However, biases of measurement are found in many other fields of science. An example of a biased study would be to find the weight vs. age relation for all Americans by weighing only members of health clubs. Most active health club members tend to be lighter than the average, and so the average derived would be lower than the true average weight of Americans.

    This exercise asks you to make comparisons between two different samples of stars. The bright star table was selected on the basis of apparent brightness NOT the luminosity of the stars. The near star table is all stars within 5 parsecs (about 15-16 lightyears) from the Sun.


    1. The first thing an astronomer does when faced with a pile of data is gaze at it, contemplates it, and wait for inspiration. Look over the two lists of stars and compare them to the star we know best, the Sun:

      1. Characterize the average properties of stars in the "Near Star List" as compared to the Sun. (mention Luminosity, color, and temperature.) "Nearby stars tend to be...."
      2. Characterize the average properties of stars in the "Bright Star List" as compared to the Sun. (mention Luminosity, color, and temperature.) "Apparently bright stars tend to be...."

      Plot log(L/LSun) versus Temperature for both the lists of nearest stars and brightest stars on the attached graph. Use contrasting colors or symbols so that the two samples of stars are clearly distinguished. The plot you have made will be an HR diagram. Label the region of the diagram where the main-sequence stars, Red Giant stars and White Dwarf stars are found.

    2. In a brief sentence or two, comment on the differences in location on your plot of these two groups of stars.

    3. Capella has approximately the same temperature as the Sun, yet it is 140 times as bright as the Sun. We know that the luminosity of a star is


      Knowing this, can you propose an explanation for the higher luminosity of Capella?

    4. Using this formula,


      and the lists, find the radius of the hot main-sequence star Vega, the very hot main-sequence star Hadar and the cool main-sequence star Ross 614-A as ratios of the radius of the Sun.

      	RVega/RSun  =    
      	RHadar/RSun  =   
      	RRoss 614-A/RSun  =    
      Note: In order to find L/LSun from the lists, you need to know about logarithms. Here is a quick reminder:


      means that


      Let's use a real number to work this out. Suppose that x=2, so that




      and therefore


      So the star is 100 times as luminous as the Sun.

    5. From the above calculation, do you see any trend between the size of a main-sequence star and its temperature? If so, what is it?

    6. For each list of stars, the nearest stars and the brightest stars, count the number of stars that fall into each of these temperature ranges: 3000 or less; 3001 to 5000; 5001 to 7000, 7001 to 10,000; greater than 10,000. Make a bar graph for each set using the second diagram. Again, use contrasting colors for the two samples so they can be easily distinguished from one another.

      Note: some star systems have more than one star in them; count each star in the system individually. For example the 40 Erid system is made of three stars, each of different temperature.

    7. Comment briefly on the differences between two samples of stars on the histogram you have drawn.

    8. We are not able to catalog all the stars in our Galaxy. However, if we assume that the Sun is situated in a typical piece of Galaxy, we should be able to assemble a sample of stars which accurately reflects the population of the whole Galaxy (e.g. when pollsters want to find out the President's approval rating, they don't ask ALL Americans, but rather they assemble a sample of ~1000 typical Americans and assume that this sample accurately reflects the whole population.)

      Which list (the bright star list or the near star list)would best be a representative of the total population of the Galaxy? Explain why!

    9. Besides giving us insight into the soul and disposition of stars, the HR diagram can be used to more pragmatic ends. You can use the HR Diagram you constructed to find the distances to stars via the method of spectroscopic parallax. Listed below are the apparent magnitudes and spectral types of six main sequence stars.

      Spectroscopic parallax distance determination

      Star Apparent
      Magnitude (m)
      Magnitude (M)
      m - M Distance
      Sirius -1.4 A1      
      Spica 1.0 B1      
      Barnard's Star 9.5 M4 V      
      61 Cygni A 5.2 K5 V      
      CN Leonis 3.5 M6 V      
      Tau Cet 3.5 G8      

      Use the spectral types and the HR diagram to estimate their absolute magnitudes. The difference between the apparent and absolute magnitudes is called the distance modulus. Calculate the distance modulus (m-M) for these six stars. The distance to a star (in parsecs) is given by:


      Calculate the distance to each of these stars. What assumptions are you making as you derive your distance estimate? How accurate do you think your distance estimate is?

    Table 1: Bright Stars
    Star M(V) log(L/Lsun) Temp Type Star M(V) log(L/Lsun) Temp Type
    Sun 4.8 0.00 5840 G2 Sirius A 1.4 1.34 9620 A1
    Canopus -3.1 3.15 7400 F0 Arcturus -0.4 2.04 4590 K2
    Centauri A
    4.3 0.18 5840 G2 Vega 0.5 1.72 9900 A0
    Capella -0.6 2.15 5150 G8 Rigel -7.2 4.76 12140 B8
    Procyon A 2.6 0.88 6580 F5 Betelgeuse -5.7 4.16 3200 M2
    Achemar -2.4 2.84 20500 B3 Hadar -5.3 4.00 25500 B1
    Altair 2.2 1.00 8060 A7 Aldebaran -0.8 2.20 4130 K5
    Spica -3.4 3.24 25500 B1 Antares -5.2 3.96 3340 M1
    Fomalhaut 2.0 1.11 9060 A3 Pollux 1.0 1.52 4900 K0
    Deneb -7.2 4.76 9340 A2 Beta Crucis -4.7 3.76 28000 B0
    Regulus -0.8 2.20 13260 B7 Acrux -4.0 3.48 28000 B0
    Adhara -5.2 3.96 23000 B2 Shaula -3.4 3.24 25500 B1
    Bellatrix -4.3 3.60 23000 B2 Castor 1.2 1.42 9620 A1
    Gacrux -0.5 2.10 3750 M3 Beta Centauri -5.1 3.94 25500 B1
    Alpha Centauri B 5.8 -0.42 4730 K1 Al Na'ir -1.1 2.34 15550 B5
    Miaplacidus -0.6 2.14 9300 A0 Elnath -1.6 2.54 12400 B7
    Alnilam -6.2 4.38 26950 B0 Mirfak -4.6 3.74 7700 F5
    Alnitak -5.9 4.26 33600 O9 Dubhe 0.2 1.82 4900 K0
    Alioth 0.4 1.74 9900 A0 Peacock -2.3 2.82 20500 B3
    Kaus Australis -0.3 2.02 11000 B9 Theta Scorpii -5.6 4.14 7400 F0
    Atria -0.1 1.94 4590 K2 Alkaid -1.7 2.58 20500 B3
    Alpha Crucis B -3.3 3.22 20500 B3 Avior -2.1 2.74 4900 K0
    Delta Canis Majoris -8.0 5.10 6100 F8 Alhena 0.0 1.90 9900 A0
    Menkalinan 0.6 1.66 9340 A2 Polaris -4.6 3.74 6100 F8
    Mirzam -4.8 3.82 25500 B1 Delta Vulpeculae 0.6 1.66 9900 A0

    Table 2: Nearby Stars
    Star M(V) log(L/Lsun) Temp Type Star M(V) log(L/Lsun) Temp Type
    Sun 4.8 0.00 5840 G2 *Proxima
    15.5 -4.29 2670 M5.5
    Centauri A
    4.3 0.18 5840 G2 *Alpha
    Centauri B
    5.8 -0.42 4900 K1
    Barnard's Star 13.2 -3.39 2800 M4 Wolf 359 (CN Leo) 16.7 -4.76 2670 M6
    HD 93735 10.5 -2.30 3200 M2 *L726-8 ( A) 15.5 -4.28 2670 M6
    *UV Ceti (B) 16.0 -4.48 2670 M6 *Sirius A 1.4 1.34 9620 A1
    *Sirius B 11.2 -2.58 14800 DA Ross 154 13.1 -3.36 2800 M4
    Ross 248 14.8 -4.01 2670 M5 Epsilon Eridani 6.1 -0.56 4590 K2
    Ross 128 13.5 -3.49 2800 M4 L 789-6 14.5 -3.90 2670 M6
    *GX Andromedae 10.4 -2.26 3340 M1 *GQ Andromedae 13.4 -3.45 2670 M4
    Epsilon Indi 7.0 -0.90 4130 K3 *61 Cygni A 7.6 -1.12 4130 K3
    *61 Cygni B 8.4 -1.45 3870 K5 *Struve 2398 A 11.2 -2.56 3070 M3
    *Struve 2398 B 11.9 -2.88 2940 M4 Tau Ceti 5.7 -0.39 5150 G8
    *Procyon A 2.6 0.88 6600 F5 *Procyon B 13.0 -3.30 9700 DF
    Lacaille 9352 9.6 -1.93 3340 M1 G51-I5 17.0 -4.91 2500 M7
    YZ Ceti 14.1 -3.75 2670 M5 BD +051668 11.9 -2.88 2800 M4
    Lacaille 8760 8.7 -1.60 3340 K5.5 Kapteyn's Star 10.9 -2.45 3480 M0
    *Kruger 60 A 11.9 -2.85 2940 M3.5 *Kruger 60 B 13.3 -3.42 2670 M5
    BD -124523 12.1 -2.93 2940 M3.5 Ross 614 A 13.1 -3.35 2800 M4
    Wolf 424 A 15.0 -4.09 2670 M5 van Maanen's Star 14.2 -3.78 13000 DB
    TZ Arietis 14.0 -3.70 2800 M4 HD 225213 10.3 -2.23 3200 M22
    Altair 2.2 1.00 8060 A7 AD Leonis 11.0 -2.50 2940 M3.5
    *40 Eridani A 6.0 -0.50 4900 K1 *40 Eridani B 11.1 -2.54 10000 DA
    *40 Eridani C 12.8 -3.20 2940 M3.5 *70 Ophiuchi A 5.8 -0.40 4950 K0
    *70 Ophiuchi B 7.5 -1.12 3870 K5 EV Lacertae 11.7 -2.78 2800 M4

    Black Holes blackhole.html

    Black Holes

    Because we can't actually go and grab a black hole, and bring it into the lab, and because we've never actually observed one, i.e. we have no data, we can only conduct "thought experiments" to explore their properties. Following are a few thought experiments to help you think about what's happening near and around a black hole.
    1. Imagine a big rubber sheet. It is very stiff, and not easily stretched, but it does have some "give" to it. Roll some golf balls across it. What happens to them? The golf balls start to roll on the big rubber sheet and then stop.
    2. Now put a bowling ball (very much heavier than a golf ball) in the middle of the sheet, so that it makes a big, slope-sided pit. Roll some more golf balls. What happens when:
      1. They are far from the bowling ball? The continue to roll.
      2. They come closer than the edge of the dip? They slow down.
      3. They go directly towards the bowling ball? They slow down and push against the bowling ball.
    3. In each of the three above cases, what happens if the golf balls are moving very quickly? They continue to roll and come to a sudden complete stop when in contact with the bowling ball. What if they are moving very slowly? They stop more quickly.
    4. What happens to the depth and width of the pit as the golf balls fall into the center near the bowling ball? (It may be easiest to imagine if you imagine putting lots of golf balls in.) It fills up with golf balls. Or the more the golf balls the more likely the bowling ball begins to roll. Expand.
    5. All of the above relates to ordinary stuff. Stars, people, planets, everything, interacts in this way because of gravity. In the case of black holes, things are a bit different. In this case, it is more accurate to think of the bowling balls as holes in the sheet, rather than as objects that sit on it. But they still affect the sheet in the same way. So. Imagine that at the bottom of the pit, where the bowling ball sits, there is a hole. Now think again about what happens when you roll the golf balls down the pit, directly towards the hole. They go away, and can never come back. When they do this, they make the pit deeper and wider. Why? The golf balls are giving off more energy or gravity as they go down into the hole, and they can not return.
    6. The hole is a good analogy for the event horizon of a black hole. (Except, of course, an object with the mass of a bowling ball does not have an event horizon that is the radius of the bowling ball!) Objects outside the event horizon will know that the black hole is there, because the sheet is sloping, but they won't get captured unless they come within the event horizon. Think about light for a moment, as though it were, say, grains of sand rolling across the sheet. What happens to the light as it passes the pit? What happens when it gets to the hole? The light begins to fade, and then the light disappears from view.
    7. Now, suppose that you roll another bowling ball across the sheet. What happens to the sheet when the second bowling ball falls in after the first? The sheet can become wrinkled or torn or flattened by additional bowling balls due to size of bowling balls. Would this affect your golf balls and grains of sand? How? What happens to the hole? Yes. It can cause the golf balls to slow down, and the hole is being filled up. What happens to the size of the pit? The pit is expanding becomes bigger in size.
    8. None of these thought experiments take into account the relativistic effects (length contraction and time dilation). Imagine for a moment that you are travelling close to the black hole. Because you are in a strong gravitational field, your rulers are shorter, and your seconds are longer than elsewhere in the Galaxy. Look out into the Galaxy, and describe what you see. Consider the lifetimes of stars, the distances between them, their motions in your sky, and how they die. Add anything else that occurs to you. This particular question is really good "bus fodder". As you are standing there like a piece of degenerate neutron matter, closer to your neighbors than you really want to be, you can think about what the Galaxy would look like to you if you lived very slowly, and were very small.

    I see very dim stars, very far away. The Galaxy would appear to be moving slowly in slow motion, and be very big in size from a distance. Stars maybe dimmer. Short Questions about Galaxies

    Short Questions about Galaxies galquest.html

    1. (a) What is the Astronomy definition of "metals"?
      (b) What does the fraction of metals observed in a star tell you about the gas that the star formed from?
      Assume that the amount of each element in the outer parts of a star is the same as in the cloud of gas from which it formed.

    2. Describe two differences between the two major populations of stars (labelled Population I and Population II) in terms of properties of the stars or where they are found. (Aside from the difference in the fraction of metals in the stars).

    3. Why must the star responsible for an HII region be a hot star rather than a cool star?

    4. Why wouldn't you expect to detect strong 21 cm emission from an HII region?

    5. How does the diffuse light in the galaxy compare to the average color of bright stars in the galaxy?

    6. If the distribution of globular clusters was even in all directions, as viewed from Earth, whaere would the Sun be in the Galaxy?

    7. What is the evidence that most of the mass in our Galaxy lies in some as-yet-undetected form?

    8. Why are young stars mostly found in the disk of our Galaxy?

    9. Describe the density wave theory of spiral arms.

    10. Briefly characterize the three major types of galaxies according to the Hubble system of classification:
      (Treat barred and unbarred galaxies as one type).
      (a) In terms of the shape of the Galaxies.
      (b) In terms of what they contain in gas and stars.

    11. What is it in clusters of galaxies that produces the X-rays we observe coming from the clusters?

    12. Describe what we think is the fundamental power source for Quasars.

    13. We believe galaxies we see close to us might be different to galaxies we see very far away. The galaxies far away were a lot younger when the light we see coming from them was made.

      a) Explain how you might expect the young age of distant galaxies to make them appear different to the old ones near us.

      b) Describe how the rapid movement of distant galaxies away from us due to the expansion of the universe makes them appear different.

    14. Supernova type Ia (caused by exploding white dwarfs) are used as standard candles to measure the distance to far galaxies. Briefly describe how this works.

    Distance to the Center of the Milky Way mwcenter.html

    Distance to the Center of the Milky Way

    Adapted from Learning Astronomy by Doing Astronomy by Ana Larson


    In this exercise, you will use the locations of globular clusters in the halo to estimate the distance of the Sun from the center of the Milky Way.

    Background and Theory

    In the not-too-distant past, astronomers though that the Sun was at the center of our galaxy, the Milky Way. Observations and determinations of distances were hampered by the lack of knowledge of interstellar dust, which blocks much of the starlight from distant parts of the galaxy (including the galactic center). It was not until the distances to globular clusters were determined using the RR Lyrae stars that a more accurate picture of the size and shape of our galaxy was constructed. By determining the distribution of the globular clusters, Harlow Shapley was able to determine the diameter of the galaxy, and the distanc to the galactic center.

    1. Using the polar graph in Figure 1, plot the galactic longitude versus distance for the globular clusters in Table 1. The Sun is at the center of this polar graph. Note that the distance given is not the actual distance, since we have projected a 3-dimensional space onto a 2-dimensional piece of paper. The actual distances are greater than those given here.

    2. Estimate the center of the distribution of globular clusters, and mark it on the graph. Describe how you defined the center of the distribution.
    3. Determine the distance from the Sun to the center of the distribution.
    4. Determine the direction to the center of the distribution. This is the direction to the center of the galaxy.
    5. In which constellation does the center of the galaxy lie?
    6. At what time of year is this constellation most conspicuous? Hint: check a planisphere, or the textbook.
    7. Why is the Milky Way Galaxy more spectacular in the summer than in the winter? (ignore weather conditions!)
    8. Describe the two dimensional space distribution of the globular clusters.
    9. How do we know the Sun is not at the center of this distribution?
    10. During their long orbit around the center of the Milky Way Galaxy, each globular cluster will cross through the plane of the disk. Why do we find most globular clusters far out in the halo? (Hint: Do Kepler's laws apply to globular clusters?)

      Figure 1: Polar Plot of the Distribution of Globular Clusters

      Table 1: Globular Cluster Data
      NGC # Gal.
        NGC # Gal.
        NGC # Gal.
        NGC # Gal.
      104 306 3.5   6273 357 7   288 147 0.3   6284 358 16.1
      362 302 6.6   6287 0 16.6   1904 228 14.4   6293 357 9.7
      2808 283 8.9   6333 5 12.6   Pal 4 202 30.9   6341 68 6.5
      4147 251 4.2   6356 7 18.8   4590 299 11.2   6366 18 16.7
      5024 333 3.4   6397 339 2.8   5053 335 3.1   6402 21 14.1
      5139 309 5   6535 27 15.3   5272 42 2.2   6656 9 3
      5634 342 17.6   6712 27 5.7   5694 331 27.4   6717 13 14.4
      Pal 5 1 24.8   6723 0 7   5897 343 12.6   6752 337 4.8
      5904 4 5.5   6760 36 8.4   6093 353 11.9   6779 62 10.4
      6121 351 4.1   Pal 10 53 8.3   6541 349 3.9   6809 9 5.5
      O 1276 22 25   Pal 11 32 27.2   6626 7 4.8   6838 56 2.6
      6638 8 15.1   6864 20 31.5   6144 352 16.3   6934 52 17.3
      6171 3 15.7   6981 35 17.7   6205 59 4.8   7078 65 9.4
      6218 15 6.7   7089 54 9.9   6229 73 18.9   7099 27 9.1
      6235 359 18.9   Pal 12 31 25.4   6254 15 5.7   7492 53 15.8
      6266 353 11.6        

      Short Questions about Cosmology

      Short Questions about Cosmology cosmquest.html

      1. The Cosmic Microwave Background was as bright as a star: a blackbody with a temperature of 3000 degrees K.

        a) Discuss the similarity between the photosphere of a star and the Last Scattering surface at redshift 1000 where the Cosmic Microwave Background was generated.

        Light can be scattered. b) Why is the Cosmic Microwave Background not as bright as a star today? A lot of the Cosmic Microwave Background has cooled off into colder temperatures and or disappeared.

      2. a) In the very hot early universe there were as many protons, anti-protons, electrons and positrons (anti-electrons) as photons. Where are most of the protons, anti-protons, electrons and positrons now?

        b) Why is there anything left now? eg. Why is there matter?

      3. Under what conditions is the expansion age of the Universe the same as the length of time since the Big Bang?

      4. What is meant by the statement that the surface of a ball has no center?

      5. Why does the CMB look like a 2.73 K blackbody when it was emitted by material that was 3000 K?

      6. How can globular clusters be used to place a lower limit on the age of the Universe?

      7. Why were no heavy elements produced in the Big Bang?

        The temperatures were extremely hot during the big bang. It is thought everything happened at once.
      8. a) Explain why an open universe (one that will never collapse on itself) is expected to have less matter in it than a closed universe (a universe that will eventually stop expanding and collapse).

        open universe, which is infinite, not only do you not re- turn to your starting point, but more space than you expect explain why there was originally more matter than antimatter. An open universe, corresponding to omega less than one, will expand forever. Matter will spread thinner and thinner. Galaxies will exhaust their gas supply for forming new stars, and old stars will eventually burn out, leaving only dust and dead stars. The universe will become quite dark and, as the temperature of the universe will approaches absolute zero, quite cold. The universe will not end, exactly, just peter out in a Big Chill. b) The age of the universe is roughly one divided by the expansion rate now: one divided by the Hubble constant. The true age is less because the universe was expanding faster in the past so the average value of one divided by the expansion rate is less than it is now. Would you expect an open universe to be younger or older than a closed one and why?

      9. a) Describe the advanced stages of closed and open universes: the long term fate of the universe in each case.

        b) Which do you find more appealing?

      Universe Expansion expansion.html Is the Universe Really Expanding?

      Is the tranquil universe that we observe in the warm summer skies really a universe peacefully at rest? You have heard that it is not; other people and your teachers claim that it is expanding. Frankly, any rational, thinking, observant person would be puzzled by this assertion. Just look up on a clear night. There isn't a trace of direct sensory evidence to support such an outlandish-sounding notion.

      So, you might reply, perhaps the Universe expands so slowly that the effects are not noticeable on scales of a century or more. I would reply that there's an equal possibility that the Universe is contracting, or that the motions of galaxies are slow and random (turbulent).

      To resolve these conflicts we need to gather some evidence.

      This brings us to the 1920s and Edwin Hubble. Hubble was exploring the distances to whirlpool nebulae --- what we now call galaxies. He had vast amounts of time on a huge new telescope. Hubble and his contemporaries devised new methods to estimate distances to galaxies, some of which required spectra of the light from galaxies to be measured. Once the spectra were obtained, Hubble was very surprised to note that the fainter, more distant galaxies had larger redshifts. Indeed, the pattern was best observable by selecting a class of objects that have the same shapes (so that he could be fairly certain that the objects were intrinsically the same kinds of galaxies). Then all you have to do is to plot the redshifts of those galaxies against their brightnesses.

      Let's see what you think. Here are modern velocity-distance graphs for three samples of galaxies.

      Recall our earlier discussion of the properties of stars. We found that the H-R diagram changed, depending on which sets of stars we analyzed. That is, data selection procedures will affect (bias) the patterns one finds in the data as well as the interpretations of these patterns.
      So to be cautious, we've selected the galaxies for the velocity-distance plots in three different ways.

      Firstly, we simply picked the 22 nearest galaxies. These objects are probably representative of all galaxies except for their distances. Secondly, the brightest 25 galaxies were graphed. Thirdly, a list of galaxies of the same appearance was selected, and the brightest members of this subclass were plotted. This might be useful since we plot objects whose intrinsic properties (luminosity, mass, whatever) are the same. Notice how the ranges of the axes change from graph to graph!


      Work with a partner. In the spirit of interpreting patterns in the data, carefully consider the graphs above and the biases in the way the galaxies were chosen. Next, sketch what you would expect for the velocity-distance graph if the Universe were static (all galaxies locked in place with respect to each other), turbulent (galaxies moving randomly with respect to each other), rotating (galaxies moving like planets around the Sun), uniformly expanding (galaxies moving apart in such a way that they maintain their relative positions while receding from each other), and uniformly contracting (as for expanding, but all galaxies approaching). You might also consider some hybrid models, such as a rotating universe with small random motions of galaxies.

      Now you interpret the data patterns. What is the simplest cosmological model consistent with the observations? Keep this in mind: the Universe behaves in only one way. Whatever interpretation you prefer, be sure that it accounts for all of the data in the three graphs, or at least as much of the data as possible.


      First, prepare schematic velocity-distance graphs of your expectations for a static, turbulent, rotating, expanding, and contracting universe. You can put all of these on the front side of a sheet of paper with your name and section on it. Then, on another sheet (or the reverse side of the first sheet), very clearly and concisely state your conclusion(s) about the state of the universe's global motions based on your interpretation of the data shown in the three graphs above.

      Short, Miscellaneous Questions miscquest.html

      Short Questions about Miscellaneous Topics

      Physical Principles physprinc.html Physical Principles
      1. What would happen to the Earth's orbit if the mass of the Sun were instantaneaously doubled? Would the Earth move closer to or further from the Sun?

      2. What if a giant trash compactor in the sky came and compressed the Sun to half its current volume? What would happen to the Earth's orbit then?

      3. If the Moon's angular momentum were cut to less than a third of what it is now but the mass remained the same: How would the Moon's orbit change?

      4. Which exerts a stronger gravitational attraction on you, your friend standing 3 meters away from you or the planet Jupiter? (Relevant info about Jupiter is in table 8-1 of your book, page 182.)

      5. Draw a thermal radiation curve (intensity versus wavelength) of an object that is at a temperature of about 6000 degrees K. Where is the high frequency end on your graph? What happens to the peak of the curve as you heat the object?

      6. Which releases more microwaves: a star at 6,000 degrees Kelvin or a star at 10,000 degrees Kelvin?

      7. Two stars are the same color. Star A is 9 times fainter than star B. Which is further away? How much further?

      8. The atom at right just absorbed a microwave photon.
        What does the conservation of energy say must happen to the electron?

      9. A moment later, the electron drops to the ground state. The conservation of energy says that a photon must be released by the atom. Is that photon shorter or longer than a microwave?

      10. Helium is the second element in the periodic table. It has two protons and two neutrons, and two electrons. If you add an extra neutron, is it still helium? If you take away one of the electrons, is it still helium? If you add an extra proton, is it still helium?

      Marble Estimation marbles.html

      Estimating Marbles in a Beaker

      On the first day of class, the class guessed how many marbles were contained in a large glass beaker. Now you are going to make a better (more scientific) estimate of the number of marbles in that beaker.

      Below are given the dimensions of the beaker (diameter and height), as well as the diameter of a marble. With this information, make a better guess at how many marbles are contained in the beaker. Diameter of beaker base: 127 mm.
      Height of beaker: 188 mm.
      Average diameter of a marble: 14 mm.

      The point of the assignment is not just to get the right number of marbles, the point is to explain how you approached the problem and got your answer. What approximations or assumptions did you make? Why did you make those approximations?

      In one half to one full page:

      1. Explain your Method for coming up with the number of marbles
      2. Include any approximations or assumptions you made
      3. Include all calculations you did (after all you have real numbers now)
      4. Include the result you get for the number of marbles in the beaker
      Be sure to think about how the marble fit in the beaker. Why is a simple calculation and division of the two volumes unlikely to give you the right answer?

      From: Ana Larson <> [Take]
      To: <>
      Subject: Astro C101 results
      Date: 01/12/04 10:07am
      Robert, you got 36/100 on the final exam.  You did the best on supernova
      questions, blackholes, and pulsars.

      This score gives you 45% for the quarter.  Because you were so conscientious
      in submitting the answers to the review questions (even though they were not
      graded), your decimal grade for the quarter is 0.7 -- essentially due to
      "extra credit" for this effort.

      Thanks for being in the class.


      Ana Marie Larson, PhD
      Astronomy Education

      Wet Anthrax or wet ricin wanted to convert some of its deadly anthrax or ricin into a dry powder the art, developed in 1959, of weaponizing Bacillus anthracis without milling. the microbiologists, showing them how to freeze-dry a slurry of anthrax simulant how to purify it to a trillion spores per gram in a centrifuge; and how to remove the electrostatic charge, to prevent clumping. had employed the less sophisticated method of acetone extraction to produce a pound of dry anthrax in a single day. enough to kill thousands of people. designing and testing germ agents. On lab animals like rats. Anthrax, Bacillus anthracis, is a bacterial pathogen. This rod-shaped microbe is commonly found in soil and is ingested by sheep, cows, horses, and goats it is labeled as a vetrinary disease. Anthrax is what's called a gram positive bacterium. This means it has the type of cell walls which are harmless, unlike the cell walls of gram negative bacteria, which attack tissue. anthrax can only attack tissue by producing a special toxin which it excretes. One cell or spore does not produce enough toxin to start an infection. Anthrax is deadly in its spore form. When environmental conditions are detrimental to the bacteria, the rod shaped pathogen desicates. Soon after, the cell breaks and begins sporulating. In this stage, the bacteria can remain dorment, surviving for decades. Then, when environmental conditions are favorable, the spore germinates and returns to its rod shaped form and begins forming clusters. Since the human body acts as a culture medium for the bacteria, anthracis is not likely to sporulate inside the human body; due to this, anthrax is not contagious. CLICK ON THE WEB ADDRESS BELOW TO PUBLISH, EDIT, OR DELETE THIS POSTING. If your email program doesn't recognize the web address below as an active link, please copy and paste the following address into your web browser: PLEASE KEEP THIS EMAIL - you will need it to publish and manage your posting! Your posting will expire off the site 30 days after it was created. Sea Stars Field Trip Measure your sea star from one ray to another a diameter of the wheel animal? The diameter is ½ inch. How many arms does your sea star have? 5 arms radiate from a centered disk. Can you see the eyes? Yes, except the eye spots are primitive light sensors are at the tip of the end of each arm. Each arm has a short sensory tentacle at its end that responds to chemicals and vibrations in the water, and a red photosensitive eyespot. A sea star often lifts the end of a arm to perceive light and movement. Describe what happened to sand particles. Describe the madreporite on your sea star color, texture. The sea star is brown, and spiny hard skin animal. On the aboral surface is a sieve-like plate termed the madreporite, which connects the internal canals of the water vascular system with the exterior. The madreporite leads to a vertical tube stone canal which joins a circular canal called the ring canal. Describe the tube feet on your sea star. The underside of the body of the sea star bears a mouth at the center and a groove running along each arm. The grooves contain rows of tiny, flexible appendages called tube feet. Sea stars move by means of the tube feet, which are operated by a hydraulic, or water vascular system. Sea Stars move very slowly along the seabed using tiny tube feet. Action of the tube feet in a sea star in motion. Is There a patter to the movement? Describe what you see? Sea stars do not tolerate that much dryness. longitudinal muscles of the tube foot contract, forcing water into the now relaxed ampulla. This shortens the tube foot. Sea Stars Field Trip Measure your sea star from one ray to another a diameter of the wheel animal? The diameter is ½ inch. How many arms does your sea star have? 5 arms radiate from a centered disk. Can you see the eyes? Yes, except the eye spots are primitive light sensors are at the tip of the end of each arm. Each arm has a short sensory tentacle at its end that responds to chemicals and vibrations in the water, and a red photosensitive eyespot. A sea star often lifts the end of a arm to perceive light and movement. Describe what happened to sand particles. Describe the madreporite on your sea star color, texture. The sea star is brown, and spiny hard skin animal. On the aboral surface is a sieve-like plate termed the madreporite, which connects the internal canals of the water vascular system with the exterior. The madreporite leads to a vertical tube stone canal which joins a circular canal called the ring canal. Describe the tube feet on your sea star. The underside of the body of the sea star bears a mouth at the center and a groove running along each arm. The grooves contain rows of tiny, flexible appendages called tube feet. Sea stars move by means of the tube feet, which are operated by a hydraulic, or water vascular system. Sea Stars move very slowly along the seabed using tiny tube feet. Action of the tube feet in a sea star in motion. Is There a patter to the movement? Describe what you see? Sea stars do not tolerate that much dryness. longitudinal muscles of the tube foot contract, forcing water into the now relaxed ampulla. This shortens the tube foot. 1 ounce into 4 ounces of liquid.