Supplementary Problems

1. Imagine that you are floating in space above the north pole looking at the earth.  Would you see the earth rotating clockwise or counterclockwise?

2. Imagine that you were an omnipotent being and could manipulate the earth's orientation in space at will.  With the earth still orbiting the sun along the same path that it now follows, what could you do to make the seasons on earth more extreme?

3. Calculate the earth's speed in miles per hour due to the earth's rotation about the sun.  Calculate the earth's speed in miles per second.  Whew!  That's pretty darn fast!  Given that speed, how far have you travelled in your lifetime due to the earth's rotation around the sun?

Essay 1. In a well written, well organized essay that does not exceed 2 double-spaced typewritten pages, please address the following topics: What was the Copernican revolution?  Include a brief discussion of both its scientific and theological/philosophical impacts on society.  Give an example of a modern day scientific issue that raises similar theological/philosophical questions, and briefly discuss why this issue raises similar questions.  Finally give an example of how the theological/philosophical questions raised by this contemporary issue are manifest in modern society.  Your example could (but need not necessarily) include references to pertinent current events, newspaper/magazine articles, movies, songs, etc. as appropriate.
This essay will count about the same in your grade as a quiz.  It will be graded based on 1) Whether and how well it addresses the topics posed above (70 %) and 2) How well it is written and organized (30%).

4. At the earth, what is the total amount of power received per unit area due to the sun?  To answer this question consider that the sun emits light equally in all directions.  This means that at a radius R away from the sun, the total amount of the sun's power is spread over the surface area of a sphere of that radius.  How does the amount of power per unit area from the sun compare to the amount of power per unit area received from a 100 W light bulb located on the ceiling about 3 m above you?

5. First answer this problem for visible light.  Then determine what wavelength of light is required so that diffraction becomes the primary limiting factor determining the resolution of the telescope.  In what region of the electromagnetic spectrum do we find this wavelength of light?

6. In order to resolve these two stars, we decide to observe them in a different wavelength using the Hubble Space Telescope.  What is the maximum wavelength we could use which would still allow us to resolve these stars?  What other technique could we potentially use to resolve these two stars? (Hint there is a picture in your book of a double-star taken by this technique.)

7. Would we still have an oxygen and nitrogen atmosphere on this new less dense earth?

8. You are standing outside on a bright sunny day.  Although you can't see the moon because it is daytime, you know the phase of the moon is new.  Consider how much you would weigh if the sun and the moon exerted no gravitational forces on you (ie your weight due only to the earth), and call this Fearth.  Now consider that the sun and moon do exert forces on you.  In this situation do these forces act to effectively increase or decrease your weight as you would read it on a standard bathroom scale?   Calculate the fractional change in your weight due to the sun and the moon pulling on you in this configuration.  Recall that fractional change is given as: (old weight - new weight)/old weight.  In this calculation you will probably find it helpful to find Fsun and Fmoon in units of Fearth.  If you weight 150 pounds due only to the earth, how much do you now weigh given the sun, moon, earth alignment?  Could you measure the effect of such an alignment on a standard bathroom scale?  How about a doctor's scale?  If you weighed yourself again at midnight on the same day (and assuming that your weight didn't change for other reasons) would you weigh the same, more or less? Why?

9. What is unusual about Venus's rotation?  What is unusual about Uranus's rotation?  Why are these deviations unexpected?  How can we account for them?

10. Some years from now the population on earth may come to exceed the capacity of Earth to support that population.  Some have suggested that at that time we will begin to colonize other planets (or possibly the moon).  Which planet would you choose to colonize?  Give several reasons for your choice of planet.  Also, for each planet you did not choose, state the main reason why not.

11.  Explain why Venus is the brightest planet in the night sky.  Explain why Jupiter is the second brightest planet in the night sky.

12. Compare the temperature of the sun's surface and core to temperatures we have experienced here on Earth.  One good reference temperature is the melting point of stainless steel at 1800 K.  This is probably one of the hottest regularly occuring events on Earth.  Another reference point is the hottest temperatures ever experienced on Earth, which occured during nuclear explosions.  The "Little Boy" that exploded in Hiroshima had a temperature of about 300,000 K at the center and about 6000 K on the ground below.

13. How are absolute and apparent magnitude related to luminosity and apparent apparent brightness?

14. How do astronomers measure the quantities necessary to plot a star on an HR diagram?

15. The following information is what astronomers can actually measure about the star Sirius A (think about how they measure each of these quantities):  parallax = 0.379'', apparent magnitude = -1.44, and the spectrum of the light it emits look like the image below.  Note that this spectrum came from the "Blackbody and stellar temperature" physlet in your ebook.  From this information figure out where Sirius A should fall on an HR diagram.  Compare your answer to the position of Sirius A on the HR diagram of Figure 10.14.

Now do the same calculation for Arcturus which has parallax = 0.09", apparent magnitude = -0.04 and a spectrum as shown below.  Again figure out where Arcturus should fall on an HR diagram and compare your answer to Figure 10.14.

16. In your discussion of the chain of events leading to the formation of a Sun-like star, focus on the evolution of the primordial gas cloud to a protostar and then to a star.  Be sure you give the properties of each of these phases as well as how and why the phases evolve from one to the next.

17. How can one star be hotter than another and yet less luminous?

18. What is an emission nebula and how do we observe it?  What is a dark dust cloud and how do we observe it?

19. Each "burning" of a subsequent element results from a similar series of steps.  Describe those steps and explain qualitatively why each occurs.

20. In order for Neon to fuse it must be moving at a velocity of about 1200 km/s or greater.  In Figure 12.17, what is approximate temperature of the "Neon fusion" layer?

21. Explain the saying "We are all stardust."

22. What is a nova and why does it occur?  What is a supernova and why does it occur?

23. How can you estimate the age of a star cluster by looking at its HR diagram?

24. Also calculate the Schwarzschild radius for a 3 solar mass black hole.

25. Consider that you are lying (paper thin and probably not very cognizant of your surroundings) on the surface of a 10 km radius neutron star at the equator.  This neutron star happens also be millisecond pulsar.  How fast are you moving as a result of the rotation of the neutron star?  How does this speed compare to the speed of light?

26. A tidal force results when one side of an object is pulled with stronger gravity than the other side.  As we discussed in class, Earth's gravity is less on the top of a mountain than it is at sea level, because at the top of the mountain you are further from the center of the Earth.  Taking this further, Earth's gravity is slightly less at your head than at your feet.  The difference between the gravitational acceleration (g) at your head and your feet is the tidal force on you from Earth.  Of course for Earth this tidal force is negligible across such a short distance (however it is responsible for the tidal locking of the Moon).  However, for a black hole the tidal forces are large even across a distance as short as the distance between your head and your feet.  If the tidal force you feel is greater than your body's ability to hold itself together, you will be ripped apart.  This is what would happen if you fell into a black hole.
a. Calculate the tidal force on a person falling feet first into a 3 solar mass black hole (eg calculate the difference in g between the persons head and feet) at the Schwarzschild radius. Since "endurance tests" (and would you want to volunteer for these tests?) suggest that humans get ripped apart when the tidal force exceeds 10g (ie ten times Earth's surface gravity), would you be ripped apart at this point?
b. Would you need to be further away or closer to the black hole to avoid being ripped apart?

27.  Consider that the mass of the universe (should we capitalize this word?) is about 10⁵³ kg.  Calculate the Schwarzschild radius for an object this massive.  How does this radius compare to the size of the universe?  What are the implications of your calculation and what does this have to do with capitalizing the word "universe"?

28. For that same distance of 20 kpc calculate what the mass would have to be for the universe to be moving with Keplerian motion.  Now pick another distance greater than 20 kpc and calculate what the mass would have to be for the universe to be moving with Keplerian motion.  How do these two values compare and what do they represent?   Finally, calculate the amount of dark matter present in the galaxy out to 20 kpc.

29.  If you see the Milky Way, it crosses the whole sky.  Why is that?

30.  A Cepheid star with a pulse period of 5 days is discovered.  Its average apparent brightness is measured to be 7.9 * 10^-14 W/m².  How far away from us is this Cepheid?

31. How would you measure each of the quantities given (eg velocity at a given distance from the center)?

32. The book states that a 10⁴⁰ W quaser would have to consume 10 solar size stars per year to fuel itself.  Do some calculations to prove this statement.

33.  We have been studying the universe on many length scales starting with small ones and moving to larger.  With the exception of the universe itself, we have now reached the largest length scale that exists.  By looking back through the text, find "typical" numbers for each quantity in the chart below.  As indicated in the chart, then divide each subsequent number by the previous one to begin to acquire some appreciation for how large our universe actually is.

34. What is the evidence for dark matter within a galaxy?  What is the evidence for dark matter between galaxies?

35. In the early universe less than two minutes after the Big Bang, electrons were created out of pure energy.  Knowing the mass of the electron, calculate the approximate temperature required for this process to occur, assuming a single photon carries enough energy to create a single electron.  Hint: You will need to use the equation E=hf and Wien's law.

36. Eight galaxies are each located at the corners of a cube.  The present distance from a galaxy to its nearest neighbor is 10 Mpc, and the entire cube (being located in our universe) is expanding according to Hubble's law.  Calculate the recession velocity of the galaxy at one corner of the cube to a) a nearest neighbor galaxy; b) to the galaxy diagonally across one face of the cube; and c) to the galaxy diagonally across the whole cube.

37. Consider that you want to search the frequency band around the waterhole for signals from extraterrestrials.  Each frequency band/channel you need to search needs to be about 100 Hz wide.  How many channels must you search?  Now consider that you must stay on each channel for a minimum of 10⁶ times the oscillation period of that channel (ie you must collect 10⁶ "waves" from that channel before you can be somewhat sure of finding any periodic signal present), how long must you look at a given star in order to collect this minimum amount of information in each channel?  For ease of calculation use the longest period from the waterhole in your calculations.  Finally, there are about 20,000 stars within 100 lightyears of us.   Given the time necessary per star that you calculated above, how long would it take to search these stars?  Consider the Drake equation calculation we did in class.   How long would a civilization have to last in order to achieve a 100 ly average separation between civilization in our galaxy?