HOMEWORK SET #2
DUE: 03 OCTOBER

• show all steps in the simple required calculations. That way, if you make an arithmetic error on a question, it still may be possible for us to assign partial credit.

• write complete sentences. Be legible! We can't give a grade to something we can't read.

• cleanly labeled diagrams are almost always helpful and sometimes are required for a complete explanation.

• come to the help sessions if you are not absolutely clear on how to do any of the questions.

1. Suppose that magically one day our Sun is taken away and in its place is put a star that is one-third times the Sun's mass. First, compute the length of our new "year" (in days, say) if we insist in keeping the Earth at a distance of 1 AU from the new star, just as we now are from the Sun. Then compute how far away we would orbit this new star (in AU, say) if we instead insisted on keeping the length of the year the same as it is now. Comment!

2. Compare your weight now (we are nearly at sea level) to the weight you would have on top of Mount Everest. It is OK to keep this answer as a ratio, or you can turn it into an actual number of pounds less or more that you would weigh when on Mount Everest. Comment!

3. What is the altitude above the Earth's surface of a "geosynchronous" satellite (one that always hovers above the same spot on the Earth)? Hint: begin with Kepler's Third Law. Comment!

4. The planet Neptune was predicted to exist before it was actually discovered, because the planet Uranus was obviously being pulled away from its expected orbit by the gravitational pull of some other object. At the point in time when Uranus and Neptune are lined up exactly on the same side of the Sun, Neptune and the Sun pull on Uranus in opposite directions. What is the ratio of the gravitational forces of these two objects on Uranus at this time? Comment!

5. Compare the Earth-Moon force of gravity on the side of the Earth facing to the Moon to the force on the side facing away from the Moon. Do the same thing for the Earth-Sun force of gravity. This should tell you why the Moon has a higher tidal influence on the Earth than the Sun does, right? Comment!

6. Compare the light-gathering powers of a) a typical amateur astronomer's telescope (D= 6 inches), the original McDonald Observatory telescope (D= 82 inches) and c) the new Hobby-Eberly Telescope (D= 360 inches, approximately).

7. The Andromeda galaxy is our nearest very large neighboring spiral galaxy. What is the angular diameter of the main stellar part of the Andromeda galaxy (it is 40 kpc across and 670 kpc away from us)? How does this compare with the angular size of the moon? What is the angular diameter of the diameter of the bright nucleus (which is 3 pc in size) at the center of the Andromeda Galaxy?

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