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Astronomy 3 - Problem Set 2

1.  If you visited an asteroid 30 km in radius with a mass of
  4x10^17 kg, what would be the circular velocity at its surface?  A
  major league fastball travels 90 mph.  Could a good pitcher throw a
  baseball into orbit around the asteroid?

2. Using the universal law of gravitation to answer the following question. a)
How does quadrupling the distance between two objects affect the gravitational
force between them? b) Compare the gravitational force between the Earth and
the Sun to that between Jupiter and Sun.  Jupiter's mass is 318 times that of
the Earth and its distance from the Sun is 5.2 times that of the Earth's
distance. c) Suppose the Sun were magically replaced by a star with twice
as much mass.  What would happen to the gravitational force between the Sun
and the Earth?

3a)Suppose around another star with the same mass as the Sun, there is a planet
at 1 AU with twice the mass of the Earth, what would its orbit be?  b) Suppose
a solar system has a star that is four times as massive as our Sun.  If that
solar system has a planet the same size as Earth orbiting at a distance of 1AU
what is the orbital period of the planet? Explain.

4. Use the data in Table 4.1 in chapter 4 of the book, a) compare the energy of
a 1-megaton hydrogen bomb to the energy released by a major earth quake. b) If
the US obtained all its energy from oil, how much oil would be needed each
year?  compare the Sun' annual energy output to the energy released by a
supernova?

5.  Einstein's general theory of relativity predicts the curvature
  of space-time, but here on Earth we have little opportunity to
  observe such effects.  Find an astronomical situation in which
  space-time curvature is evident from our observations, and describe
  the effect of the curvature on what we see when we view these
  objects.

6.  How does the light gathering power of the largest telescope in
  the world compare with that of the human eye?  (Hint: Assume that
  the pupil of your eye can open to about 0.8 cm.)  

7.  A spy satellite orbiting 400 km above Earth is supposedly
  capable of counting individual people in a crowd.  What is the
  minimum diameter of the telescope that the satellite must carry?
  (Hint: Use the small-angle formula.)