Astronomy 201 

Problem Set TWO

  1. At what height above the Earth's surface would you find a geosynchronously (orbital period P = 24 hours) orbiting satellite?
  2. a. Show that an asteroid at a = 3.28 AU (just outside the orbit of the largest asteroid, Cerees) is in a 1:2 commensurability with (i.e., has a period half as large as that of) Jupiter.

  3. b. Calculate the semi-major axis for an asteroid for which it's orbital period would be three times smaller than that of Jupiter.
    c. From  Histogram of Minor planets as a function of semimajor axis , what conclusion can you draw about asteroids with orbital periods exactly half or one-third that of Jupiter?
  4. Assume we have an spacecraft in a circular orbit whose mass is much smaller than that of the planet around which it orbits.   If the mass of the spacecraft is instantly decreased (it drops a large payload), how will the spacecraft's orbit change?  {Your answer will be qualitative, not quantitative.  Think about the change in the force of gravitational attraction between the primary and secondary and the affect that change will have on the motion of the spacecraft; then think about how that change in motion will become manifest in the parameters of the spacecraft orbit.}