Problem Set TWO

Due Friday, January 25, 2001, at beginning of class.

Answer Key

At what height above the Earth's surface would you find a geosynchronously
(orbital period P = 24 hours) orbiting satellite?

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.
b. Calculate the semimajor 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 onethird
that of Jupiter?

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.}