Chapter 11, Problem 54EAP

Prometheus and Pandora. These two moons orbit Saturn at 139,350 and 141,700 kilometers, respectively.

1. Using Newton’s version of Kepler’s third law, find their two orbital periods. Find the percent difference in their distances from Saturn and in their orbital periods.
2. Consider the two in a race around Saturn: In one Prometheus orbit, how far behind is Pandora (in units of time)? In how many Prometheus orbits will Pandora have fallen behind by one of its own orbital periods? Convert this number of periods back into units of time. This is how often the satellites pass by each other.