In March 2006, two small satellites were discovered orbiting Pluto, one at a distance of 48,000 km and the other at 64,000 km. Pluto already was known to have a large satellite Charon, orbiting at 19,600 km with an orbital period of 6.39 days. Assuming that the satellites do not affect each other, find the orbital periods of the two small satellite? ithout? using the mass of Pluto.

Solution 26E Step 1 Gravitational force between pluto and charon = Centripetal force exerted by charon 2 2 That is, GMm/R = m R Where, R - Radius of charon orbiting around pluto M - mass of pluto m - Mass of charon - angular speed of charon 3 2 Or, GM/R = We know that, = 2 / T 3 2 2 That is, GM/R = 4 / T 2 2 3 Or, we can write, T = 4 R / GM 2 3 Since, G and M are constants for Pluto, we can write, T R