Question

Calculate the orbital radius of a geostationary satellite orbiting Saturn, where a day is 10.6 hrs? (MS = 5.7x1026 kg, rS = 5.4x107 m)

Answer 1

In order to find the orbital radius, we need to use Kepler's third law's equation

The formula states:

T^2/R^3 = 4pi^2/G(m)

Since the satellite is geostationary, weknow that the period of the satelitte is going to be 10.6 hours

Plugging in everything we know already

(10.6)^2/R^3 = 4pi^2/G(5.7*10^26)

(10.6)^2/4pi^2/G(5.7*10^26) = R^3

solve for R^3 = 1.08*10^17

R = 476523 m from the surface of Saturn

5.4*10^7 + 476523 = 54476523 meters for the orbital radius