Question

The period of the Moon’s orbit is 27.0 days. The radius of the moon’s orbit is 3.8 x 10 8 m. The period of a geostationary satellite is 1.0 day. What is the radius of the geostationary satellite’s orbit?

Answer 1

The radius can be found by Kepler's third law:

$$\frac{T_m^2}{T_s^2}=\frac{a_m^3}{a_s^3},\\\space\\ a_s=a_m\sqrt[3]{T_s^2/T_m^2}=126.7·10^6\text{ m}.$$