Consider a satellite of mass \(M\) revolving in a circular orbit around the earth, which is located at the center of its orbit. If a satellite is at height \(h\) above earths surface the radius of the orbit \(r = R _e\) th where \(R _e\) is radius of earth. The gravitational force between \(M _e\) and \(M\) provides the centripetal force for circular motion

or \(V ^2=\frac{ GM _e}{ R _e+ h } \quad V =\sqrt{\frac{ GM _e}{ R _e+ h }}\)

Hence orbital velocity depends on height of the satellite above earth's surface. Time period if satellite is time taken to complete one revolution.

\(T =\frac{2 \pi r }{ V }=2 \pi\left( R _{ e }+ h \right)\)

\(\sqrt{ Re _{ e }+ h } / GM _{ e }\)

\(T ^2=\frac{4 \pi^2\left( R _e+ h \right)^3}{ GM _e}\) where \(r = R _{ e }+ h\)