Answer to Question #15271 in Mechanics | Relativity for Priyanka

Question

Obtain an expression for the time period of a satellite orbiting the earth

Answer 1

The gravitation force is equal to the centripetal force:

GMm/r² = mV²/r, or GM/r = mV² ==> V = √(GM/r).
T = 2pi*r / V

So,

T = 2pi*r / √(GM/r).

Here T is the time period, r is the orbit radius, G is the gravity constant, and M is the the mass of the Earth.