Question

What is the velocity and period of a satellite orbiting planet earth?

Answer using a Gravitacional approach*

Answer 1

The Gravitational Force between the earth and the satellite = Fg = (G.M.m)/r2 ……………… (1)

The centripetal force acting on the satellite = Fc = mV2/r    ……………………….. (2)

Here, M is the mass of earth and m is the mass of the satellite which is having a uniform circular motion in a circular track of radius r around the earth. V is the linear velocity of the satellite at a point on its circular track.

Now this r is the sum of the radius of the earth(R) and the height(h) of the satellite from the surface of the earth.

r = R + h

Now equating, equation 1 and 2 we get,

Fg = Fc

=> (G.M.m)/r2 = mV2/r

  V = [(GM)/r]1/2 ……………………………….. (3)

This is the first equation or expression of Orbital Velocity of a satellite. Here r = R +h

You can calculate the speed of a satellite around an object using the equation

The satellite travels around the entire circumference of the circle — which is

if r is the radius of the orbit — in the period, T. This means the orbital speed must be

giving you

If you solve this for the period of the satellite, you get