Question

Find the energy necessary to put 4 kg , initially at rest on Earth's surface, into geosynchronous orbit.

Answer 1

In a geosynchronous orbit the distance from the center of earth is r = 42241.1 km and the velocity is 3.1 km/s



IF R is the radius of earth , the altitude h of the satellite from the earth’s surface is
h = 42241.1- 6371 = 35870.1 km

The potential energy of the satellite of mass 4kg is is 4*v^2h/r
The kinetic energy of the satellite of mass 4 kg is 4*v^2/2.
Total energy is 4*(v^2/2 + v^2h/r)
4*((3.1e3)^2/2 + (3.1e3)^2*35870.1e3/42241.1e3)= 5.188 e+7 J.
This much energy is needed for a satellite which is initially at rest on Earth's surface, into geosynchronous orbit.