Question

A satellite of mass m is orbiting the earth in a circular orbit of radius r. It starts losing energy slowly at a constant rate C due to friction. If Me and Re denote the mass and radius of the earth respectively, show the the satellite falls on the earth in a limit t given by

Answer 1

Let velocity of satellite in its orbit of radius r be v then we have

When satellite approaches earth's surface, if its velocity becomes v', then it is given as

The total initial energy of satellite at a distance r is

The total final energy of satellite at a distance R_e is

As satellite is loosing energy at rate C, if it takes a time t in reaching earth, we have