A satellite of mass m is orbiting the earth in a circular orbit of radius r.It starts loosing energy due to air resistance at the rate of C J\s.Then what time taken by the satelite to reach the earth.

initial energy= -GmM/2r, M is mass of earth,

let a be radius of earth

satellite will reach earth when its energy reduces to -GmM/2a

Then answer is -(GMm/C) (1/r-1/R) = t Where M ans R r the respective mass and radius of the Earth.