Question

A small satellite of mass m is in circular orbit of radius r around a planet of mass M and radius R, where M>>m.

a) For full marks, derive the potential, kinetic, and total energy of the satellite in terms of G, M, m, and r assuming that the potential energy is zero at r=infinity.

b) What is the minimum amount of energy that the booster rockets must provide for the satellite to escape?

c) Now we take into accouny that the planet had a thin atmosphere, and the fricition from the atmosphere is F=-bv^2 where b is a constant and v is the directoon of motion. What is the loss of energy in one orbital period in terms if G, M, r, and b. Assume that the loss is small enough that r doesnt change much in one orbit.

Answer 1

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