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A satellite of mass m is orbiting the earth, mass M , in a circular orbit of radius ra . Unfortunately a piece of space debris left by a passing rocket lies directly in the satellite's path. The piece of debris has the same mass m as the satellite. The debris collides with the satellite and sticks to the satellite. Assume that the debris has negligible speed just before the collision. After the collision, the satellite and debris enter an elliptical orbit around the earth. The distance of closest approach to the earth of the satellite and the debris is rp . Let G be the universal constant of gravity. You may assume that M>>m .

(a) Find an expression for the speed v0 of the satellite before the collision. You may express your answer in terms of M, ra and G as needed.

v0=

(b) Calculate the ratio ra/rp .

ra/rp=

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  1. rp = ra/7

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