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A satellite is going around the earth in...

A satellite is going around the earth in an elliptical orbit and has maximum and minimum distance from the centre of earth equal to 10r and r respectively. It was planned to fire on board rocket so as to increase the energy of the satellite by maximum amount. Assume that the rocket is fired for a small time (almost instantaneous) and gives an impulse J to the satellite in forward direction. Take J to be small compared to overall momentum of the satellite.

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