Setting gravitational potential energy to zero at infinity, with MMars = 6.42 ×

Question

Setting gravitational potential energy to zero at infinity, with MMars = 6.42 × 10^23 kg and RMars = 3.4 × 10^6 m,

Suppose you give the object the right speed for a circular orbit, but you got the direction of the velocity wrong, so the object (let’s call it a satellite) ends up in an elliptical orbit instead, falling towards Mars. If the initial angular momentum was Li , how will the angular momentum of the satellite compare to Li when it is at a height of 300 km above Mars’ surface? Carefully explain how you found your answer.

Explanation / Answer

Here, angular momentum =   m * v * r

=>   initial angular momentum = Li

=>    angular momentum when it is at a height of 300 km   =   (Li/3.4 × 106) * (3.7 * 106)

                                                                                              =   1.0882 * Li

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