Setting gravitational potential energy to zero at infinity, and using MJ = 1.90 Ã 1027 kg, and RJ = 7.15 Ã 107 m, please answer the following questions about an object near Jupiter.
(a) How many Joules of potential energy does a 500 kg object-Jupiter system have, if the object is two Jupiter radii above the surface of Jupiter?
(b) What speed would a 500 kg object have to have at this height to escape Jupiters pull?
(c) What would be the angular momentum of the object at this speed and location (assume velocity is perpendicular to displacement vector)?
(d) If the gravitational force of Jupiter is the only force on the object, at what speed would the object be able to maintain a stable circular orbit at this height above the surface of Jupiter?
(e) It turns out that the velocity found in part (d) was used, but the insertion angle was not exactly perpendicular, and so the orbit started to decay just due to the pull of Jupiterâs gravity. 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 500 km above Jupiterâs surface? Carefully explain how you found your answer.