A satellite of mass m is in an elliptical orbit (that satisfies Kepler’s laws) about a body of mass M, with m negligible compared to M.
a) Find the total energy of the satellite as a function of its speed, v, and distance, r, from the body it is orbiting.
b) At the maximum and minimum distance between the satellite and the body, and only there, the angular momentum is simply related to the speed and distance. Use this relationship and the result of part (a) to obtain a relationship between the extreme distances and the satellite’s energy and angular momentum.
c) Solve the result of part (b) for the maximum and minimum radii of the orbit in terms of the energy and angular momentum per unit mass of the satellite.
d) Transform the results of part (c) into expressions for the semimajor axis, a, and eccentricity of the orbit, e, in terms of the energy and angular momentum per unit mass of the satellite.
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