Question

Using the conservation laws, demonstrate that the total mechanical energy of a planet of mass m moving around the Sun along an ellipse depends only on its semi-major axis a. Find this energy as a function of a.

Answer 1

From the previous problem, if r₁, r₂ are the maximum and minimum distances from the sun to the planet and v₁, v₂ are the corresponding velocities, then, say,

E=1/2mv₂²-γmm_s/r₂