A planet is in an elliptical orbit around a star. Which of the following best represents the mechanical energy E_planet of just the planet and the mechanical energy Es_tar-planet of the star-planet system as functions of time for one complete orbit?
Ei = Ef (?)
The Attempt at a Solution
The planet has both PE and KE, and when it is further away from the star, it is travelling much faster so KE goes up while PE goes down due to increased r. And when it's near the star, r increased so PE goes up but KE decreases due to slower speed. But the sum of PE and KE should be equal anytime.
For star-planet, the PE is -GmM/r, so I chose the answer A, but apparently the answer is C and I'm having a hard time understanding why.