# Mechanical energy for planet in elliptical orbit around star

JessicaHelena

## Homework Statement

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

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The planet has both PE and KE, and when it is further away from the star, it is traveling 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.

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## Answers and Replies

Homework Helper
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.
Like you, I would have chosen answer A, including both the planet's kinetic and gravitational potential energy in the planet's "total mechanical energy".

However, it appears that "mechanical energy of just the planet" is intended not to include any gravitational potential energy based on the planet's position in the gravitational field of the star.

The "mechanical energy of the star-planet system" does include the gravitational potential energy (-GmM/r) just as you indicate along with their kinetic energies. The total is constant and negative, as indicated by both A and C.

JessicaHelena
@jbriggs444 — then when the problem says "ME of just the planet", should I normally think of simply the KE? Does these kinds of things apply to other situations?