Does Mechanical Energy of a Planet Change in an Elliptical Orbit?

[mancity]

Homework Statement

Given an elliptical planetary orbit of a planet and a star, do:
(a) the mechanical energy of the planet change during the orbit? If so, describe the motion.
(b) the mechanical energy of the planet-star system change during the orbit? If so, describe the motion.

Relevant Equations

ME=KE+PE

Obviously the mechanical energy of the total system remains the same.

But I'm having a hard time determining of the ME of the planet is constant or if it is changing.

 

[PeroK]

Homework Statement: Given an elliptical planetary orbit of a planet and a star, do:
(a) the mechanical energy of the planet change during the orbit? If so, describe the motion.

But I'm having a hard time determining of the ME of the planet is constant or if it is changing.

What's the precise definition of the ME of a planet that is part of a two-body system?