Potential energy in center of mass frame.

[center o bass]

Homework Statement

I am trying to find the total energy of a twobody system (two planets orbiting each other) in the center of mass frame. And I was so wondering how to think about this problem.. I know that the kinetic energy in the center of mass is just the sum of the kinetic energies relative tot CM.. But how is this regarding potential energy?

Potential energy is an energy associated with two bodies relative position with each other, not the CM... and the potential energy of one body relative to another one has to be the same as the one relative to the other. But I'm only used to calculate the potential energy of body A relative to body B. A transformation into CM, means that I suddenly don't have a relative position on either of the bodies. I am a bit confused by this.

How do I think about this and what positionvector r should i use in the potential energy formula?

 

[kuruman]

Does potential energy depend on the velocity of either object?
Does your choice of CM as the origin affect the reference point where the potential energy is zero?

If the answer to both these questions is "No", then the potential energy in the CM frame is the same as in some other frame.