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Consider two different separated spheres in otherwise empty space that are bound to each other in...

Consider two different separated spheres in otherwise empty space that are bound to each other in a steady state by only gravity (they aren’t in contact, and no other forces are acting on either one of them). In order to maintain a steady state, they must be orbiting around each other. In this situation the center of mass must move with constant velocity; assume it is at rest. The two could follow elliptical paths, however assume the paths are both circular. Prove that the center of mass is the central point about which each of them orbits.

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