The Two-Body Problem: Going from Six Variables to One.

Photo: Rhett Allain. The two-body problem.

Suppose you have two objects interacting with a central force — where by “central force” we mean that the potential energy only depends on the relative position of the two objects. This two-body problem could be a a binary star system or two masses connected by springs. It doesn’t matter as long as the force acting on the two masses only acts along a line connecting them.