Say I have two bodies, idealized as points with mass, in Galilean spacetime [itex]A^4[/itex]. When thinking about the 2-body problem (just two bodies with interaction forces in the entire universe), one usually goes from the 3-dim. to the 2-dimensional problem using some special idea. I read the following claim: For any initial conditions on those 2 bodies, one can find an inertial system such that the motion of those two bodies takes place in a fixed plane, for all time. Why is that?