Past exam of the physics B course of the University of Cambridge / 2014 / Paper 2 / Section B / B8 / c

For two bodies interacting through $U({\mathbf{r}}_1-{\mathbf{r}}_2)$, defineTheir kinetic energy separates exactly:Without external forces, the centre of mass moves uniformly while $\mu \ddot{\mathbf{r}}=-\nabla U$. The relative orbit is a one-body problem with reduced mass $\mu$, not generally either individual mass. For $m_2\gg m_1$, $\mu \simeq m_1$; for equal masses $m$, $\mu =m/2$. If the interaction is central, relative angular momentum is conserved and the relative motion is planar.