= Solution
For two bodies interacting through $U(\mathbf r_1-\mathbf r_2)$, define
$$
\mathbf R=\frac{m_1\mathbf r_1+m_2\mathbf r_2}{M},\quad
\mathbf r=\mathbf r_1-\mathbf r_2,\quad
M=m_1+m_2,\quad\mu=\frac{m_1m_2}{M}.
$$
Their <kinetic energy> separates exactly:
$$
T=\frac12M\dot{\mathbf R}^{\,2}+\frac12\mu\dot{\mathbf r}^{\,2}.
$$
Without external forces, the <centre of mass> moves uniformly while $\mu\ddot{\mathbf r}=-\nabla U$. \b[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.
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