Rigid Body

Two bodies of masses m_1 and m_2 move under the action of their mutual gravitation.
Let \vec{r}_1 and \vec{r}_2 be the position vectors in a space-fixed coordinate system, and \vec{r}=\vec{r}_1-\vec{r}_2.
Find the equation of motion for \vec{r}_1, \vec{r}_2 and \vec{r} in the center-of-mass system.