Einstein–Infeld–Hoffmann equations

Summary

The Einstein–Infeld–Hoffmann equations are the equations of motion of $N$ gravitating point masses in general relativity at the first post-Newtonian order. They add to Newton's inverse-square accelerations correction terms of relative size $v^2/c^2$ and $GM/(rc^2)$, which depend on the velocities and on the other bodies. They were derived from the Einstein field equations themselves, showing that the motion of bodies follows from the field equations. They are used for precise solar-system ephemerides and as the starting point of the relativistic n-body problem.