Central configuration

Summary

A central configuration is an arrangement of point masses in which the gravitational acceleration of each body points towards the centre of mass. Its size is proportional to the distance of the body from the centre of mass, with the same constant for all bodies. Released from rest, such an arrangement collapses homothetically, and given the right rotation in the plane it turns rigidly. Central configurations give the simplest explicit solutions of the n-body problem, in which the shape of the configuration never changes. They also govern the shape of the bodies near a total collision. See the definition.