Stability at potential maxima: The L4 and L5 points of the restricted three-body problem

The restricted three-body problem, which treats the motion of an infinitesimal particle due to the gravitational attraction of two massive primaries moving on circular orbits about one another, provides an example of motion which is stable at potential maxima. In a reference frame rotating with the two primaries’ orbital angular velocity, the potential felt by a test particle in the plane of the primaries’ orbit has maxima at the two points which form equilateral triangles with the primaries. This potential is the sum of the gravitational potential and a term representing the position-dependent centrifugal force. The maxima, called L4 and L5, are stable locations for the test particle thanks to the velocity-dependent Coriolis force, which is not incorporated in the potential function. Any energy-dissipating process would tend to drive the test particle away from one of these stable points. These phenomena may run counter to common experience and physical intuition.