Solar and planetary destabilization of the Earth–Moon triangular Lagrangian points

In the restricted circular three-body problem, two massive bodies travel on circular orbits about their mutual center of mass and gravitationally perturb the motion of a massless particle. The triangular Lagrange points, L 4 and L 5 , form equilateral triangles with the two massive bodies and lie in their orbital plane. Provided the primary is at least 27 times as massive as the secondary, orbits near L 4 and L 5 can remain close to these locations indefinitely. More than 2200 cataloged asteroids librate about the L 4 and L 5 points of the Sun–Jupiter system, and five bodies have been discovered around the L 4 point of the Sun–Neptune system. Small satellites have also been found librating about the L 4 and L 5 points of two of Saturnʹs moons. However, no objects have been discovered around the Earth–Moon L 4 and L 5 points. Using numerical integrations, we show that orbits near the Earth–Moon L 4 and L 5 points can survive for over a billion years even when solar perturbations are included, but the further addition of the far smaller perturbations from other planets destabilize these orbits within several million years. Thus, the lack of observed objects in these regions cannot be used as a constraint on Solar System formation, nor on the tidal evolution of the Moonʹs orbit.