Lagrange Points

CORE DEFINITION

Lagrange points (also known as libration points) are positions in celestial mechanics where a small object, under the gravitational influence of two massive orbiting bodies, is in mechanical equilibrium. Mathematically, this involves solutions to the restricted three-body problem. Normally, the gravitational forces of the two massive bodies on any point are unbalanced, altering the orbit of any object at that point. At Lagrange points, the gravitational forces of the two large bodies and the centrifugal force balance each other. This makes Lagrange points excellent locations for satellites, as the fuel required for orbit corrections to maintain the desired orbit is minimized. For any combination of two orbiting bodies, there are five Lagrange points, L1 through L5, all lying in the orbital plane of the two large bodies. The Sun-Earth system has five Lagrange points, and the Earth-Moon system also has five 'distinct' Lagrange points. L1, L2, and L3 lie on the line passing through the centers of the two large bodies, while L4 and L5 are each located at the third vertex of an equilateral triangle formed by the centers of the two large bodies. When the mass ratio of the two bodies is sufficiently large, L4 and L5 are stable points, meaning that objects can orbit around them and they tend to attract objects into them.