Lagrangian Point

Lagrangian Point

The Lagrangian points ( /ləˈɡrɑːndʒiən/; also Lagrange points, L-points, or libration points) are the five positions in an orbital configuration where a small object affected only by gravity can theoretically be part of a constant-shape pattern with two larger objects (such as a satellite with respect to the Earth and Moon). The Lagrange points mark positions where the combined gravitational pull of the two large masses provides precisely the centripetal force required to orbit with them.

Lagrangian points are the constant-pattern solutions of the restricted three-body problem. For example, given two massive bodies in orbits around their common center of mass, there are five positions in space where a third body, of comparatively negligible mass, could be placed so as to maintain its position relative to the two massive bodies. As seen in a rotating reference frame matching the angular velocity of the two co-orbiting bodies, the gravitational fields of two massive bodies combined with the satellite's acceleration are in balance at the Lagrangian points, allowing the third body to be relatively stationary with respect to the first two bodies.