# Lagrangian points

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## Lagrangian points

(lă-**grayn**-jee-ăn) Five locations in space where a small body can maintain a stable orbit despite the gravitational influence of two much more massive bodies, orbiting about a common center of mass. They are named after the French mathematician J.L. Lagrange who first suggested their existence in 1772. A Lagrangian point 60° ahead of Jupiter in its orbit around the Sun, and another 60° behind Jupiter, are the average locations of members of the Trojan group of asteroids; these points are denoted L

_{4}and L

_{5}. The three other Lagrangian points in the Sun–Jupiter gravitational field do not permit stable asteroid orbits owing to the perturbing influence of the other planets. In any system these three points lie on the line joining the centers of mass of the two massive bodies and are denoted L

_{1}(the

*inner Lagrangian point*) and L

_{2}and L

_{3}(the

*outer Lagrangian points*); small bodies here would be in unstable equilibrium (see equipotential surfaces).

## Lagrangian points

[lə′grän·jē·ən ‚poins] (astronomy)

Five points in the orbital plane of two massive objects orbiting about a common center of gravity at which a third object of negligible mass can remain in equilibrium; three points of instable equilibrium are located on the line passing through the centers of mass of the two bodies, and two points of stable equilibrium are located in the orbit of the less massive body, 60° ahead of or behind it.

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