# Lagrangian point

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Lagrangian point
one of five points in the orbital plane of two bodies orbiting about their common center of gravity at which another body of small mass can be in equilibrium.
[1960-65; named after J. L. LAGRANGE; see -IAN]

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in astronomy, a point in space at which a small body, under the gravitational influence of two large ones, will remain approximately at rest relative to them. The existence of such points was deduced by the French mathematician and astronomer Joseph-Louis Lagrange in 1772. In 1906 the first examples were discovered: these were minor planets moving in Jupiter's orbit, under the influence of Jupiter and the Sun. (See also Trojan planets.)

In each system of two heavy bodies (e.g., Sun-Jupiter, or Earth-Moon) there exist five theoretical Lagrangian points, but only two are stable—i.e., will tend to retain small bodies despite slight perturbations by outside gravitational influences. Each stable point forms one tip of an equilateral triangle having the two massive bodies at the other vertices.

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Universalium. 2010.

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• Lagrangian point — The Lagrangian points (IPA en|ləˈgreɪndʒiən, IPA fr|lagʁɑ̃ʒjɑ̃; also Lagrange point, L point, or libration point), are the five positions in an orbital configuration where a small object affected only by gravity can theoretically be stationary… …   Wikipedia

• Lagrangian point — [lə grɒLagrangian pointʒɪən] noun Astronomy each of five points in the plane of orbit of one body around another at which a small third body can remain stationary with respect to the others. Origin C19: named after the Italian born French… …   English new terms dictionary

• Lagrangian point — one of the solutions to the three body problem discovered by the eighteenth century French mathematician Lagrange. The two stable Lagrangian points, L 4 and L 5, lie in the orbit of the primary body, leading and trailing it by a 60 degree arc.… …   Mechanics glossary

• lagrangian point — noun Usage: usually capitalized L Etymology: Joseph L. Lagrange died 1813 Italian born geometer and astronomer in France + English ian : any of five points at which a small object (as a satellite) will be in gravitational equilibrium with and… …   Useful english dictionary

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• Lagrangian Grassmannian — In mathematics, the Lagrangian Grassmannian is the smooth manifold of Lagrangian subspaces of a real symplectic vector space V. Its dimension is n(n+1)/2 (where the dimension of V is 2n). It may be identified with the homogeneous space U(n)/O(n)… …   Wikipedia

• Lagrangian function — /leuh grayn jee euhn/, Physics. See kinetic potential. [1900 05; named after J. L. LAGRANGE; see IAN] * * * ▪ physics also called  Lagrangian        quantity that characterizes the state of a physical system. In mechanics, the Lagrangian function …   Universalium