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Lagrangian point
In celestial mechanics, the Lagrangian points (; also Lagrange points, L-points, or libration points) are positions in an orbital configuration of two large bodies where a small object affected only by gravity can maintain a stable position relative to the two large bodies. 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. There are five such points, labeled L1 to L5, all in the orbital plane of the two large bodies. The first three are on the line connecting the two large bodies and the last two, L4 and L5, each form an equilateral triangle with the two large bodies. The two latter points are stable, which implies that objects can orbit around them in a rotating coordinate system tied to the two large bodies.
Several planets have minor planets near their L4 and L5 points (trojans) with respect to the Sun, with Jupiter in particular having more than a million of these. Artificial satellites have been placed at L1 and L2 with respect to the Sun and Earth, and Earth and the Moon for various purposes, and the Lagrangian points have been proposed for a variety of future uses in space exploration.
==History==
The three collinear Lagrange points (L1, L2, L3) were discovered by Leonhard Euler a few years before Lagrange discovered the remaining two.〔 (16MB)〕〔Leonhard Euler, (De motu rectilineo trium corporum se mutuo attrahentium ) (1765)〕
In 1772, Joseph-Louis Lagrange published an "Essay on the three-body problem". In the first chapter he considered the general three-body problem. From that, in the second chapter, he demonstrated two special constant-pattern solutions, the collinear and the equilateral, for any three masses, with circular orbits.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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