Lagrange Points, Trojan Points

Lagrange Points (image from 'Basics of Space Flight - Chapter 5. Planetary Orbits', courtesy NASA/JPL-Caltech)In a gravitational system composed of a small body orbiting a much larger one (such as a planet and star or a moon and planet), there are five special points in the vicinity of two orbiting masses where a third, smaller mass can orbit at a fixed distance from the larger masses. More precisely, the Lagrange Points mark positions where the gravitational pull of the two large masses precisely equals the centripetal force required to rotate with them.

Of the five Lagrange points, three are unstable and two are stable. The unstable Lagrange points - labeled L1, L2 and L3 - lie along the line connecting the two large masses. The stable Lagrange points - labeled L4 and L5 - form the apex of two equilateral triangles that have the large masses at their vertices. This means that the two stable points lie in the small body’s orbit 60 degrees ahead and behind it, and thus equidistant from the small and large bodies. These are called Trojan points.

The Trojan points of a gas giant near an asteroid belt commonly collect a cluster of asteroids. The name comes from the first such cluster discovered by Terrans at Jupiter in the Sol system: the asteroids were named after mythical heros of the fabled Trojan War on old Earth.

(MT-ENCYC: p42, 1120; "Lagrange Points", WMAP Observatory site; "Basics of Space Flight - Chapter 5. Planetary Orbits", JPL site)

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