Trojan Asteroids

The Italian-French mathematician Joseph Lagrange (1736-1812) showed that the three-body problem could be solved for a few special cases analytically. In 1772 he discovered five special points in the vicinity of two orbiting masses where a third, much smaller mass can orbit at a fixed distance from the larger masses (Lagrange 1788). More precisely, the Lagrange points mark positions where the gravitational pull of the two large masses equals the centripetal force required to rotate with them. The Lagrangian points are the five stationary solutions of the restricted three-body problem (=RTBP)- in this idealized problem a massless body moves under the gravitational influence of two massive bodies, which themselves are on circular orbits - , as it is demonstrated in the figure below.

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