In orbital mechanics, a libration point orbit (LPO) is a quasiperiodic orbit around a Lagrange point. Libration is a form of orbital motion exhibited, for example, in the Earth–Moon system. Trojan bodies also exhibit libration dynamics.
Two varieties of libration point orbits amenable to Lyapunov stability are halo orbits and Lissajous orbits
The Jupiter trojans, commonly called trojan asteroids or simply trojans, are a large group of asteroids that share the planet Jupiter's orbit around the Sun. Relative to Jupiter, each trojan librates around one of Jupiter's stable Lagrange points: either L4, existing 60° ahead of the planet in its orbit, or L5, 60° behind. Jupiter trojans are distributed in two elongated, curved regions around these Lagrangian points with an average semi-major axis of about 5.2 AU.
The first Jupiter trojan discovered, 588 Achilles, was spotted in 1906 by German astronomer Max Wolf. More than 15,300 Jupiter trojans have been found as of October 2025. By convention, they are each named from Greek mythology after a figure of the Trojan War, hence the name "trojan". The total number of Jupiter trojans larger than 1 km in diameter is believed to be about 1 million, approximately equal to the number of asteroids larger than 1 km in the asteroid belt. Like main-belt asteroids, Jupiter trojans form families.