Asteroids located near the equilateral lagrangian stability points of the Sun-Jupiter system (see illustration). As shown by J. L. Lagrange in 1772, these are two of the five stable points in the circular, restricted, three-body system, the other three points being located along a line through the two most massive bodies in the system. In 1906 Max Wolf discovered an asteroid located near the lagrangian point preceding Jupiter in its orbit. Within a year, two more were found, one of which was located near the following lagrangian point. It was quickly decided to name these asteroids after participants in the Trojan War as given in Homer's Iliad.

Lagrangian points and Trojan asteroids.
The term “Trojans” is sometimes used in a generic sense to refer to hypothetical objects occupying the equilateral lagrangian points of other pairs of bodies. In 1990 Edward Bowell discovered an asteroid, later named (5261) Eureka, occupying the following lagrangian point of the planet Mars, and in 2001 the first Trojan of Neptune (2001 QR322) was discovered. As of December 2003, as many as five additional potential Martian Trojans had been discovered. As of August 2004 there were 1682 known Jupiter Trojans. See also Asteroid.