Co-orbital configuration

In astronomy, a co-orbital configuration is a configuration of two or more astronomical objects (such as asteroids, moons, or planets) orbiting at the same, or very similar, distance from their primary, i.e. they are in a 1:1 mean-motion resonance. (or 1:−1 if orbiting in opposite directions). There are several classes of co-orbital objects, depending on their point of libration. The most common and best-known class is the trojan, which librates around one of the two stable Lagrangian points (Trojan points), and , 60° ahead of and behind the larger body respectively. Another class is the horseshoe orbit, in which objects librate around 180° from the larger body. Objects librating around 0° are called quasi-satellites. An exchange orbit occurs when two co-orbital objects are of similar masses and thus exert a non-negligible influence on each other. The objects can exchange semi-major axes or eccentricities when they approach each other. Orbital parameters that are used to describe the relation of co-orbital objects are the longitude of the periapsis difference and the mean longitude difference. The longitude of the periapsis is the sum of the mean longitude and the mean anomaly and the mean longitude is the sum of the longitude of the ascending node and the argument of periapsis . Trojan (celestial body) Trojan objects orbit 60° ahead of () or behind () a more massive object, both in orbit around an even more massive central object. The best known example are the asteroids that orbit ahead of or behind Jupiter around the Sun. Trojan objects do not orbit exactly at one of either Lagrangian points, but do remain relatively close to it, appearing to slowly orbit it. In technical terms, they librate around = (±60°, ±60°). The point around which they librate is the same, irrespective of their mass or orbital eccentricity. There are several thousand known trojan minor planets orbiting the Sun. Most of these orbit near Jupiter's Lagrangian points, the traditional Jupiter trojans.