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.
Parameters
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 .
Trojans
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.
Trojan minor planets
There are several thousand known trojan minor planets orbiting the Sun. Most of these orbit near Jupiter's Lagrangian points, the traditional Jupiter trojans. , there are also 13 Neptune trojans, 7 Mars trojans, 2 Uranus trojans ( and ) and 2 Earth trojans ( and (614689) 2020 XL5 ) known to exist. As yet no Saturnian trojans have been observed.
Trojan moons
The Saturnian system contains two sets of trojan moons. Both Tethys and Dione have two trojan moons each, Telesto and Calypso in Tethys's and respectively, and Helene and Polydeuces in Dione's and respectively.
Polydeuces is noticeable for its wide libration: it wanders as far as ±30° from its Lagrangian point and ±2% from its mean orbital radius, along a tadpole orbit in 790 days (288 times its orbital period around Saturn, the same as Dione's).
Trojan planets
A pair of co-orbital exoplanets was proposed to be orbiting the star Kepler-223, but this was later retracted.
The possibility of a trojan planet to Kepler-91b was studied but the conclusion was that the transit-signal was a false-positive.
One possibility for the habitable zone is a trojan planet of a giant planet close to its star.
The reason why no trojan planets have been discovered could be that tides destabilize their orbits.
Formation of the Earth–Moon system
According to the giant impact hypothesis, the Moon formed after a collision between two co-orbital objects: Theia, thought to have had about 10% of the mass of Earth (about as massive as Mars), and the proto-Earth. Their orbits were perturbed by other planets, bringing Theia out of its trojan position and causing the collision.
Horseshoe orbits
Objects in a horseshoe orbit librate around 180° from the primary. Their orbits encompass both equilateral Lagrangian points, i.e. and .
Co-orbital moons
The Saturnian moons Janus and Epimetheus share their orbits, the difference in semi-major axes being less than either's mean diameter. This means the moon with the smaller semi-major axis will slowly catch up with the other. As it does this, the moons gravitationally tug at each other, increasing the semi-major axis of the moon that has caught up and decreasing that of the other. This reverses their relative positions proportionally to their masses and causes this process to begin anew with the moons' roles reversed. In other words, they effectively swap orbits, ultimately oscillating both about their mass-weighted mean orbit.