Co-orbital configuration

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 ({\lambda}= \varpi + M) and the mean longitude is the sum of the longitude of the ascending node and the argument of periapsis (\varpi = \Omega + \omega) . ==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 examples are the large population of 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 ({\Delta}{\lambda}, {\Delta}\varpi) = (±60°, ±60°). The point around which they librate is the same, irrespective of their mass or orbital eccentricity. The possibility of a trojan planet to Kepler-91b was studied but the conclusion was that the transit-signal was a false-positive. In April 2023, a group of amateur astronomers reported two new exoplanet candidates co-orbiting, in a horseshoe exchange orbit, close to the star GJ 3470 (this star has a confirmed planet GJ 3470 b). However, the mentioned study is only in preprint form on arXiv, and it has not yet been peer reviewed and published in a reputable scientific journal. Unrelated to the aforementioned claim, a strong candidate of a trojan planet in the GJ 3470 system was found by the TROY project and published in Astronomy & Astrophysics, based on the radial velocity data. In July 2023, the possible detection of a cloud of debris co-orbital with the proto-planet PDS 70 b was announced. This debris cloud could be evidence of a Trojan planetary-mass body or one in the process of forming. 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 definitively detected could be that tides destabilize their orbits. Theia: 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 . More resonant near-Earth objects (NEOs) have since been discovered. These include 54509 YORP, , , , , and which exist in resonant orbits similar to Cruithne's. and are the only two identified Earth trojans. Hungaria asteroids were found to be one of the possible sources for co-orbital objects of the Earth with a lifetime up to ~58 kyrs. ==Quasi-satellite==

Quasi-satellites are co-orbital objects that librate around 0° from the primary. Low-eccentricity quasi-satellite orbits are highly unstable, but for moderate to high eccentricities such orbits can be stable. and 469219 Kamoʻoalewa. ==Exchange orbits==

In addition to swapping semi-major axes like Saturn's moons Epimetheus and Janus, another possibility is to share the same axis, but swap eccentricities instead. ==See also==