Inastronomy, aco-orbital configuration is a configuration of two or moreastronomical objects (such asasteroids,moons, orplanets) orbiting at the same, or very similar, distance from their primary; i.e., they are in a1:1 mean-motion resonance. (or 1:-1 if orbiting inopposite directions).[1]
There are several classes of co-orbital objects, depending on their point oflibration. The most common and best-known class is thetrojan, which librates around one of the two stableLagrangian points (Trojan points), L4 and L5, 60° ahead of and behind the larger body respectively. Another class is thehorseshoe orbit, in which objects librate around 180° from the larger body. Objects librating around 0° are calledquasi-satellites.[2]
Anexchange orbit occurs when two co-orbital objects are of similar masses and thus exert a non-negligible influence on each other. The objects can exchangesemi-major axes oreccentricities when they approach each other.
Orbital parameters that are used to describe the relation of co-orbital objects are thelongitude of the periapsis difference and themean longitude difference. The longitude of the periapsis is the sum of the mean longitude and themean anomaly and the mean longitude is the sum of thelongitude of the ascending node and theargument of periapsis.
Trojan objects orbit 60° ahead of (L4) or behind (L5) 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 behindJupiter around theSun. Trojan objects do not orbit exactly at one of eitherLagrangian 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.[2]
There are several thousand known trojan minor planets orbiting the Sun. Most of these orbit near Jupiter's Lagrangian points, the traditionalJupiter trojans. As of 2015[update], there are also 13Neptune trojans, 7Mars trojans, 2Uranus trojans ((687170) 2011 QF99 and(636872) 2014 YX49), and 2Earth trojans (2010 TK7 and(614689) 2020 XL5 ) that are known to exist. No Saturnian trojans have been observed until the discovery of 2019 UO14.
The Saturnian system contains two sets of trojan moons. BothTethys andDione have two trojan moons each,Telesto andCalypso in Tethys's L4 and L5 respectively, andHelene andPolydeuces in Dione's L4 and L5 respectively.
Polydeuces is noticeable for its widelibration: it wanders as far as ±30° from its Lagrangian point and ±2% from its mean orbital radius, along atadpole orbit in 790 days (288 times its orbital period around Saturn, the same as Dione's).
A pair of co-orbitalexoplanets was proposed to be orbiting the starKepler-223, but this was later retracted.[3]
The possibility of a trojan planet toKepler-91b was studied but the conclusion was that the transit-signal was a false-positive.[4]
In April 2023, a group ofamateur astronomers reported two new exoplanet candidates co-orbiting, in ahorseshoe exchange orbit, close to the star GJ 3470 (this star has a confirmed planetGJ 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.[5][6] Unrelated to the aforementioned claim, a strong candidate of Trojan planet in the GJ 3470 system was found by the TROY project and published inAstronomy & Astrophysics, based on the radial velocity data.[7]
In July 2023, the possible detection of a cloud of debris co-orbital with the proto-planetPDS 70 b was announced. This debris cloud could be evidence of a Trojanplanetary-mass body or one in the process of forming.[8][9]
One possibility for thehabitable zone is a trojan planet of agiant planet close to itsstar.[10]
The reason why no trojan planets have been definitively detected could be that tides destabilize their orbits.[11]
According to thegiant impact hypothesis, theMoon formed after a collision between two co-orbital objects:Theia, thought to have had about 10% of the mass of Earth (about as massive asMars), and the proto-Earth. Their orbits were perturbed by other planets, bringing Theia out of its trojan position and causing the collision.
Objects in a horseshoe orbit librate around 180° from the primary. Their orbits encompass both equilateral Lagrangian points, i.e. L4 and L5.[2]
TheSaturnian moonsJanus andEpimetheus 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 slowly catches 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.
A small number of asteroids have been found which are co-orbital with Earth. The first of these to be discovered, asteroid3753 Cruithne, orbits the Sun with a period slightly less than one Earth year, resulting in an orbit that (from the point of view of Earth) appears as a bean-shaped orbit centered on a position ahead of the position of Earth. This orbit slowly moves further ahead of Earth's orbital position. When Cruithne's orbit moves to a position where it trails Earth's position, rather than leading it, the gravitational effect of Earth increases the orbital period, and hence the orbit then begins to lag, returning to the original location. The full cycle from leading to trailing Earth takes 770 years, leading to a horseshoe-shaped movement with respect to Earth.[12]
More resonantnear-Earth objects (NEOs) have since been discovered. These include54509 YORP,(85770) 1998 UP1,2002 AA29,(419624) 2010 SO16,2009 BD, and2015 SO2 which exist in resonant orbits similar to Cruithne's.2010 TK7 and(614689) 2020 XL5 are the only two identifiedEarth trojans.
Hungaria asteroids were found to be one of the possible sources for co-orbital objects of the Earth with a lifetime up to ~58kyrs.[13]
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.[2] From a co-rotating perspective the quasi-satellite appears to orbit the primary like aretrograde satellite, although at distances so large that it is not gravitationally bound to it.[2] Two examples ofquasi-satellites of theEarth are2014 OL339[14]and469219 Kamoʻoalewa.[15][16]
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.[17]
