View source for Co-orbital configuration

{{Short description|Configuration of two or more astronomical objects}}
In [[astronomy]], a '''co-orbital configuration''' is a configuration of two or more [[astronomical object]]s (such as [[asteroid]]s, [[natural satellite|moon]]s, or [[planet]]s) orbiting at the same, or very similar, distance from their primary; i.e., they are in a [[Orbital resonance|1:1 mean-motion resonance]]. (or 1:-1 if orbiting in [[Retrograde and prograde motion|opposite directions]]).<ref>{{cite journal
 | last = Morais | first = M.H.M.
 |author2=F. Namouni
 | title = Asteroids in retrograde resonance with Jupiter and Saturn
 | journal = [[Monthly Notices of the Royal Astronomical Society Letters]] 
 | arxiv = 1308.0216|bibcode = 2013MNRAS.436L..30M |doi = 10.1093/mnrasl/slt106 | volume=436 | year=2013 | pages=L30–L34| doi-access = free
 }}</ref>

There are several classes of co-orbital objects, depending on their point of [[libration]]. The most common and best-known class is the [[trojan (astronomy)|trojan]], which librates around one of the two stable [[Lagrangian point]]s (Trojan points), {{L4|nolink=yes}} and {{L5|nolink=yes}}, 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-satellite]]s.<ref name=coorbplanet>[https://arxiv.org/PS_cache/arxiv/pdf/1004/1004.0726v1.pdf Dynamics of two planets in co-orbital motion]</ref>

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 axis|semi-major axes]] or [[orbital eccentricity|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]] <math>({\lambda}= \varpi + M) </math> and the mean longitude is the sum of the [[longitude of the ascending node]] and the [[argument of periapsis]] <math>(\varpi = \Omega + \omega) </math>.

==Trojans==
[[File:Lagrange very massive.svg|250px|thumb|Trojan points are the points labelled {{L4}} and {{L5}}, highlighted in red, on the orbital path of the secondary object (blue), around the primary object (yellow).]]
{{Main article|Trojan (celestial body)}}
Trojan objects orbit 60° ahead of ({{L4|nolink=yes}}) or behind ({{L5|nolink=yes}}) 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 point]]s, but do remain relatively close to it, appearing to slowly orbit it. In technical terms, they librate around <math>({\Delta}{\lambda}, {\Delta}\varpi)</math> = (±60°, ±60°). The point around which they librate is the same, irrespective of their mass or orbital eccentricity.<ref name=coorbplanet/>

===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 trojan]]s. {{As of|2015}}, there are also 13 [[Neptune trojan]]s, 7 [[Mars trojan]]s, 2 [[Uranus trojan]]s ({{mpl|(687170) 2011 QF|99}} and {{mpl|(636872) 2014 YX|49}}), and 2 [[Earth trojan|Earth trojans]] ({{mpl|2010 TK|7}} and [[(614689) 2020 XL5|(614689) 2020 XL<sub>5</sub>]] ) that are known to exist. No Saturnian trojans have been observed until the discovery of 2019 UO14.

===Trojan moons===
The Saturnian system contains two sets of trojan moons. Both [[Tethys (moon)|Tethys]] and [[Dione (moon)|Dione]] have two trojan moons each, [[Telesto (moon)|Telesto]] and [[Calypso (moon)|Calypso]] in Tethys's {{L4|nolink=yes}} and {{L5|nolink=yes}} respectively, and [[Helene (moon)|Helene]] and [[Polydeuces (moon)|Polydeuces]] in Dione's {{L4|nolink=yes}} and {{L5|nolink=yes}} 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 [[exoplanet]]s was proposed to be orbiting the star [[Kepler-223]], but this was later retracted.<ref>{{cite web |url=https://www.newscientist.com/article/dn20160-two-planets-found-sharing-one-orbit.html |title=Two planets found sharing one orbit |work=New Scientist |date=24 February 2011}}</ref>

The possibility of a trojan planet to [[Kepler-91b]] was studied but the conclusion was that the transit-signal was a false-positive.<ref>{{cite journal | arxiv=1511.01068 | doi=10.1088/0004-637X/814/2/147 | title=Characterization of Kepler-91B and the Investigation of a Potential Trojan Companion Using Exonest | year=2015 | last1=Placek | first1=Ben | last2=Knuth | first2=Kevin H. | last3=Angerhausen | first3=Daniel | last4=Jenkins | first4=Jon M. | journal=The Astrophysical Journal | volume=814 | issue=2 | page=147 | bibcode=2015ApJ...814..147P | s2cid=118366565 }}</ref>

In April 2023, a group of [[Amateur astronomy|amateur astronomers]] reported two new exoplanet candidates co-orbiting, in a [[Horseshoe orbit|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.<ref>{{Cite encyclopedia|title=The Extrasolar Planet Encyclopaedia — GJ 3470 d|url=https://exoplanet.eu/catalog/gj_3470_d--8659/|encyclopedia=[[Extrasolar Planets Encyclopaedia]]|access-date=2023-04-28}}</ref><ref>{{Cite encyclopedia|title=The Extrasolar Planet Encyclopaedia — GJ 3470 e|url=https://exoplanet.eu/catalog/gj_3470_e--8660/|encyclopedia=[[Extrasolar Planets Encyclopaedia]]|access-date=2023-04-28}}</ref> Unrelated to the aforementioned claim, a strong candidate of Trojan planet in the GJ 3470 system was found by the TROY project and published in [[Astronomy & Astrophysics]], based on the radial velocity data.<ref name="Balsalobre-Ruza2024">{{cite journal |last1=Balsalobre-Ruza |first1=O. |last2=Lillo-Box |first2=J. |display-authors=etal|date=September 2024 |title=The TROY project III. Exploring co-orbitals around low-mass stars |journal=[[Astronomy & Astrophysics]] |volume=689 |pages=A53 |doi=10.1051/0004-6361/202450717 |arxiv=2407.04677 |bibcode=2024A&A...689A..53B }}</ref>

In July 2023, the possible detection of a cloud of debris co-orbital with the proto-planet [[PDS 70|PDS 70 b]] was announced. This debris cloud could be evidence of a Trojan [[Planetary-mass object|planetary-mass body]] or one in the process of forming.<ref>{{cite journal |last1=Balsalobre-Ruza |first1=O. |last2=de Gregorio-Monsalvo |first2=I. |display-authors=etal |date=July 2023 |title=Tentative co-orbital submillimeter emission within the Lagrangian region L5 of the protoplanet PDS 70 b |journal=[[Astronomy & Astrophysics]] |volume=675 |issue= |pages=A172 |doi=10.1051/0004-6361/202346493 |arxiv=2307.12811 |bibcode=2023A&A...675A.172B|s2cid=259684169 }}</ref><ref name="eso2311">{{cite web |url=https://www.eso.org/public/news/eso2311/ |title=Does this exoplanet have a sibling sharing the same orbit? |date=19 July 2023 |publisher=[[European Southern Observatory|ESO]] |access-date=19 July 2023}}</ref>

One possibility for the [[habitable zone]] is a trojan planet of a [[giant planet]] close to its [[star]].<ref>{{cite journal | arxiv=astro-ph/0408079 | doi=10.1051/0004-6361:200400075 | title=Extrasolar Trojan planets close to habitable zones | year=2004 | last1=Dvorak | first1=R. | last2=Pilat-Lohinger | first2=E. | last3=Schwarz | first3=R. | last4=Freistetter | first4=F. | journal=Astronomy & Astrophysics | volume=426 | issue=2 | pages=L37–L40 | bibcode=2004A&A...426L..37D | s2cid=15637771 }}</ref>

The reason why no trojan planets have been definitively detected could be that tides destabilize their orbits.<ref>{{cite journal | url=https://www.sciencedirect.com/science/article/abs/pii/S0019103522001968 | doi=10.1016/j.icarus.2022.115087 | title=Do tides destabilize Trojan exoplanets? | year=2022 | last1=Dobrovolskis | first1=Anthony R. | last2=Lissauer | first2=Jack J. | journal=Icarus | volume=385 | page=115087 | arxiv=2206.07097 | bibcode=2022Icar..38515087D | s2cid=248979920 }}</ref>

====Formation of the Earth–Moon system====
According to the [[giant impact hypothesis]], the [[Moon]] formed after a collision between two co-orbital objects: [[Theia (planet)|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==
[[File:Epimetheus-Janus Orbit.png|thumb|right|300px|[[Rotating reference frame|Rotating-frame]] depiction of the [[horseshoe orbit|horseshoe]] exchange orbits of Janus and Epimetheus]]
[[File:Animation of Epimetheus orbit - Rotating reference frame.gif|thumb|300px|right|Animation of Epimetheus{{'s}} orbit - Rotating reference frame<br>{{legend2| Darkkhaki| Saturn}}{{·}}{{legend2| Lime| Janus }}{{·}}{{legend2|Magenta|Epimetheus}}]]
{{Main article|Horseshoe orbit}}

Objects in a horseshoe orbit librate around 180° from the primary. Their orbits encompass both equilateral Lagrangian points, i.e. {{L4|nolink=yes}} and {{L5|nolink=yes}}.<ref name=coorbplanet/>

===Co-orbital moons===
{{See also|Epimetheus (moon)#Orbit}}
The [[Saturn]]ian moons [[Janus (moon)|Janus]] and [[Epimetheus (moon)|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 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.

===Earth co-orbital asteroids===
A small number of asteroids have been found which are co-orbital with Earth. The first of these to be discovered, asteroid [[3753 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.<ref>{{cite journal|doi=10.1111/j.1365-2966.2011.18595.x|title=A long-lived horseshoe companion to the Earth|year=2011|last1=Christou|first1=A. A.|last2=Asher|first2=D. J.|journal=Monthly Notices of the Royal Astronomical Society|volume=414|issue=4|pages=2965|doi-access=free |arxiv = 1104.0036 |bibcode = 2011MNRAS.414.2965C |s2cid=13832179 }}</ref>

More resonant [[near-Earth object]]s (NEOs) have since been discovered. These include [[54509 YORP]], {{mpl|(85770) 1998 UP|1}}, {{mpl|2002 AA|29}}, {{mpl|(419624) 2010 SO|16}}, {{mpl|2009 BD|}}, and {{mpl|2015 SO|2}} which exist in resonant orbits similar to Cruithne's. {{mpl|2010 TK|7}} and {{mpl|(614689) 2020 XL|5}} are the only two identified [[Earth trojan]]s. 

[[Hungaria asteroid|Hungaria asteroids]] were found to be one of the possible sources for co-orbital objects of the Earth with a lifetime up to ~58 [[kyr]]s.<ref>{{cite journal|doi=10.1093/mnras/stu2016|title=The Hungaria region as a possible source of Trojans and satellites in the inner Solar system|year=2014|last1=Galiazzo|first1=M. A.|last2=Schwarz|first2=R.|journal=Monthly Notices of the Royal Astronomical Society|volume=445|issue=4|pages=3999|doi-access=free |arxiv = 1612.00275 |bibcode = 2014MNRAS.445.3999G}}</ref>

==Quasi-satellite==
{{Main article|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.<ref name=coorbplanet/> From a co-rotating perspective the quasi-satellite appears to orbit the primary like a [[Retrograde motion|retrograde satellite]], although at distances so large that it is not gravitationally bound to it.<ref name=coorbplanet/> Two examples of [[quasi-satellite|quasi-satellites]] of the [[Earth]] are {{mpl|2014 OL|339}}<ref name=dynamics>{{Cite journal | title=Asteroid 2014 OL339: yet another Earth quasi-satellite |first1=Carlos |last1=de la Fuente Marcos |last2=de la Fuente Marcos |first2=Raúl |journal=[[Monthly Notices of the Royal Astronomical Society]] | arxiv = 1409.5588 | bibcode = 2014MNRAS.445.2961D | doi = 10.1093/mnras/stu1978 | volume=445 |issue=3 | pages=2985–2994|year=2014 |doi-access=free }}</ref>
and [[469219 Kamoʻoalewa]].<ref name="NASA-20160615">{{cite web |last1=Agle |first1=DC |last2=Brown |first2=Dwayne |last3=Cantillo |first3=Laurie |title=Small Asteroid Is Earth's Constant Companion |url=http://www.jpl.nasa.gov/news/news.php?feature=6537 |date=15 June 2016 |work=[[NASA]] |access-date=15 June 2016 }}</ref><ref name=2016HO3>{{cite journal | title = Asteroid (469219) 2016 HO3, the smallest and closest Earth quasi-satellite |first1=Carlos |last1=de la Fuente Marcos |last2=de la Fuente Marcos |first2=Raúl | journal = [[Monthly Notices of the Royal Astronomical Society]] | date = 2016 | volume = 462 | issue = 4 | pages = 3441–3456 | arxiv = 1608.01518| doi = 10.1093/mnras/stw1972 |doi-access=free |bibcode = 2016MNRAS.462.3441D}}</ref>

==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.<ref>{{cite journal|doi=10.1111/j.1365-2966.2010.17453.x | bibcode=2011MNRAS.410..455F | volume=410 | issue=1 | title=Exchange orbits: a possible application to extrasolar planetary systems? | year=2010 | journal=Monthly Notices of the Royal Astronomical Society | pages=455–460 | last1 = Funk | first1 = B.| doi-access=free }}</ref>

==See also==
{{Portal|Astronomy}}
* [[Double planet]]
* [[Kordylewski cloud]]
* [[Xuntian|Chinese Space Station Telescope]]

==References==
{{reflist}}
* {{cite journal | url=http://www.iop.org/EJ/article/0004-637X/571/1/528/55113.html | author=Eric B. Ford and Matthew J. Holman | title=Using Transit Timing Observations to Search for Trojans of Transiting Extrasolar Planets | journal=The Astrophysical Journal Letters | volume=664 | issue=1 | year=2007 | pages=L51–L54 | doi= 10.1086/520579 |bibcode = 2007ApJ...664L..51F |arxiv = 0705.0356 | s2cid=14285948 }}

==External links==
{{Commonscat|Co-orbital objects}}
*[https://web.archive.org/web/20140903190527/http://ssdbook.maths.qmw.ac.uk/animations/Coorbital.mov QuickTime animation of co-orbital motion] from Murray and Dermott
*[https://web.archive.org/web/20120419014802/http://planetary.org/news/2006/0120_Cassini_Observes_the_Orbital_Dance_of.html Cassini Observes the Orbital Dance of Epimetheus and Janus] The Planetary Society
*[http://www.trojanplanets.appstate.edu/ A Search for Trojan Planets] Web page of group of astronomers searching for extrasolar trojan planets at Appalachian State University

{{DEFAULTSORT:Co-Orbital Configuration}}
[[Category:Co-orbital objects| ]]