Editing Lagrange point (section)

==Natural objects at Lagrange points==
{{Main|List of objects at Lagrange points}}
Due to the natural stability of {{L4|nolink=yes}} and {{L5|nolink=yes}}, it is common for natural objects to be found orbiting in those Lagrange points of planetary systems. Objects that inhabit those points are generically referred to as '[[Trojan (astronomy)|trojans]]' or 'trojan asteroids'. The name derives from the names that were given to asteroids discovered orbiting at the Sun–[[Jupiter]] {{L4|nolink=yes}} and {{L5|nolink=yes}} points, which were taken from mythological characters appearing in [[Homer]]'s ''[[Iliad]]'', an [[epic poem]] set during the [[Trojan War]]. Asteroids at the {{L4|nolink=yes}} point, ahead of Jupiter, are named after Greek characters in the ''Iliad'' and referred to as the "[[List of Jupiter Trojans (Greek camp)|Greek camp]]". Those at the {{L5|nolink=yes}} point are named after Trojan characters and referred to as the "[[List of Jupiter Trojans (Trojan camp)|Trojan camp]]". Both camps are considered to be types of trojan bodies.

As the Sun and Jupiter are the two most massive objects in the Solar System, there are more known Sun–Jupiter trojans than for any other pair of bodies. However, smaller numbers of objects are known at the Lagrange points of other orbital systems:
* The Sun–Earth {{L4|nolink=yes}} and {{L5|nolink=yes}} points contain interplanetary dust and at least two asteroids, {{mpl|2010 TK|7}} and {{mpl|2020 XL|5}}.<ref>{{Cite web |url=https://www.space.com/12443-earth-asteroid-companion-discovered-2010-tk7.html |title=First Asteroid Companion of Earth Discovered at Last |first=Charles Q. |last=Choi |website=Space.com |date=27 July 2011 }}</ref><ref>{{Cite web |url=https://www.nasa.gov/home/hqnews/2011/jul/HQ_11-247_WISE_Trojan.html |title=NASA - NASA's Wise Mission Finds First Trojan Asteroid Sharing Earth's Orbit |website=www.nasa.gov }}</ref><ref name="Hui2021">{{cite journal
 |first1      = Man-To |last1 = Hui
 |first2      = Paul A. |last2 = Wiegert |author-link2=Paul Wiegert 
 |first3      = David J. |last3 = Tholen |author-link3=David J. Tholen
 |first4      = Dora |last4 = Föhring
 |title       = The Second Earth Trojan 2020 XL5
 |journal = The Astrophysical Journal Letters
 |date        = November 2021
 |volume = 922
 |issue = 2
 |pages = L25
 |doi = 10.3847/2041-8213/ac37bf
 |arxiv      = 2111.05058
 |bibcode = 2021ApJ...922L..25H
 |s2cid = 243860678
 |doi-access = free
 }}</ref>
* The Earth–Moon {{L4|nolink=yes}} and {{L5|nolink=yes}} points contain concentrations of [[Interplanetary dust cloud|interplanetary dust]], known as [[Kordylewski cloud]]s.<ref>{{cite journal|title=Celestial mechanics and polarization optics of the Kordylewski dust cloud in the Earth-Moon Lagrange point L5 - Part I. Three-dimensional celestial mechanical modelling of dust cloud formation |first1=Judit |last1=Slíz-Balogh |first2=András |last2=Barta |first3=Gábor |last3=Horváth |journal=Monthly Notices of the Royal Astronomical Society |volume=480 |issue=4 |pages=5550–5559 |date=2018 |doi=10.1093/mnras/sty2049|doi-access=free |arxiv=1910.07466 |bibcode=2018MNRAS.480.5550S }}</ref><ref>{{cite journal|title=Celestial mechanics and polarization optics of the Kordylewski dust cloud in the Earth-Moon Lagrange point L5. Part II. Imaging polarimetric observation: new evidence for the existence of Kordylewski dust cloud |first1=Judit |last1=Slíz-Balogh |first2=András |last2=Barta |first3=Gábor |last3=Horváth |journal=Monthly Notices of the Royal Astronomical Society |volume=482 |issue=1 |pages=762–770  |date=2019 |doi=10.1093/mnras/sty2630|arxiv=1910.07471 |bibcode=2019MNRAS.482..762S |doi-access=free }}</ref> Stability at these specific points is greatly complicated by solar gravitational influence.<ref>{{cite journal|url=http://www.rfreitas.com/Astro/SearchIcarus1980.htm |title=A Search for Natural or Artificial Objects Located at the Earth–Moon Libration Points |first1=Robert |last1=Freitas |first2=Francisco |last2=Valdes |journal=[[Icarus (journal)|Icarus]] |volume=42 |issue=3 |pages=442–447 |date=1980 |doi=10.1016/0019-1035(80)90106-2 |bibcode=1980Icar...42..442F|url-access=subscription }}</ref>
* The Sun–[[Neptune]] {{L4|nolink=yes}} and {{L5|nolink=yes}} points contain several dozen known objects, the [[Neptune trojan]]s.<ref name="ntrojans">{{cite web | title=List Of Neptune Trojans | publisher=Minor Planet Center | url=http://www.minorplanetcenter.org/iau/lists/NeptuneTrojans.html |access-date=27 October 2010| archive-url = https://web.archive.org/web/20110725075646/http://www.minorplanetcenter.org/iau/lists/NeptuneTrojans.html |archive-date=25 July 2011 | url-status=live}}</ref>
* [[Mars]] has four accepted [[Mars trojan]]s: [[5261 Eureka]], {{mpl|1999 UJ|7}}, {{mpl|1998 VF|31}}, and {{mpl|2007 NS|2}}.
* Saturn's moon [[Tethys (moon)|Tethys]] has two smaller moons of Saturn in its {{L4|nolink=yes}} and {{L5|nolink=yes}} points, [[Telesto (moon)|Telesto]] and [[Calypso (moon)|Calypso]]. Another Saturn moon, [[Dione (moon)|Dione]] also has two Lagrange co-orbitals, [[Helene (moon)|Helene]] at its {{L4|nolink=yes}} point and [[Polydeuces (moon)|Polydeuces]] at {{L5|nolink=yes}}. The moons wander [[azimuth]]ally about the Lagrange points, with Polydeuces describing the largest deviations, moving up to 32° away from the Saturn–Dione {{L5|nolink=yes}} point.
* One version of the [[giant impact hypothesis]] postulates that an object named [[Theia (planet)|Theia]] formed at the Sun–Earth {{L4|nolink=yes}} or {{L5|nolink=yes}} point and crashed into Earth after its orbit destabilized, forming the Moon.<ref name=belbruno-2005>{{cite journal |first1=Edward |last1=Belbruno |author-link1=Edward Belbruno |first2=J. Richard |last2=Gott III |author-link2=J. Richard Gott |title=Where Did The Moon Come From? |journal=The Astronomical Journal |volume=129 |issue=3 |pages=1724–1745 |date=2005 |doi=10.1086/427539 |arxiv=astro-ph/0405372 |bibcode=2005AJ....129.1724B |s2cid=12983980 }}</ref>
* In [[binary star]]s, the [[Roche lobe]] has its apex located at {{L1|nolink=yes}}; if one of the stars expands past its Roche lobe, then it will lose matter to its [[companion star]], known as [[Roche lobe overflow]].<ref>{{cite journal |title=Equipotential Surfaces and Lagrangian Points in Nonsynchronous, Eccentric Binary and Planetary Systems |last1=Sepinsky |first1=Jeremy F. |last2=Willems |first2=Bart |last3=Kalogera |first3=Vicky |author-link3=Vicky Kalogera |journal=The Astrophysical Journal |volume=660 |issue=2 |pages=1624–1635 |date=May 2007 |doi=10.1086/513736 |arxiv=astro-ph/0612508 |bibcode=2007ApJ...660.1624S |s2cid=15519581 }}</ref>

Objects which are on [[horseshoe orbit]]s are sometimes erroneously described as trojans, but do not occupy Lagrange points. Known objects on horseshoe orbits include [[3753 Cruithne]] with Earth, and Saturn's moons [[Epimetheus (moon)|Epimetheus]] and [[Janus (moon)|Janus]].