View source for Jupiter trojan

{{short description|Asteroid sharing the orbit of Jupiter}}
{{Use dmy dates|date=October 2019}}
[[File:InnerSolarSystem-en.png|thumb|upright=1.4|The [[asteroid]]s of the [[inner Solar System]] and [[Jupiter]]
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{{legend2|#6ad768|border=1px solid #2B9929|'''''Jupiter trojans'''''}}<br />
{{legend2|#d39300|border=1px solid #855D00|[[Hilda asteroid]]s}}
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{{legend2|#e9e9e9|border=1px solid #999999|[[Asteroid belt]]}}<br />
{{legend2|#007DD6|border=1px solid #00508A|[[Orbit]]s of [[planet]]s}}
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The Jupiter trojans are divided into two groups: The [[Greek camp]] in front of and the [[Trojan camp]] trailing behind Jupiter in their orbit.
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The '''Jupiter trojans''', commonly called '''trojan asteroids''' or simply '''trojans''', are a large group of [[asteroid]]s that share the planet [[Jupiter]]'s orbit around the [[Sun]]. Relative to Jupiter, each [[Trojan (celestial body)|trojan]] [[Libration point orbit|librates]] around one of Jupiter's stable [[Lagrangian point|Lagrange points]]: either ''{{L4|nolink=yes}}'', existing 60° ahead of the planet in its orbit, or ''{{L5|nolink=yes}}'', 60° behind. Jupiter trojans are distributed in two elongated, curved regions around these Lagrangian points with an average [[semi-major axis]] of about 5.2&nbsp;[[Astronomical unit|AU]].<ref name=Yoshida2005/>

The first Jupiter trojan discovered, [[588 Achilles]], was spotted in 1906 by German astronomer [[Max Wolf]].<ref name=Nicholson1961/> More than 9,800 Jupiter trojans have been found {{as of|2021|5|lc=on}}.<ref name="MPC-Trojan-count" /> By convention, they are each named from [[Greek mythology]] after a figure of the [[Trojan War]], hence the name "trojan". The total number of Jupiter trojans larger than 1&nbsp;km in diameter is believed to be about {{Nowrap|1 million}},<ref name=Yoshida2005/> approximately equal to the number of asteroids larger than 1&nbsp;km in the [[asteroid belt]].<ref>{{cite journal | last1=Tedesco | first1=E. F. | last2=Desert | first2=F.-X. | title=The Infrared Space Observatory Deep Asteroid Search | journal=The Astronomical Journal | year=2002 | volume=123 | issue=4 | pages=2070–2082 | bibcode=2002AJ....123.2070T|  doi=10.1086/339482 | doi-access=free }}</ref> Like main-belt asteroids, Jupiter trojans form [[Asteroid family#All families|families]].<ref name=Jewitt2004/>

{{As of|2004}}, many Jupiter trojans showed to observational instruments as dark bodies with reddish, featureless [[spectrum|spectra]]. No firm evidence of the presence of water, or any other specific compound on their surface has been obtained, but it is thought that they are coated in [[tholin]]s, organic polymers formed by the Sun's radiation.<ref name="Dotto2006" /> The Jupiter trojans' densities (as measured by studying [[binary star|binaries]] or rotational lightcurves) vary from 0.8 to 2.5&nbsp;g·cm<sup>−3</sup>.<ref name=Jewitt2004/> Jupiter trojans are thought to have been captured into their orbits during the early stages of the [[Formation and evolution of the Solar System|Solar System's formation]] or slightly later, during the [[planetary migration|migration]] of giant planets.<ref name=Jewitt2004/>

The term "Trojan Asteroid" specifically refers to the asteroids co-orbital with Jupiter, but the general term "[[trojan (astronomy)|trojan]]" is sometimes more generally applied to other [[Small Solar System body|small Solar System bodies]] with similar relationships to larger bodies: [[Mars trojan]]s, [[Neptune trojan]]s, [[Uranus trojan]]s and [[Earth trojan]]s are known to exist.<ref name="Nep">{{cite journal|last=Sheppard|first=S. S.|author2=C. A. Trujillo|date=28 July 2006|title=A thick cloud of Neptune Trojans and their colors|journal=Science|location=New York|volume=313|issue=5786|pages=511–514|oclc=110021198|doi=10.1126/science.1127173|pmid=16778021|bibcode=2006Sci...313..511S|s2cid=35721399 |url=http://pdfs.semanticscholar.org/8108/b7ca960285556143472a74bdf6d1ef4f4b4b.pdf|archive-url=https://web.archive.org/web/20200412144806/http://pdfs.semanticscholar.org/8108/b7ca960285556143472a74bdf6d1ef4f4b4b.pdf|url-status=dead|archive-date=12 April 2020}}</ref><ref>{{Cite web |url=http://www.nasa.gov/mission_pages/WISE/news/wise20110727.html |title=NASA's WISE Mission Finds First Trojan Asteroid Sharing Earth's Orbit 27 July 2011 |access-date=29 July 2011 |archive-url=https://web.archive.org/web/20170502055548/https://www.nasa.gov/mission_pages/WISE/news/wise20110727.html |archive-date=2 May 2017 |url-status=live }}</ref><ref>{{cite journal|last1=Connors|first1=Martin|first2=Paul|last2=Wiegert|first3=Christian|last3=Veillet|title=Earth's Trojan asteroid|journal=Nature|volume=475|issue=7357|pages=481–483|date=28 July 2011|doi=10.1038/nature10233|bibcode=2011Natur.475..481C|pmid=21796207|s2cid=205225571 }}</ref> Temporary [[Venus]] trojans and [[Saturn]] trojans exist, as well as for [[1 Ceres]] and [[4 Vesta]]. The term "Trojan asteroid" is normally understood to specifically mean the Jupiter trojans because the first Trojans were discovered near Jupiter's orbit and Jupiter currently has by far the most known Trojans.<ref name="MPC-Trojan-count" />

== Observational history ==
[[File:Maximilian Franz Joseph Cornelius Wolf.jpg|thumb|right|upright|[[Max Wolf|Maximilian Franz Joseph Cornelius Wolf]] (1890)—the discoverer of the first trojan]]

In 1772, Italian-born mathematician [[Joseph-Louis Lagrange]], in studying the [[restricted three-body problem]], predicted that a small body sharing an orbit with a planet but lying 60° ahead or behind it will be trapped near these points.<ref name=Nicholson1961/> The trapped body will [[libration|librate]] slowly around the point of equilibrium in a [[tadpole orbit|tadpole]] or [[horseshoe orbit]].<ref name=Marzari2002/> These leading and trailing points are called the {{L4|nolink=yes}} and {{L5|nolink=yes}} [[Lagrange point]]s.<ref name=Jewitt2000/>{{refn|The three other points—L<sub>1</sub>, L<sub>2</sub> and L<sub>3</sub>—are unstable.<ref name=Marzari2002/>|group=Note}} The first asteroids trapped in Lagrange points were observed more than a century after Lagrange's hypothesis. Those associated with Jupiter were the first to be discovered.<ref name=Nicholson1961/>

[[Edward Emerson Barnard|E. E. Barnard]] made the first recorded observation of a trojan, {{mpl|(12126) 1999 RM|11}} (identified as A904 RD at the time), in 1904, but neither he nor others appreciated its significance at the time.<ref name=Barnard1904>{{cite web|date=1 October 1999|title=The Earliest Observation of a Trojan|publisher=Harvard-Smithsonian Center for Astrophysics (CfA)|author=Brian G. Marsden|url=http://www.cfa.harvard.edu/iau/pressinfo/TheFirstTrojanObs.html|access-date=20 January 2009|archive-url=https://web.archive.org/web/20081114082429/http://www.cfa.harvard.edu/iau/pressinfo/TheFirstTrojanObs.html|archive-date=14 November 2008|url-status=live}}</ref> Barnard believed he had seen the recently discovered [[Moons of Saturn|Saturnian satellite]] [[Phoebe (moon)|Phoebe]], which was only two [[arc-minute]]s away in the sky at the time, or possibly an asteroid. The object's identity was not understood until its orbit was calculated in 1999.<ref name=Barnard1904/>

The first accepted discovery of a trojan occurred in February 1906, when astronomer [[Max Wolf]] of [[Heidelberg-Königstuhl State Observatory]] discovered an [[asteroid]] at the {{L4|nolink=yes}} [[Lagrangian point]] of the [[Sun]]–[[Jupiter]] system, later named [[588 Achilles]].<ref name=Nicholson1961/> In 1906–1907 two more Jupiter trojans were found by fellow German astronomer [[August Kopff]] ([[624 Hektor]] and [[617 Patroclus]]).<ref name=Nicholson1961/> Hektor, like Achilles, belonged to the {{L4|nolink=yes}} swarm ("ahead" of the planet in its orbit), whereas Patroclus was the first asteroid known to reside at the {{L5|nolink=yes}} Lagrangian point ("behind" the planet).<ref name=Einarsson1913/> By 1938, 11 Jupiter trojans had been detected.<ref name=Wyse1938/> This number increased to 14 only in 1961.<ref name=Nicholson1961/> As instruments improved, the rate of discovery grew rapidly: by January 2000, a total of 257 had been discovered;<ref name=Jewitt2000/> by May 2003, the number had grown to 1,600.<ref name=Fernandes2003/> {{As of|2018|October}} there are 4,601 known Jupiter trojans at {{L4|nolink=yes}} and 2,439 at {{L5|nolink=yes}}.<ref name="MPC-count-by-camp" />

== Nomenclature ==
The custom of naming all asteroids in Jupiter's {{L4|nolink=yes}} and {{L5|nolink=yes}} points after famous heroes of the [[Trojan War]] was suggested by [[Johann Palisa]] of [[Vienna]], who was the first to accurately calculate their orbits.<ref name=Nicholson1961/>

Asteroids in the leading ({{L4|nolink=yes}}) orbit are named after [[Ancient Greece|Greek]] heroes (the "Greek node or camp" or "[[Achilles]] group"), and those at the trailing ({{L5|nolink=yes}}) orbit are named after the heroes of [[Troy]] (the "Trojan node or camp").<ref name=Nicholson1961/> The asteroids [[617 Patroclus]] and [[624 Hektor]] were named before the Greece/Troy rule was devised, resulting in a "Greek spy", [[Patroclus]], in the Trojan node and a "Trojan spy", [[Hector]], in the Greek node.<ref name=Wyse1938/><ref name="spies">{{cite web|title=Trojan Asteroids|url=http://astronomy.swin.edu.au/cosmos/T/Trojan+Asteroids|website=Cosmos|publisher=Swinburne University of Technology|access-date=13 June 2017|archive-url=https://web.archive.org/web/20170623182748/http://astronomy.swin.edu.au/cosmos/T/Trojan+Asteroids|archive-date=23 June 2017|url-status=live}}</ref>

In 2018, at its 30th General Assembly in Vienna, the [[International Astronomical Union]] amended the naming convention for Jupiter trojans, allowing for asteroids with ''[[Absolute magnitude#Solar System bodies (H)|H]]'' larger than 12 (that is, a [[mean diameter]] smaller than approximately 22 kilometers, for an assumed albedo of 0.057) to be named after Olympic athletes, because there are now far more known Jupiter trojans than available names of [[List of Trojan War characters|Greek and Trojan warriors]] that fought in the Trojan war.<ref>{{Cite web |title=MPEC 2020-T164 |url=https://minorplanetcenter.net/mpec/K20/K20TG4.html |access-date=2024-07-20 |website=minorplanetcenter.net}}</ref>

== Numbers and mass ==
[[File:Lagrange points.jpg|thumb|right|A [[gravitational potential]] contour plot showing Earth's Lagrangian points; {{L4|nolink=yes}} and {{L5|nolink=yes}} are ahead (above) and behind (below) the planet, respectively. Jupiter's Lagrangian points are similarly situated in its much larger orbit.]]

Estimates of the total number of Jupiter trojans are based on deep surveys of limited areas of the sky.<ref name=Yoshida2005/> The {{L4|nolink=yes}} swarm is believed to hold between 160,000 and 240,000 asteroids with diameters larger than 2&nbsp;km and about 600,000 with diameters larger than 1&nbsp;km.<ref name=Yoshida2005/><ref name=Jewitt2000/> If the {{L5|nolink=yes}} swarm contains a comparable number of objects, there are more than {{Nowrap|1 million}} Jupiter trojans 1&nbsp;km in size or larger. For the objects brighter than [[Absolute magnitude#Solar System bodies (H)|absolute magnitude]] 9.0 the population is probably complete.<ref name=Fernandes2003/> These numbers are similar to that of comparable asteroids in the asteroid belt.<ref name=Yoshida2005/> The total mass of the Jupiter trojans is estimated at 0.0001 of the mass of Earth or one-fifth of the mass of the asteroid belt.<ref name=Jewitt2000/>

Two more recent studies indicate that the above numbers may overestimate the number of Jupiter trojans by several-fold. This overestimate is caused by (1) the assumption that all Jupiter trojans have a low [[albedo]] of about 0.04, whereas small bodies may have an average albedo as high as 0.12;<ref name=Fernandes2009/> (2) an incorrect assumption about the distribution of Jupiter trojans in the sky.<ref name=Nakamura2008/> According to the new estimates, the total number of Jupiter trojans with a diameter larger than 2&nbsp;km is {{nowrap|6,300 ± 1,000}} and {{nowrap|3,400 ± 500}} in the L<sub>4</sub> and L<sub>5</sub> swarms, respectively.<ref name=Nakamura2008/> These numbers would be reduced by a factor of 2 if small Jupiter trojans are more reflective than large ones.<ref name=Fernandes2009/>

The number of Jupiter trojans observed in the {{L4|nolink=yes}} swarm is slightly larger than that observed in {{L5|nolink=yes}}. Because the brightest Jupiter trojans show little variation in numbers between the two populations, this disparity is probably due to observational bias.<ref name=Jewitt2004/> Some models indicate that the {{L4|nolink=yes}} swarm may be slightly more stable than the {{L5|nolink=yes}} swarm.<ref name=Marzari2002/>

The largest Jupiter trojan is [[624 Hektor]], which has a mean diameter of 203&nbsp;±&nbsp;3.6&nbsp;km.<ref name=Fernandes2003/> There are few large Jupiter trojans in comparison to the overall population. With decreasing size, the number of Jupiter trojans grows very quickly down to 84&nbsp;km, much more so than in the asteroid belt. A diameter of 84&nbsp;km corresponds to an absolute magnitude of 9.5, assuming an [[albedo]] of 0.04. Within the 4.4–40&nbsp;km range the Jupiter trojans' size distribution resembles that of the main-belt asteroids. Nothing is known about the masses of the smaller Jupiter trojans.<ref name=Marzari2002/> The size distribution suggests that the smaller Trojans may be the products of collisions by larger Jupiter trojans.<ref name=Jewitt2004/>

{{JPL SBDB Jupiter Trojans}}

== Orbits ==
[[File:AnimatedOrbitOf624Hektor.gif|thumb|Animation of the orbit of 624 Hektor (blue), set against the orbit of Jupiter (outer red ellipse)]]

Jupiter trojans have orbits with radii between 5.05 and 5.35&nbsp;AU (the mean semi-major axis is 5.2&nbsp;±&nbsp;0.15&nbsp;AU), and are distributed throughout elongated, curved regions around the two Lagrangian points;<ref name=Yoshida2005/> each swarm stretches for about 26° along the orbit of Jupiter, amounting to a total distance of about 2.5&nbsp;AU.<ref name=Jewitt2000/> The width of the swarms approximately equals two [[Hill radius|Hill's radii]], which in the case of Jupiter amounts to about 0.6&nbsp;AU.<ref name=Marzari2002/> Many of Jupiter trojans have large [[orbital inclination]]s relative to Jupiter's orbital plane—up to 40°.<ref name=Jewitt2000/>

Jupiter trojans do not maintain a fixed separation from Jupiter. They slowly librate around their respective equilibrium points, periodically moving closer to Jupiter or farther from it.<ref name=Marzari2002/> Jupiter trojans generally follow paths called [[tadpole orbit]]s around the Lagrangian points; the average period of their libration is about 150 years.<ref name=Jewitt2000/> The amplitude of the libration (along the Jovian orbit) varies from 0.6° to 88°, with the average being about 33°.<ref name=Marzari2002/> Simulations show that Jupiter trojans can follow even more complicated trajectories when moving from one Lagrangian point to another—these are called [[horseshoe orbit]]s (currently no Jupiter Trojan with such an orbit is known, though [[(316179) 2010 EN65|one]] is known [[Neptune trojan|for Neptune]]).<ref name=Marzari2002/>

=== Dynamical families and binaries ===
Discerning [[collisional family|dynamical families]] within the Jupiter trojan population is more difficult than it is in the asteroid belt, because the Jupiter trojans are locked within a far narrower range of possible positions. This means that clusters tend to overlap and merge with the overall swarm. By 2003 roughly a dozen dynamical families were identified. Jupiter-trojan families are much smaller in size than families in the asteroid belt; the largest identified family, the Menelaus group, consists of only eight members.<ref name=Jewitt2004/>

In 2001, [[617 Patroclus]] was the first Jupiter trojan to be identified as a [[Minor-planet moon|binary asteroid]].<ref name="Merline">{{cite web|last=Merline|first=W. J.|date=2001|url=http://cbat.eps.harvard.edu/iauc/07700/07741.html#Item2|title=IAUC 7741: 2001fc; S/2001 (617) 1; C/2001 T1, C/2001 T2|access-date=25 October 2010|archive-url=https://web.archive.org/web/20110719210034/http://cbat.eps.harvard.edu/iauc/07700/07741.html#Item2|archive-date=19 July 2011|url-status=live}}</ref> The binary's orbit is extremely close, at 650&nbsp;km, compared to 35,000&nbsp;km for the primary's [[Hill sphere]].<ref name=Marchis2006/> The largest Jupiter trojan—[[624 Hektor]]— is probably a [[contact binary (asteroid)|contact binary]] with a moonlet.<ref name=Jewitt2004/><ref name=IAUC8732>{{cite web|url=http://cbat.eps.harvard.edu/iauc/08700/08732.html#Item1|title=IAUC 8732: S/2006 (624) 1|access-date=23 July 2006|archive-url=https://web.archive.org/web/20110719210046/http://cbat.eps.harvard.edu/iauc/08700/08732.html#Item1|archive-date=19 July 2011|url-status=live}} (Satellite Discovery)</ref><ref name=Lacerda2007/>

== Physical properties ==
[[File:624Hektor-LB1-mag15.jpg|thumb|right|Trojan [[624 Hektor]] (indicated) is similar in [[apparent magnitude|brightness]] to [[dwarf planet]] [[Pluto]].]]

Jupiter trojans are dark bodies of irregular shape. Their [[geometric albedo]]s generally vary between 3 and 10%.<ref name=Fernandes2003/> The average value is 0.056&nbsp;±&nbsp;0.003 for the objects larger than 57&nbsp;km,<ref name=Jewitt2004/> and 0.121&nbsp;±&nbsp;0.003 (R-band) for those smaller than 25&nbsp;km.<ref name=Fernandes2009/> The asteroid [[4709 Ennomos]] has the highest albedo (0.18) of all known Jupiter trojans.<ref name=Fernandes2003/> Little is known about the masses, chemical composition, rotation or other physical properties of the Jupiter trojans.<ref name=Jewitt2004/>

=== Rotation ===
The rotational properties of Jupiter trojans are not well known. Analysis of the rotational [[light curve]]s of 72 Jupiter trojans gave an average rotational period of about 11.2&nbsp;hours, whereas the average period of the control sample of asteroids in the asteroid belt was 10.6&nbsp;hours.<ref name=Barucci2002/> The distribution of the rotational periods of Jupiter trojans appeared to be well approximated by a [[Maxwell distribution|Maxwellian function]],<ref group="Note">The Maxwellian function is <math>F=\begin{smallmatrix}\frac{1}{\sqrt{2\pi}\sigma}P^2\exp(-(P-P_0)^2/\sigma^2)\end{smallmatrix}</math>, where <math>P_0</math> is the average rotational period, <math>\sigma</math> is the [[Statistical dispersion|dispersion]] of periods.</ref> whereas the distribution for main-belt asteroids was found to be non-Maxwellian, with a deficit of periods in the range 8–10&nbsp;hours.<ref name=Barucci2002/> The Maxwellian distribution of the rotational periods of Jupiter trojans may indicate that they have undergone a stronger collisional evolution compared to the asteroid belt.<ref name=Barucci2002/>

In 2008 a team from [[Calvin College]] examined the [[light curve]]s of a debiased sample of ten Jupiter trojans, and found a [[median]] spin period of 18.9 hours. This value was significantly higher than that for main-belt asteroids of similar size (11.5 hours). The difference could mean that the Jupiter trojans possess a lower average density, which may imply that they formed in the [[Kuiper belt]] (see below).<ref>{{cite journal|last1=Molnar|first1=Lawrence A.|last2=Haegert|first2=Melissa J.|last3=Hoogeboom|first3=Kathleen M.|date=April 2008|title=Lightcurve Analysis of an Unbiased Sample of Trojan Asteroids|journal=The Minor Planet Bulletin|publisher=Association of Lunar and Planetary Observers|volume=35|issue=2|pages=82–84|oclc=85447686|bibcode=2008MPBu...35...82M}}</ref>

=== Composition ===
[[Spectroscopy|Spectroscopically]], the Jupiter trojans mostly are [[D-type asteroid]]s, which predominate in the outer regions of the asteroid belt.<ref name=Jewitt2004/> A small number are classified as [[P-type asteroid|P]] or [[C-type asteroid]]s.<ref name=Barucci2002/> Their spectra are red (meaning that they reflect more light at longer wavelengths) or neutral and featureless.<ref name=Fernandes2003/> No firm evidence of water, organics or other chemical compounds has been obtained {{as of|2007|lc=on}}. [[4709 Ennomos]] has an albedo slightly higher than the Jupiter-trojan average, which may indicate the presence of water ice. Some other Jupiter Trojans, such as [[911 Agamemnon]] and [[617 Patroclus]], have shown very weak absorptions at 1.7 and 2.3&nbsp;μm, which might indicate the presence of organics.<ref>{{cite journal|title=Spectroscopic Search for Water Ice on Jovian Trojan Asteroids|last1=Yang|first1=Bin|last2=Jewitt|first2=David|date=2007|journal=The Astronomical Journal|volume=134|issue=1|pages=223–228|doi=10.1086/518368|url=http://www.iop.org/EJ/abstract/1538-3881/134/1/223/|access-date=19 January 2009|bibcode=2007AJ....134..223Y|doi-access=free}}</ref> The Jupiter trojans' spectra are similar to those of the [[Moons of Jupiter#Irregular satellites|irregular moons of Jupiter]] and, to a certain extent, [[comet nuclei]], though Jupiter trojans are spectrally very different from the redder Kuiper belt objects.<ref name=Yoshida2005/><ref name=Jewitt2004/> A Jupiter trojan's spectrum can be matched to a mixture of water ice, a large amount of carbon-rich material ([[charcoal]]),<ref name=Jewitt2004/> and possibly [[magnesium]]-rich [[silicate]]s.<ref name=Barucci2002/> The composition of the Jupiter trojan population appears to be markedly uniform, with little or no differentiation between the two swarms.<ref>{{cite journal|title=The surface composition of Jupiter trojans: Visible and near-infrared survey of dynamical families|author=Dotto, E.|author2=Fornasier, S.|author3=Barucci, M. A.|journal=Icarus|volume=183|issue=2|date=August 2006|pages=420–434|doi=10.1016/j.icarus.2006.02.012|bibcode=2006Icar..183..420D|display-authors=etal}}</ref>

A team from the [[Keck Observatory]] in Hawaii announced in 2006 that it had measured the density of the binary Jupiter trojan [[617 Patroclus]] as being less than that of water ice (0.8&nbsp;g/cm<sup>3</sup>), suggesting that the pair, and possibly many other Trojan objects, more closely resemble [[comet]]s or Kuiper belt objects in composition—water ice with a layer of dust—than they do the main-belt asteroids.<ref name=Marchis2006/> Countering this argument, the density of Hektor as determined from its rotational lightcurve (2.480&nbsp;g/cm<sup>3</sup>) is significantly higher than that of 617 Patroclus.<ref name=Lacerda2007/> Such a difference in densities suggests that density may not be a good indicator of asteroid origin.<ref name=Lacerda2007/>

== Origin and evolution ==

Two main theories have emerged to explain the formation and evolution of the Jupiter trojans. The first suggests that the Jupiter trojans formed in the same part of the [[Solar System]] as Jupiter and entered their orbits while it was forming.<ref name=Marzari2002/> The last stage of Jupiter's formation involved runaway growth of its mass through the accretion of large amounts of [[hydrogen]] and [[helium]] from the [[protoplanetary disk]]; during this growth, which lasted for only about 10,000 years, the mass of Jupiter increased by a factor of ten. The [[planetesimal]]s that had approximately the same orbits as Jupiter were caught by the increased gravity of the planet.<ref name=Marzari2002/> The capture mechanism was very efficient—about 50% of all remaining planetesimals were trapped. This hypothesis has two major problems: the number of trapped bodies exceeds the observed population of Jupiter trojans by four [[order of magnitude|orders of magnitude]], and the present Jupiter trojan asteroids have larger orbital inclinations than are predicted by the capture model.<ref name=Marzari2002/> Simulations of this scenario show that such a mode of formation also would inhibit the creation of similar trojans for [[Saturn]], and this has been borne out by observation: to date no trojans have been found near Saturn.<ref>{{cite journal|title=The growth of Jupiter and Saturn and the capture of Trojans |last1=Marzari|first1=F. |last2=Scholl|first2=H. |journal=Astronomy and Astrophysics|volume=339|pages=278–285|date=1998|bibcode=1998A&A...339..278M}}</ref> In a variation of this theory Jupiter captures trojans during its initial growth then migrates as it continues to grow. During Jupiter's migration the orbits of objects in horseshoe orbits are distorted causing the L4 side of these orbits to be over occupied. As a result, an excess of trojans is trapped on the L4 side when the horseshoe orbits shift to tadpole orbits as Jupiter grows. This model also leaves the Jupiter trojan population 3–4 orders of magnitude too large.<ref name="Pirani_etal_2019">{{cite journal |last1=Pirani |first1=S. |last2=Johansen |first2=A. |last3=Bitsch |first3=B. |last4=Mustill |first4=A. J. |last5=Turrini |first5=D. |title=Consequences of planetary migration on the minor bodies of the early solar system |journal=Astronomy & Astrophysics |date=2019 |volume=623 |page=A169 |doi=10.1051/0004-6361/201833713 |arxiv=1902.04591 |bibcode=2019A&A...623A.169P |s2cid=119546182 }}</ref>

The second theory proposes that the Jupiter trojans were captured during the migration of the giant planets described in the [[Nice model]]. In the Nice model the orbits of the giant planets became unstable {{Nowrap|500–600 million}} years after the Solar System's formation when Jupiter and Saturn crossed their 1:2 mean-motion [[orbital resonance|resonance]]. Encounters between planets resulted in [[Uranus]] and [[Neptune]] being scattered outward into the primordial [[Kuiper belt]], disrupting it and throwing millions of objects inward.<ref name=Levison2007/> When Jupiter and Saturn were near their 1:2 resonance the orbits of pre-existing Jupiter trojans became unstable during a secondary resonance with Jupiter and Saturn. This occurred when the period of the trojans' libration about their Lagrangian point had a 3:1 ratio to the period at which the position where Jupiter passes Saturn circulated relative to its perihelion. This process was also reversible allowing a fraction of the numerous objects scattered inward by Uranus and Neptune to enter this region and be captured as Jupiter's and Saturn's orbits separated. These new trojans had a wide range of inclinations, the result of multiple encounters with the giant planets before being captured.<ref name="Morbidelli">{{cite journal|last=Morbidelli|first=A.|author2=Levison, H. F.|author3=Tsiganis, K.|author4=Gomes, R.|date=26 May 2005|title=Chaotic capture of Jupiter's Trojan asteroids in the early Solar System|journal=Nature|volume=435|issue=7041|pages=462–465|oclc=112222497|url=http://www.oca.eu/michel/PubliGroupe/MorbyNature2005.pdf|doi=10.1038/nature03540|pmid=15917801|bibcode=2005Natur.435..462M|s2cid=4373366 |access-date=19 January 2009|archive-url=https://web.archive.org/web/20090731120551/http://www.oca.eu/michel/PubliGroupe/MorbyNature2005.pdf|archive-date=31 July 2009|url-status=dead}}</ref> This process can also occur later when Jupiter and Saturn cross weaker resonances.<ref name=Nesvorny_2013>{{cite journal|last=Nesvorný|first=David|author2=Vokrouhlický, David |author3=Morbidelli, Alessandro |title=Capture of Trojans by Jumping Jupiter|journal=The Astrophysical Journal|date=2013|volume=768|issue=1|page=45|doi=10.1088/0004-637X/768/1/45|arxiv=1303.2900|bibcode=2013ApJ...768...45N|s2cid=54198242 }}</ref>

In a [[Jumping-Jupiter scenario|revised version]] of the Nice model Jupiter trojans are captured when Jupiter encounters an ice giant during the instability. In this version of the Nice model one of the ice giants (Uranus, Neptune, or a lost [[Five-planet Nice model|fifth planet]]) is scattered inward onto a Jupiter-crossing orbit and is scattered outward by Jupiter causing the orbits of Jupiter and Saturn to quickly separate. When Jupiter's semi-major axis jumps during these encounters existing Jupiter trojans can escape and new objects with semi-major axes similar to Jupiter's new semi-major axis are captured. Following its last encounter the ice giant can pass through one of the libration points and perturb their orbits leaving this libration point depleted relative to the other. After the encounters end some of these Jupiter trojans are lost and others captured when Jupiter and Saturn are near weak mean motion resonances such as the 3:7 resonance via the mechanism of the original Nice model.<ref name="Nesvorny_2013"/>

The long-term future of the Jupiter trojans is open to question, because multiple weak resonances with Jupiter and Saturn cause them to behave chaotically over time.<ref name=Robutal2005/> Collisional shattering slowly depletes the Jupiter trojan population as fragments are ejected. Ejected Jupiter trojans could become temporary satellites of Jupiter or [[Jupiter-family comet]]s.<ref name=Jewitt2004/> Simulations show that the orbits of up to 17% of Jupiter trojans are unstable over the age of the Solar System.<ref>{{cite journal|title=Chaotic Diffusion And Effective Stability of Jupiter trojans |author=Kleomenis Tsiganis |author2=Harry Varvoglis |author3=Rudolf Dvorak |publisher=Springer|journal=Celestial Mechanics and Dynamical Astronomy|volume=92|date=April 2005|doi=10.1007/s10569-004-3975-7|pages=71–87|issue=1–3|bibcode = 2005CeMDA..92...71T |s2cid=123648472 }}</ref> Levison et al. believe that roughly 200 ejected Jupiter trojans greater than 1&nbsp;km in diameter might be travelling the Solar System, with a few possibly on Earth-crossing orbits.<ref name=Levison1997>{{cite journal|title=Dynamical evolution of Jupiter's Trojan asteroids|author=Levison, Harold F. |author2=Shoemaker, Eugene M. |author3=Shoemaker, Carolyn S.|journal=Nature|volume=385|issue=6611|pages=42–44|date=1997|doi=10.1038/385042a0|bibcode = 1997Natur.385...42L |s2cid=4323757 }}</ref> Some of the escaped Jupiter trojans may become Jupiter-family comets as they approach the Sun and their surface ice begins evaporating.<ref name=Levison1997/>

== Exploration ==
On 4 January 2017 NASA announced that ''[[Lucy (spacecraft)|Lucy]]'' was selected as one of their next two [[Discovery Program]] missions.<ref>{{Cite news|url=https://www.nasa.gov/press-release/nasa-selects-two-missions-to-explore-the-early-solar-system/|title=NASA Selects Two Missions to Explore the Early Solar System|last=Northon|first=Karen|date=4 January 2017|newspaper=NASA|access-date=5 January 2017|archive-url=https://web.archive.org/web/20170105003614/https://www.nasa.gov/press-release/nasa-selects-two-missions-to-explore-the-early-solar-system/|archive-date=5 January 2017|url-status=live}}</ref> ''Lucy'' is set to explore seven<ref>{{cite web |title=Tour |url=http://lucy.swri.edu/mission/Tour.html |website=Lucy Mission Website |publisher=NASA |access-date=5 October 2021 |archive-date=8 September 2018 |archive-url=https://web.archive.org/web/20180908073839/http://lucy.swri.edu/mission/Tour.html |url-status=live }}</ref> Jupiter trojans. It was launched on October 16, 2021, and will arrive at the {{L4}} Trojan cloud in 2027 after two Earth gravity assists and a fly-by of a main-belt asteroid. It will then return to the vicinity of Earth for another gravity assist to take it to Jupiter's {{L5}} Trojan cloud where it will visit [[617 Patroclus]].<ref name="round 1">{{cite news |last1=Dreier |first1=Casey |last2=Lakdawalla |first2=Emily |url=http://www.planetary.org/blogs/casey-dreier/2015/09301336-discovery-downselect.html |title=NASA announces five Discovery proposals selected for further study |work=The Planetary Society |date=30 September 2015 |access-date=1 October 2015 |archive-url=https://web.archive.org/web/20151002190608/http://www.planetary.org/blogs/casey-dreier/2015/09301336-discovery-downselect.html |archive-date=2 October 2015 |url-status=live }}</ref>

== See also ==
{{colbegin}}
* [[Comet Shoemaker–Levy 9]]
* [[List of Jupiter trojans (Greek camp)]]
* [[List of Jupiter trojans (Trojan camp)]]
* [[List of Jupiter-crossing minor planets]]
* [[List of objects at Lagrangian points]]
{{colend}}

== Notes ==
<references group=Note/>

== References ==
{{Reflist|30em|refs=

<ref name="MPC-Trojan-count">{{cite web |title=Trojan Minor Planets |publisher=Minor Planet Center |url=http://www.minorplanetcenter.org/iau/lists/Trojans.html |access-date=14 October 2018 |archive-url=https://web.archive.org/web/20170629211349/http://www.minorplanetcenter.org/iau/lists/Trojans.html |archive-date=29 June 2017 |url-status=live }}</ref>

<ref name="MPC-count-by-camp">{{cite web |title=List of Jupiter trojans |publisher=Minor Planet Center |url=http://www.minorplanetcenter.net/iau/lists/JupiterTrojans.html |access-date=14 October 2018 |archive-url=https://web.archive.org/web/20180612141250/https://www.minorplanetcenter.net/iau/lists/JupiterTrojans.html |archive-date=12 June 2018 |url-status=live }}</ref>

<ref name="Dotto2006">{{cite journal |title=The surface composition of Jupiter Trojans: Visible and near-infrared survey of dynamical families |journal=Icarus |pages=420–434 |year=2006 |volume=183 |issue=2 |last1=Dotto |first1=E |last2=Fornasier |first2=S |last3=Barucci |first3=M.A |last4=Licandr o|first4=J |last5=Boehnhardt |first5=H |last6=Hainaut |first6=O |last7=Marzari |first7=F |last8=De Bergh |first8=C |last9=De Luise |first9=F |doi=10.1016/j.icarus.2006.02.012|bibcode=2006Icar..183..420D}}</ref>

<ref name="Jewitt2000">{{cite journal |last=Jewitt |first=David C. |author2=Trujillo, Chadwick A. |author3=Luu, Jane X. |title=Population and size distribution of small Jovian Trojan asteroids |date=2000 |journal=The Astronomical Journal |volume=120 |issue=2 |pages=1140–7 |doi=10.1086/301453 |bibcode=2000AJ....120.1140J |arxiv=astro-ph/0004117|s2cid=119450236 }}</ref>

<ref name="Yoshida2005">{{cite journal |last=Yoshida |first=F. |author2=Nakamura, T |title=Size distribution of faint L4 Trojan asteroids |date=2005 |journal=The Astronomical Journal |volume=130 |issue=6 |pages=2900–11 |doi=10.1086/497571 |bibcode=2005AJ....130.2900Y|doi-access=free }}</ref>

<ref name="Wyse1938">{{cite journal |last=Wyse |first=A. B. | author-link=Arthur Bambridge Wyse |title=The Trojan group |date=1938 |journal=Astronomical Society of the Pacific Leaflets |volume=3 |issue=114 |pages=113–19 |bibcode=1938ASPL....3..113W}}</ref>

<ref name="Einarsson1913">{{cite journal |last=Einarsson |first=Sturla |title=The Minor Planets of the Trojan Group |date=1913 |journal=Publications of the Astronomical Society of the Pacific |volume=25 |issue=148 |pages=131–3 |bibcode=1913PASP...25..131E |doi=10.1086/122216|s2cid=122428016 }}</ref>

<ref name=Nakamura2008>{{cite journal |last1=Nakamura |first1=Tsuko |last2=Yoshida |first2=Fumi |title=A New Surface Density Model of Jovian Trojans around Triangular Libration Points |date=2008 |journal=Publications of the Astronomical Society of Japan |volume=60 |issue=2 |pages=293–296 |bibcode=2008PASJ...60..293N |doi=10.1093/pasj/60.2.293|doi-access=free }}</ref>

<ref name="Nicholson1961">{{cite journal |last=Nicholson |first=Seth B. |title=The Trojan asteroids |date=1961 |journal=Astronomical Society of the Pacific Leaflets |volume=8 |issue=381 |pages=239–46 |bibcode=1961ASPL....8..239N}}</ref>

<ref name="Marzari2002">{{cite book |last=Marzari |first=F. |author2=Scholl, H. |author3=Murray C. |author4=Lagerkvist C. |date=2002 |chapter=Origin and Evolution of Trojan Asteroids |title=Asteroids III |publisher=University of Arizona Press |pages=725–38 |location=Tucson, Arizona |chapter-url=http://www.lpi.usra.edu/books/AsteroidsIII/pdf/3007.pdf |access-date=17 January 2009 |archive-date=6 June 2011 |archive-url=https://web.archive.org/web/20110606010204/http://www.lpi.usra.edu/books/AsteroidsIII/pdf/3007.pdf |url-status=live }}</ref>

<ref name="Barucci2002">{{cite book |last=Barucci |first=M.A. |author2=Kruikshank, D.P. |author3=Mottola S. |author4=Lazzarin M. |date=2002 |chapter=Physical Properties of Trojan and Centaur Asteroids |title=Asteroids III |publisher=University of Arizona Press |pages=273–87 |location=Tucson, Arizona}}</ref>

<ref name="Levison2007">{{cite journal |first1=Harold F. |last1=Levison |first2=Alessandro |last2=Morbidelli |first3=Christa |last3=Van Laerhoven |title=Origin of the Structure of the Kuiper Belt during a Dynamical Instability in the Orbits of Uranus and Neptune |date=2007 |bibcode=2008Icar..196..258L |arxiv=0712.0553 |doi=10.1016/j.icarus.2007.11.035 |journal=Icarus |volume=196 |issue=1 |pages=258–273 |s2cid=7035885 |display-authors=etal}}</ref>

<ref name="Marchis2006">{{cite journal |last=Marchis |first=Franck |author2=Hestroffer, Daniel |author3=Descamps, Pascal |title=A low density of 0.8&nbsp;g&nbsp;cm<sup>−3</sup> for the Trojan binary asteroid 617 Patroclus |date=2006 |journal=Nature |volume=439 |issue=7076 |pages=565–567 |bibcode=2006Natur.439..565M |doi=10.1038/nature04350 |pmid=16452974 |arxiv=astro-ph/0602033 |s2cid=4416425 |display-authors=etal}}</ref>

<ref name="Fernandes2003">{{cite journal |last=Fernandes |first=Yanga R. |author2=Sheppard, Scott S. |author3=Jewitt, David C. |title=The albedo distribution of Jovian Trojan asteroids |date=2003 |journal=The Astronomical Journal |volume=126 |issue=3 |pages=1563–1574 |bibcode=2003AJ....126.1563F |doi=10.1086/377015|citeseerx=10.1.1.7.5611 |s2cid=15977388 }}</ref>

<ref name=Fernandes2009>{{cite journal |last1=Fernández |first1=Y. R. |last2=Jewitt |first2=D. |last3=Ziffer |first3=J. E. |title=Albedos of Small Jovian Trojans |journal=The Astronomical Journal |volume=138 |issue=1 |pages=240–250 |year=2009 |doi=10.1088/0004-6256/138/1/240 |bibcode=2009AJ....138..240F |arxiv=0906.1786|s2cid=5592793 }}</ref>

<ref name="Lacerda2007">{{cite journal |last=Lacerda |first=Pedro |author2=Jewitt, David C. |title=Densities of Solar System Objects from Their Rotational Light Curves |date=2007 |journal=The Astronomical Journal |volume=133 |issue=4 |pages=1393–1408 |doi=10.1086/511772 |bibcode=2007AJ....133.1393L |arxiv=astro-ph/0612237|s2cid=17735600 }}</ref>

<ref name="Jewitt2004">{{cite book |last1=Jewitt |first1=David C. |last2=Sheppard |first2=Scott |last3=Porco |first3=Carolyn C. |chapter=Jupiter's Outer Satellites and Trojans |title=Jupiter: The Planet, Satellites and Magnetosphere |date=2004 |publisher=Cambridge University Press |s2cid=53962019 |editor=Bagenal, Fran |editor2=Dowling, Timothy E. |editor3=McKinnon, William B. |chapter-url=https://pdfs.semanticscholar.org/5a3f/11d47003a555cd96499776edc3adfb47f5fd.pdf |access-date=30 April 2021 |archive-date=9 November 2019 |archive-url=https://web.archive.org/web/20191109164923/https://pdfs.semanticscholar.org/5a3f/11d47003a555cd96499776edc3adfb47f5fd.pdf |url-status=bot: unknown }}</ref>

<ref name="Robutal2005">{{cite journal |last=Robutal |first=P. |author2=Gabern, F. |author3=Jorba A. |title=The observed Trojans and the global dynamics around the lagrangian points of the sun–jupiter system |date=2005 |journal=Celestial Mechanics and Dynamical Astronomy |volume=92 |issue=1–3 |pages=53–69 |doi=10.1007/s10569-004-5976-y |url=http://www.cds.caltech.edu/~gabern/preprints/osterreich.pdf |bibcode=2005CeMDA..92...53R |s2cid=5759776 |url-status=dead |archive-url=https://web.archive.org/web/20090731062642/http://www.cds.caltech.edu/~gabern/preprints/osterreich.pdf |archive-date=31 July 2009  }}</ref>

}} <!-- end of reflist -->

== External links ==
{{Commons category|Jupiter trojans}}
* {{cite web |url=http://www.minorplanetcenter.org/iau/lists/Trojans.html |title=Minor Planet Center's List of Trojan Minor Planets}}
* {{cite web |last=Sheppard |first=Scott |url=http://www.dtm.ciw.edu/users/sheppard/satellites/trojan.html |title=The Trojan Page}}
* {{cite journal |last1=Lykawka |author2=Horner |title=The Capture of Trojan Asteroids by the Giant Planets During Planetary Migration |first1=P. S. |doi=10.1111/j.1365-2966.2010.16538.x |date=2010 |journal=[[Monthly Notices of the Royal Astronomical Society]] |volume=405 |issue=1383 |pages=1375–1383 |doi-access=free |arxiv=1003.2137 |bibcode=2010MNRAS.405.1375L|s2cid=54084401 }}
* [http://www.jpl.nasa.gov/news/news.php?release=2012-322 NASA's WISE Colors in Unknowns on Jupiter Asteroids] (NASA 2012-322 : 15 October 2012)
* {{YouTube |id=arvl5JQ6ll0 |title=NASA's New Discovery Missions: ''Psyche'' and ''Lucy''}}
* [https://gravitysimulator.org/solar-system/jupiter-and-its-ten-largest-trojans 3D Gravity Simulation of the Ten Largest Jupiter Trojan Asteroids] {{Webarchive|url=https://web.archive.org/web/20200611221939/https://gravitysimulator.org/solar-system/jupiter-and-its-ten-largest-trojans/ |date=11 June 2020 }}

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