Editing Jupiter trojan (section)

== 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" />