Editing Jupiter trojan (section)

== 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/>