Trojan asteroids

In 1772, the Italian–French mathematician and astronomer Joseph-Louis Lagrange obtained two constant-pattern solutions (collinear and equilateral) of the general three-body problem. In the restricted three-body problem, with one mass negligible (which Lagrange did not consider), the five possible positions of that mass are now termed Lagrangian points.

The term "trojan" originally referred to the "trojan asteroids" that orbit close to the Lagrangian points of Jupiter. These have long been named after characters from the Trojan War of Greek mythology. By convention, the asteroids orbiting near the L4 point of Jupiter are named after the characters from the Greek side of the war, whereas those orbiting near the L5 of Jupiter are from the Trojan side. There are two exceptions that were named before the convention was put in place, the Greek-themed 617 Patroclus and the Trojan-themed 624 Hektor, which were assigned to the wrong sides.[5]

Astronomers estimate that the Jupiter trojans are about as numerous as the asteroids of the asteroid belt.[6]

Later on, objects were found orbiting near the Lagrangian points of Neptune, Mars, Earth[7] and Uranus. Asteroids at the Lagrangian points of planets other than Jupiter may be called Lagrangian asteroids.[8]

Three Mars trojans are known: 5261 Eureka, (101429) 1998 VF31, and (121514) 1999 UJ7.[9] (311999) 2007 NS2 is possibly one.[citation needed]

Nine Neptune trojans[10] are known, but large Neptune trojans are expected to outnumber the large Jupiter trojans by an order of magnitude. [11][12]

2010 TK7 was confirmed to be the first known Earth trojan in 2011. It is located in the L4 Lagrangian point, which lies ahead of Earth.[13]

2011 QF99 was identified as the first Uranus trojan in 2013; it is located in the L4 Lagrangian point.