The Jupiter trojans, commonly called trojan asteroids or simply trojans, are a large group of asteroids that share the planet Jupiter's orbit around the Sun. Relative to Jupiter, each trojan librates around one of Jupiter's stable Lagrange points: either , existing 60° ahead of the planet in its orbit, or , 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 AU. The first Jupiter trojan discovered, 588 Achilles, was spotted in 1906 by German astronomer Max Wolf. More than 9,800 Jupiter trojans have been found . 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 km in diameter is believed to be about , approximately equal to the number of asteroids larger than 1 km in the asteroid belt. Like main-belt asteroids, Jupiter trojans form families. , many Jupiter trojans showed to observational instruments as dark bodies with reddish, featureless 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 tholins, organic polymers formed by the Sun's radiation. The Jupiter trojans' densities (as measured by studying binaries or rotational lightcurves) vary from 0.8 to 2.5 g·cm−3. Jupiter trojans are thought to have been captured into their orbits during the early stages of the Solar System's formation or slightly later, during the migration of giant planets. The term "Trojan Asteroid" specifically refers to the asteroids co-orbital with Jupiter, but the general term "trojan" is sometimes more generally applied to other small Solar System bodies with similar relationships to larger bodies: Mars trojans, Neptune trojans, Uranus trojans and Earth trojans are known to exist. 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. Observational history 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. The trapped body will librate slowly around the point of equilibrium in a tadpole or horseshoe orbit. These leading and trailing points are called the