TROJAN'S - JUPITER'S ASTEROIDS
 
Jupiter does not travel alone in its orbit - it is accompanied by over 400 asteroids. These asteroids, called Trojans, are found near Jupiter's Lagrange points, 60o ahead and 60o behind the orbit of Jupiter. The presence of asteroids at these locations was predicted by the French astronomer and mathematician Joseph-Louis Lagrange. Lagrange, amongst other things, was interested in celestial mechanics and in 1772 he discovered that on an orbital path there could exist points of stability marked out by an equilateral triangle.
 
It was not until 1906, however, that Max Wolf found the first Trojan, 588 Achilles. August Kopff discovered 624 Hector and 617 Patroclus shortly after. During the last two decades the pace of discovery has quickened. As of 1999 there are 473 Jupiter Trojans. There are 299 in the leading Lagrange point (L4) and 174 in the trailing Lagrange point (L5).
 

Jupiter's Trojan asteroids at the Lagrange points.
 
It is easy to imagine a neat cluster of objects coinciding with the Lagrange points, but the Trojans are quite spread out. They are found 10o to 20o either side of the 60o points. Many of them have orbits which are inclined with respect to the plane of the ecliptic by up to 30o.
 
The naming convention for the Jupiter Trojans, ascribes the leading Trojan asteroids the names of Greek warriors like Ajax, Odysseus and Agamemnon. Those of the trailing group are given the names of Trojan warriors including Paris and Agenor. The names are taken from Homer's epic of the Trojan Wars called the Illiad .The exception to the above rule conforms with the Illiad. The spies, Hector, a Trojan in the Greek camp, and Patroclus, a Greek in the Trojan camp, are found in the leading and trailing groups respectively.
 
The term "Trojan" is also used to describe objects in the Lagrange points of other bodies. In 1990 David Levy and Henry Holt found a Trojan in Mars' trailing (L5) Lagrange point. It was named 5261 Eureka. A second Mars Trojan was found in 1998, also at the L5 point.
 
Searches have concentrated on locating Venus and Earth Trojans, but none so far have been found. The Lagrange points of Saturn and Neptune have been searched too and attempts have been made to find them about our own Moon, the Trojans of which would mark out the points of an Earth centred stability triangle. However, although not Trojans, there are other co-orbital bodies in the Solar System - Saturn's moons Janus and Epimetheus are co-orbital, Telesto and Calypso are with Tethys, and Helene and Dione are co-orbital.
 
Earth shares its orbit with the asteroid 3753 Cruithne. In this case, Cruithne is not a Trojan sitting at a Lagrange point, nor is it Earth's second moon. It shares an orbit, but has a complicated horseshoe orbit. Nevertheless, the Trojans, Saturn's small moons, and 3753 Cruithne demonstrate that long-term orbital stability is not restricted to one body simply orbiting another.