Online Astronomy eText: Asteroids, Comets, and Interplanetary Debris
The Trojan Asteroids

Location of the Trojan asteroids (the Sun and Jupiter obviously not to scale)
(Modified version of image from the WMAP-2 site). For an explanation of L1, L2, etc, see Lagrange Points)

     Most asteroids are found in the region between Mars and Jupiter, and the vast majority lie closer to the Sun than the location, about 3.3 AUs from the Sun, where the orbital period would be in a 1 to 2 ratio with Jupiter's orbital period. There are, however, two fairly large groups of asteroids which orbit the Sun exactly in the orbit of Jupiter, at the L4 and L5 Lagrange points, 60 degrees ahead of and behind Jupiter. At these points, the gravitational influence of the Sun and Jupiter combine to keep the objects more or less locked in place, alternately drifting very slowly toward smaller or larger orbits, but on the average, retaining exactly the same orbital size and period as Jupiter.
     The asteroids in these groups are referred to as the Trojan asteroids, as they are named after characters in mythological histories of the penultimate battle between Greek and Trojan societies, supposedly started when Paris, a Phrygian prince and shepherd of exceptional honesty, was asked to judge which of three goddesses, Hera, Athena and Aphrodite, was the most beautiful. Each goddess attempted to bribe the judge, Aphrodite being successful in her effort by offering him the love of the most beautiful woman in the world, Helen of Sparta, subsequently called Helen of Troy. Since Helen was already the wife of the Spartan king Menelaeus, Paris' acceptance of Aphrodite's bribe incurred the enmity of the Greeks, and of course the spurned goddesses were none too pleased, and as a result, after a twenty-year siege Troy was leveled, and its inhabitants killed, enslaved or scattered to the winds.
     In a belated attempt at achieving celestial amity, asteroids in the leading group, at L4, are named after Greek characters, such as 588 Achilles, 659 Nestor, 911 Agamemnon, 1647 Menelaus and 1143 Odysseus (whose travels were chronicled in Homer's Odyssey). However, 624 Hektor, which was named after a Trojan hero before the convention was adopted, is an unwitting spy in the Greek camp. Asteroids in the trailing group, at L5, are named after Trojan characters, such as 884 Priamus, 1172 Aneas (whose travels were chronicled in Virgil's Aeneid), 1173 Anchises, and 1208 Troilus; and just as the Greek camp (technically, the Greek 'node') contains one Trojan, the Trojan camp (or node) contains one Greek, 617 Patroclus, which was actually the first asteroid discovered in the trailing group. It seems fitting that the out-of-place asteroids are named after (legendary) individuals who were killed in the War, Patroclus, the interloper at the Trojan node, having been killed by Hector, the interloper at the Greek node, who was subsequently killed by Achilles, the namesake of the first Trojan asteroid. (Patroclus is also interesting in that it is one of many asteroids which have recently been shown to have a satellite, in its case called Menoetius, after Patroclus' father.)