The Trojan Asteroids
The Trojan asteroids consist of the several hundred asteroids which are known to orbit the Sun at the distance of Jupiter. They travel in the vicinity of the two Lagrange points which are 60 degrees ahead of and behind Jupiter in orbit. The Lagrange points of Jupiter are regions where a body can orbit under the combined influence of Jupiter and the Sun.
Image Credit: NASA/Lunar and Planetary Institute
This NASA diagram shows the relative locations of the main asteroid belt and the two regions of Trojan asteroids which orbit syncronously with Jupiter.
French mathematician Joseph Louis Lagrange showed in 1772 that there are five points where a relatively small object could orbit the Sun under the influence of two other massive bodies such as the Sun and Jupiter. Three of those points are along the line joining the Sun and Jupiter, and lead to unstable orbits where the slightest disturbance could cause them to leave the orbit. The L4 and L5 points at 60° ahead and behind Jupiter in orbit are stable regions and have collected a large number of Trojan asteroids.
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Chaisson and McMillan