Some asteroids, called Trojans, lie in
the same orbit as Jupiter. To have stable orbits, without falling
into the planet, they must be 60 degrees ahead or behind the
position of the planet, in what are called the Lagrangian points of Jupiter's
orbit. Both Lagrangian points on Jupiter's orbit are populated
with a cluster of asteroids that have been captured over the life
of the Solar System. Several hundred of such asteroids are now
known, and it is estimated that there may be a thousand or
more. Curiously, there are many more objects in the leading
Lagrange point (L4) than in the trailing one (L5).
There may also be a few small asteroids in the Lagrange points of Venus and Earth that are also called Trojans. For example, asteroid 5261 Eureka is today known as a "Mars Trojan".
Lagrangian points (named for Josef Lagrange, the Italian-French mathematician who discovered them) are a set of five special points that can determined in the orbit between two large objects. In the case of the solar system, Lagrangian points are stable points in the gravitational attraction between Jupiter and the Sun: at these points, a small orbiting object can orbit at a constant distance from both the larger masses. This happens because, at those five points, the gravitational force of the large objects is exactly equal to the centripetal force required to rotate with the objects. Three of the points are unstable (L1, L2, and L3) and two are stable(L4 and L5). Each of the stable Lagrange points forms an equilateral triangle with the two large masses.