Stationary solutions for the restricted three-body problem, in which two massive bodies move in circular orbits about one another, exhibit five Lagrange points, locations at which the gravitational forces of the two heavier bodies exactly balances the centripetal force on any much lighter body. The fourth Lagrange point L4 (and also the fifth L5) is off to one side of the two heavy bodies. The lighter body can orbit around L4 or L5, which are themselves in motion.
There are many clusters of asteroids and a few moons in the solar system known as "Trojans" and "Greeks" that move with such orbits. The best known are the Trojan asteroids around Saturn.