Somewhere in the universe a trio of stars could be orbiting in a way Isaac Newton never dreamed of. Mathematicians have discovered a new choreography in which three stars trace out a figure eight. Like dancers in a Scottish reel, each star passes between the other two in turn.

Mathematicians and astronomers have long puzzled over the orbits that stars in groups of three or more might travel. Periodic orbits, those in which the stars return to their original configuration after a certain amount of time, are most tricky. Newton's theory of gravitation explained well enough why binary stars orbit each other in ellipses. But for 300 years, the only kinds of stable orbits known for groups of three or more stars have been minor variations on established themes. For example, three bodies forming an equilateral triangle can orbit stably, a pattern used for satellites and seen in the moons of Saturn. Although scientists routinely predict approximate orbits--the solutions to this "three-body problem"--using computers, finding and proving exact solutions is notoriously difficult.

Mathematician Richard Montgomery of the University of California, Santa Cruz, took a new approach: He focused on the shape of the triangle formed by all three stars rather than studying the three motions separately. Working with mathematician Alain Chenciner of the Bureau des Longitudes in Paris, Montgomery assumed the three stars have an equal mass and watched how the shape of the triangle changed as the stars move. In the optimum orbit, the triangle's shape changed the least. This also, incidentally, demonstrated that the stars would never collide--for two stars to hit each other, they would have to deform the triangle slightly more than another alternative.

They soon realized that in this solution, all three stars trace the same figure eight pattern through space. They announced the finding at a December conference in honor of Donald Saari, a leading expert on celestial mechanics. Another mathematician, Carles Simó of the University of Barcelona, probed further and showed that even stars with unequal masses could maintain the serpentine orbit.

But the stars have to be well matched. The system only works if the masses of the three stars are within one-thousandth of a percent of each other. It seems unlikely that such a system exists in nature, says Joseph Gerver, a mathematician at Rutgers University in Camden, New Jersey. "On the other hand," he says, "the universe is a big place, so who knows?"