News Release

A NEW SOLUTION TO THE THREE-BODY PROBLEM

For More Information, Contact:
Professor Richard Montgomery
University of California, Santa Cruz
Telephone: 408-459-4841, 408-457-2081
Email: rmont@math.ucsc.edu

April 5, 2001

Providence, RI---Imagine a universe containing just two planets of identical mass, set a certain distance apart.  Newton's law of gravitation describes exactly how the planets will orbit each other.  Suppose we add one more planet of the same mass, so that the three are in a random configuration.  What would the orbits of the planets then look like?

The strange answer is, no one knows.  Indeed, the great French mathematician Henri Poincaré, who worked in the late 19th and early 20th centuries, showed that in effect it is impossible to obtain a complete solution to the "three-body" problem.  A few especially simple orbits, corresponding to especially simple configurations of the bodies, have been found.  But exhibiting more complicated orbits has been an elusive goal.

Recently mathematicians Richard Montgomery and Alain Chenciner made an important advance in this problem.  With hints from computer experiments, they proved that it is possible for the three masses to move in a periodic, figure-eight pattern.

They developed an ingenious way of encoding information about the positions of the planets as they move so that some sophisticated methods from topology could be applied to prove the existence of the figure-eight orbit.

These results are described in the article "A New Solution to the Three-Body Problem," by Richard Montgomery, to appear in the May 2001 issue of the Notices of the AMS. Additional information, including animations of the new orbit, is available on a special page on the AMS Web site entitled "A new solution to the three body problem---and more," by Bill Casselman.

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