# Mathematical Digest

### Short Summaries of Articles about Mathematics

in the Popular Press

"Celestial swingers," by David Appell. *New Scientist,* 4 August 2001, pages 37-39.

This article discusses new breakthroughs in research on the n-body problem. This problem has its roots in celestial mechanics: Given n celestial bodies that are arranged in a certain way and that move under mutual gravitational attraction, what will their orbits look like? It seems like a simple problem, but in fact a complete solution has ever been found. A few orbits for 3-body arrangements were found in the 1700s and 1800s, but it wasn't until the French mathematician Henri Poincaré showed in the late 19th century that for most arrangements of bodies, the orbits are unpredictably chaotic. Then in 1999, mathematicians Alain Chenciner and Richard Montgomery proved that a figure-eight configuration for three bodies produced stable orbits. "Confirming the figure of eight has been like a dam bursting," the article says. Mathematician Carles Simó has now found a plethora of orbits for not just three bodies, but many more, as many as 799.

An article about the Chenciner-Montgomery work, "A New Solution to the Three-Body Problem, by Richard Montgomery," appeared in the May 2001 issue of the *Notices of the American Mathematical Society.* In addition, the "What's New in Mathematics" section of the AMS Web site carried a special feature about this work, A new solution to the three body problem - and more, which includes animations of the orbits.

*--- Allyn Jackson *