# Mathematical Digest

### Short Summaries of Articles about Mathematics

in the Popular Press

"Orbits of all sorts," by Donald G. Saari. *Nature,* 3 September 1998,pages 19-20.

Given a collection of n bodies under the force of mutual gravitationalattraction, how will they move? With as few as 3 bodies, such a systemdisplays sensitive dependence on initial conditions, a hallmark of chaos, andthe paths the bodies take become extremely difficult to predict.Mathematicians have for decades tried to solve whatever bits of this complexpuzzle they can. This article discusses recent progress by Gregory Buck, whohas uncovered a special class of approximate solutions to the n-body problem.Although the solutions are only approximate, Buck's approach may provide newinsights.

*--- Allyn Jackson*