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No. 139: Jan-Feb 2002

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The Spheres Can Dance To Convoluted Music

A lot has been written about the "music of the spheres." But we don't hear much about this celestial music anymore; rather, "dances of the spheres" are in vogue.

If only gravity and Newton's Laws ruled celestial motion, there would be no general solution to the hoary "three-body problem. But in the three special configurations illustrated, three bodies of equal mass can be shown to be stable. The third, the figure-of-eight, was not discovered until 1993 by C. Moore. Although mathematicians can prove it is stable, R. Montgomery admits:

There is no understanding of why the orbit is stable, from either a physical or mathematical point of view.

Certainly no figure-eight orbits have ever been observed in the cosmos so far, but who knows?.

The situation becomes really bizarre when more than three equal masses are considered. A few of the many stable, but manifestly weird, configurations are also illustrated here. These are among the simplest. To illustrate, C. Simo has found a stable choreography for 799 bodies cavorting happily and stably together in space. And he was using only his laptop!

(Appell, David; "Celestial Swingers," New Scientist, p. 36, August 4, 2001.)

From Science Frontiers #139, Jan-Feb 2002. � 2001 William R. Corliss

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