APPLETS: Planetary Ballet

Science  14 Dec 2001:
Vol. 294, Issue 5550, pp. 2255c
DOI: 10.1126/science.294.5550.2255c

What would the planets do without the sun's gravity? Most likely they'd wander off into space. But it's conceivable the solar system could stick together, with the planets traveling along nice, periodic paths. In the last 2 years, celestial theoreticians have come up with myriad possible planetary orbits for sunless systems. Get a feel for these possible paths, dubbed “choreographies” for their dancelike appearance, at this pair of Web sites featuring some nifty animations.

The new orbits represent a breakthrough in celestial mechanics, a notoriously difficult branch of mathematics. Experts first attacked the problem with the analysis of a three-body, figure-eight orbit (Science, 17 March 2000, p. 1911). Java applets created by Charlie McDowell of the University of California, Santa Cruz, animate the figure eight and various other orbits, with up to 99 planets waltzing through space. More choreographies, plus a discussion of the underlying mathematics, are available at the What's New in Mathematics Web page of the American Mathematical Society.

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