Vol. 219, No. 2, 2005

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Toshiaki Fujiwara & Richard Montgomery

Abstract

The Newtonian three-body problem with equal masses has a remarkable solution where the bodies chase each other around a planar curve having the qualitative shape and symmetries of a figure eight. Here we prove that each lobe of this curve is convex.

Keywords

figure-eight, convexity, Newtonian potential

Mathematical Subject Classification

Primary: 70F07

Authors
Toshiaki Fujiwara
College of Liberal Arts and Sciences
Kitasato University
Kitasato 1-15-1, Sagamihara
Kanagawa 228-8555
Japan
Richard Montgomery
Mathematics Department
UC Santa Cruz
Santa Cruz, CA 95064
United States