Convexity of the figure eight solution to the three-body problem

Toshiaki Fujiwara and Richard Montgomery

Vol. 219 (2005), No. 2, 271–283

DOI: 10.2140/pjm.2005.219.271

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 2000

Primary: 70F07

Milestones

Received: 2 September 2003

Revised: 5 November 2003

Published: 1 April 2005