A computer-assisted proof of Saari's conjecture for the planar three-body problem

Richard Moeckel

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

The five relative equilibria of the three-body problem give rise to solutions where the bodies rotate rigidly around their center of mass. For these solutions, the moment of inertia of the bodies with respect to the center of mass is clearly constant. Saari conjectured that these rigid motions are the only solutions with constant moment of inertia. This result will be proved here for the planar problem with three nonzero masses with the help of some computational algebra and geometry.

Original languageEnglish (US)
Pages (from-to)3105-3117
Number of pages13
JournalTransactions of the American Mathematical Society
Volume357
Issue number8
DOIs
StatePublished - Aug 2005

Keywords

  • Celestial mechanics
  • Computational algebra
  • Three-body problem

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