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


Author: Richard Moeckel
Journal: Trans. Amer. Math. Soc. 357 (2005), 3105-3117
MSC (2000): Primary 70F10, 70F15, 37N05
DOI: https://doi.org/10.1090/S0002-9947-04-03527-5
Published electronically: May 10, 2004
MathSciNet review: 2135737
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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.


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Additional Information

Richard Moeckel
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email: rick@math.umn.edu

DOI: https://doi.org/10.1090/S0002-9947-04-03527-5
Keywords: Celestial mechanics, three-body problem, computational algebra
Received by editor(s): September 11, 2003
Published electronically: May 10, 2004
Article copyright: © Copyright 2004 American Mathematical Society

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