Shooting for the Eight

A Topological Existence Proof for a Figure-Eight Orbit of the Three-Body Problem
  • Richard MoeckelEmail author
Part of the Abel Symposia book series (ABEL, volume 5)


A topological existence proof is given for a figure-eight periodic solution of the equal mass three-body problem. The proof is based on the construction of a Wazewski set W in the phase space. The figure-eight solution is then found by a kind of shooting argument in which symmetrical initial conditions entering W are followed under the flow until they exit W. A linking argument shows that the image of the symmetrical entrance states under this flow map must intersect an appropriate set of symmetrical exit states.


Celestial mechanics three-body problem symmetrical periodic solutions topological methods 


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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA

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