Inventiones mathematicae

, Volume 163, Issue 2, pp 289–312 | Cite as

Finiteness of relative equilibria of the four-body problem

  • Marshall Hampton
  • Richard Moeckel


We show that the number of relative equilibria of the Newtonian four-body problem is finite, up to symmetry. In fact, we show that this number is always between 32 and 8472. The proof is based on symbolic and exact integer computations which are carried out by computer.


Relative Equilibrium Integer Computation Exact Integer 
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Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA

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