Inventiones mathematicae

, Volume 163, Issue 2, pp 289–312

Finiteness of relative equilibria of the four-body problem


DOI: 10.1007/s00222-005-0461-0

Cite this article as:
Hampton, M. & Moeckel, R. Invent. math. (2006) 163: 289. doi:10.1007/s00222-005-0461-0


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.

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© Springer-Verlag 2005

Authors and Affiliations

  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA