Finiteness of relative equilibria of the four-body problem

Marshall Hampton, Richard Moeckel

Research output: Contribution to journalArticlepeer-review

163 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)289-312
Number of pages24
JournalInventiones Mathematicae
Issue number2
StatePublished - Feb 2006


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