Finiteness of central configurations of five bodies in the plane


We prove there are finitely many isometry classes of planar central configurations (also called relative equilibria) in the Newtonian 5-body problem, except perhaps if the 5-tuple of positive masses belongs to a given codimension 2 subvariety of the mass space.


Alain Albouy

CNRS-UMR8028, Observatoire de Paris, 77, avenue Denfert-Rochereau, 75014 Paris, France

Vadim Kaloshin

Department of Mathematics, University of Maryland, College Park, MD 20742-4015