article published yes Alain Albouy author Vadim Kaloshin author FE553552-CDE8-11E9-B324-C0EBE56974250000-0002-6051-2628 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. Princeton University Press2012 eng 0003-486X10.4007/annals.2012.176.1.10 1761535-588 yes A. Albouy and V. Kaloshin, “Finiteness of central configurations of five bodies in the plane,” <i>Annals of Mathematics</i>, vol. 176, no. 1. Princeton University Press, pp. 535–588, 2012. Albouy, A., &#38; Kaloshin, V. (2012). Finiteness of central configurations of five bodies in the plane. <i>Annals of Mathematics</i>. Princeton University Press. <a href="https://doi.org/10.4007/annals.2012.176.1.10">https://doi.org/10.4007/annals.2012.176.1.10</a> Albouy A, Kaloshin V. Finiteness of central configurations of five bodies in the plane. <i>Annals of Mathematics</i>. 2012;176(1):535-588. doi:<a href="https://doi.org/10.4007/annals.2012.176.1.10">10.4007/annals.2012.176.1.10</a> Albouy, Alain, and Vadim Kaloshin. “Finiteness of Central Configurations of Five Bodies in the Plane.” <i>Annals of Mathematics</i>, vol. 176, no. 1, Princeton University Press, 2012, pp. 535–88, doi:<a href="https://doi.org/10.4007/annals.2012.176.1.10">10.4007/annals.2012.176.1.10</a>. A. Albouy, V. Kaloshin, Annals of Mathematics 176 (2012) 535–588. Albouy, Alain, and Vadim Kaloshin. “Finiteness of Central Configurations of Five Bodies in the Plane.” <i>Annals of Mathematics</i>. Princeton University Press, 2012. <a href="https://doi.org/10.4007/annals.2012.176.1.10">https://doi.org/10.4007/annals.2012.176.1.10</a>. Albouy A, Kaloshin V. 2012. Finiteness of central configurations of five bodies in the plane. Annals of Mathematics. 176(1), 535–588. 85032020-09-18T10:47:24Z2021-01-12T08:19:44Z