A family of stacked central configurations in the planar five-body problem

Abstract

We study planar central configurations of the five-body problem where three bodies, $$m_1, m_2$$ and $$m_3$$ , are collinear and ordered from left to right, while the other two, $$m_4$$ and $$m_5$$ , are placed symmetrically with respect to the line containing the three collinear bodies. We prove that when the collinear bodies form an Euler central configuration of the three-body problem with $$m_1=m_3$$ , there exists a new family, missed by Gidea and Llibre (Celest Mech Dyn Astron 106:89–107, 2010), of stacked five-body central configuration where the segments $$m_4m_5$$ and $$m_1m_3$$ do not intersect.