A Special Family of Stacked Central Configurations: Lagrange Plus Euler in One

Abstract

We show the existence of a family of stacked central configurations in the planar five-body problem with a special property. Three bodies $$m_1$$ , $$m_2$$ and $$m_3$$ , ordered from left to right, are collinear and form an Euler central configuration, and the other two bodies $$m_4$$ and $$m_5$$ , together with $$m_2$$ are at the vertices of an equilateral triangle and form a Lagrange central configuration.