A family of stacked central configurations in the planar five-body problem - Cornelio, J. Lino; Álvarez–Ramírez, M.; Cors, Josep M. (Celestial mechanics and dynamical astronomy, 2017)
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 4 m 5 and m 1 m 3 do not intersect.