The Broucke-Hénon orbit and the Schubart orbit in the planar three-body problem with two equal masses

In this paper, we study the variational properties of two special orbits: a Schubart orbit and a Broucke-Hénon orbit. We show that under an appropriate topological constraint, a minimizer must be either a Schubart orbit or a Broucke-Hénon orbit. One of the main challenges is to prove that a Schubart orbit coincides with a minimizer connecting a collinear configuration with a binary collision and an isosceles configuration. A new geometric argument is introduced to overcome this challenge.