On the stability of homographic solutions in the restricted 8-body problem

We are concerned with existence and stability of homographic solutions in the restricted 8-body problem with partial symmetries. Six bodies make two regular triangles with distinct radii, the seventh’s body is located in the center. We are looking for the relative equilibrium and for stability conditions of the 8th body, which has infinitesimally small mass, and which is moving under the gravitational field, generated by seven bodies. The main tools we make use of are the Arnold-Moser and Markeev stability theorems.