Nested regular polygon solutions of the 2N-body problem with a central mass

Abstract

We consider an extension to the 2N-body problem where the masses are configured in the geometry of nested regular polygons. A solution exists when all N bodies in each layer of the nested polygons are of equal mass, and consists of all the bodies revolving about the center of the system with a constant angular velocity. In this work, we examine the case when a body is placed at the center of the system, and obtain a new expression for the required angular velocity of the resulting solutions in terms of the mass parameters.