A Planar Case of the n + 1 Body Problem: the 'Ring’ Problem

Abstract

Our intention in this article is to present a new model for the investigation of the motion of a particle of negligible mass in a multibody surrounding. The proposed general planar configuration consists of ν = n-1 primaries arranged in equal arcs on an ideal ring and a central body of different mass located at the centre of mass of the system. We formulate the general equations of motion and we study the stationary solutions and the zero-velocity contours for various values of ν.