Periodic Solutions in the Planar (n+1) Ring Problem with Oblateness

In the N-body ring problem, the motion of an infinitesimal particle attracted by the gravitational field of (n + 1) bodies is studied. These bodies are arranged in a planar ring configuration. This configuration consists of n primaries of equal mass m located at the vertices of a regular polygon that is rotating on its own plane about its center of mass with a constant angular velocity w. Another primary of mass m0 = betam(beta0 parameter) is placed at the center of the ring. Moreover, we assume that the central body may be an ellipsoid, or a radiation source, which introduces a new parameter epsilon. In this case, the dynamics are found to be much richer than the classical problem due to the different equilibria and bifurcation characteristics. We find families of periodic orbits and make an analysis of the orbits by studying their evolution and stability along the family for several values of the new parameter introduced.