BIFURCATIONS FROM PLANAR TO THREE-DIMENSIONAL PERIODIC ORBITS IN THE RING PROBLEM OF N BODIES WITH RADIATING CENTRAL PRIMARY

Abstract

We consider the three-dimensional motion of a massless particle in a regular polygon formation of N primary bodies, one of which is located at the system's center of mass. Assuming that the central primary is a radiation source, we apply the simplified theory suggested by Radzievskii, in order to study the effect of radiation pressure in the three-dimensional dynamics of the system. We particularly study the evolution of the zero-velocity surfaces for various values of the radiation coefficient b0 and investigate also the cases with b0 > 1 (that is, radiation surpasses gravity) since for these cases, significant changes in the dynamics occur. We then locate numerically the onset of three-dimensional periodic motion from planar periodic motion by calculating the orbits' vertical critical stability. Many families of three-dimensional periodic motions are presented and the regions of the three-dimensional space where these motions take place, are determined. We subsequently investigate how the bifurcations from planar to three-dimensional periodic orbits are affected by the increase of the primary's radiation coefficient and how the overall dynamics of the system is affected by the value of the primaries' number N.