OUT-OF-PLANE EQUILIBRIUM POINTS IN THE PHOTOGRAVITATIONAL COPENHAGEN RESTRICTED THREE-BODY PROBLEM

Abstract

This paper studies the motion of an infinitesimal body near the out of plane equilibrium points in the photogravitational restricted three-body problem in the case of two equally heavy primary bodies (Copenhagen Problem). These equilibria are determined numerically based on the three-dimensional dynamic equations. The influence of the radiation factors on the positions of these equilibria as well as the allowed regions of motion as determined by the zero velocity curves is studied in a parametric way. It is observed that their positions as well as the topology of the zero velocity curves are affected by the parameters. Finally, the stability of these points is studied, and it is found that there is a limited value of the radiation factors for which the equilibrium points are stable. This model has many applications, especially in the dynamic's behavior of extremely small objects such as dust grains and interplanetary drifters. It also has interesting applications for artificial satellites, future space colonization or even vehicles and spacecraft parking.