Effect of perturbations in Coriolis and centrifugal forces on the equilibrium points in the photogravitational restricted four-body problem: Out-of-plane case

Abstract

The photogravitational restricted four-body problem including the effect of perturbations in Coriolis and centrifugal forces is employed to describe the motion of an infinitesimal particle near the out-of-plane equilibrium points in the vicinity of three finite radiating bodies. The three bodies (P1, P2, P3) are moving in circular orbits about their common centre of mass fixed at the origin of the coordinate system, according to the solution of Lagrange where they are always at the vertices of an equilateral triangle. The fourth body P4 of infinitesimal mass does not affect the motion of the three bodies. We consider that two of the bodies (P2 and P3) have the same radiation and mass value µ while the dominant primary body p1 is of mass 1-2µ. The equilibrium points (L1z, L2z) lying out of the orbital plane of the three bodies as well as the allowed regions of motion as determined by the zero velocity curves are studied numerically. It is observed that their positions as well as the allowed regions of motion while not affected by the small perturbation in the Coriolis force, are essentially varied under the joint effects of radiation pressure parameters and centrifugal force. Finally, the stability of these points is studied, and they are found to be unstable.