Out-of-plane equilibrium points in the photogravitational restricted four-body problem

Abstract

The photogravitational restricted four-body problem is employed to describe the motion of an infinitesimal particle in the vicinity of three finite radiating bodies. The fourth body $P_{4}$ of infinitesimal mass does not affect the motion of the three bodies ($P_{1}, P_{2}, P_{3}$) that are always at the vertices of an equilateral triangle. We consider that two of the bodies ($P_{2}$ and $P_{3}$) have the same radiation and mass value $\mu$ while the dominant primary body $P_{1}$ is of mass $1 - 2\mu$. The equilibrium points ($L_{1}^{z},L_{2}^{z}$) lying out of the orbital plane of the primaries as well as the allowed regions of motion as determined by the zero velocity curves are studied numerically. Finally the stability of these points is studied and they are found to be unstable.