Out-of-Plane Equilibrium Points in the Photogravitational Hill Three-Body Problem

Abstract

This paper investigates the movement of a negligible mass body (third body) in the vicinity of the out-of-plane equilibrium points of the Hill three-body problem under the effect of radiation pressure of the primaries. We study the effect of the radiation parameters through the factors qi,i=1,2 on the existence, position, zero-velocity curves and stability of the out-of-plane equilibrium points. These equilibrium positions are derived analytically under the action of radiation pressure exerted by the radiating primary bodies. We determined that these points emerge in symmetrical pairs, and based on the values of the radiation parameters, there may be two along the Oz axis and either none or two on the Oxz plane (outside the axes). A thorough numerical investigation found that both radiation factors have a strong influence on the position of the out-of-plane equilibrium points. Our results also reveal that the parameters have impact on the geometry of the zero-velocity curves. Furthermore, the stability of these points is examined in the linear sense. To do so, the spatial distribution of the eigenvalues on the complex plane of the linearized system is visualized for a wide range of radiation parameter combinations. By a numerical investigation, it is found that all equilibrium points are unstable in general.

Keywords

• hill problem
• restricted three-body problem
• radiating primaries
• out-of-plane equilibrium points
• zero-velocity curves
• linear stability