Out-of-Plane Equilibrium Points in the Restricted Three-Body Problem with Radiation Pressure, Poynting–Robertson Drag and Angular Velocity Variation

Abstract

This chapter deals with the motion of an infinitesimal body near the out-of-plane equilibrium points in the restricted problem of three bodies under the radial component of Poynting– Robertson (P–R) drag and radiation pressure of the primaries as well as their angular velocity. In particular, the out-of-plane equilibria are first determined analytically and it is found that their existence and positions depend on the perturbing forces involved in the equations of motion. Due to the symmetry of the problem, these points appear in pairs and, depending on the parameter values, their number may be zero, two (L6,7) or four (L6,7 and L8,9). Finally, the effects of the parameters are shown on the positions of the out-of-plane equilibrium points for the binary systems Kruger-60 and Achird. An investigation of the stability of the out-of-plane equilibrium points shows that they are unstable for both binary systems.