Existence and Stability of Equilibrium Points Under the Influence of Poynting–Robertson and Stokes Drags in the Restricted Three-Body Problem

Abstract

In the framework of the circular restricted three-body problem, the dynamical effects of Stokes and Poynting–Robertson (P–R) drag forces on the existence, location, and stability of equilibrium points are investigated. It is found that under constant effects of P–R and/or Stokes drags, collinear equilibrium points cease to exist, but there are in the absence of the perturbing forces. The problem admits five non-collinear equilibrium points, and it is seen that the perturbing forces have significant effects on their positions. The linear stability of the equilibrium points is also studied in certain cases, and it is found that the stability of some of these points significantly depends on the perturbing forces. More precisely, the motion of the infinitesimal body near the non-collinear equilibrium points is unstable under the effect of both kinds of perturbing forces except from the equilibria L4 and L5 for which is stable only for Stokes drag effect, namely, the remaining parameter that corresponds to P–R drag is fixed to zero. We may conclude, therefore, that the P–R effect destroys stability of the equilibrium points.