Motion Around the Equilibrium Points in the Photogravitational R3BP under the Effects of Poynting–Robertson Drag, Circumbinary Belt and Triaxial Primaries with an Oblate Infinitesimal Body: Application on Achird Binary System

Abstract

In the present work, we study the motion of an oblate infinitesimal mass body near the equilibrium points (EPs) of the circular restricted three-body problem (R3BP) in which the radiation pressure, Poynting–Robertson (P–R) drag effect, and triaxiality of the two primary bodies are considered in the case where both of them are enclosed by a belt of homogeneous circular cluster of material points centered at the mass center of the system. We have found numerically that five or seven EPs may lie on the plane of motion depending on the values of the parameters of the system and have examined their stability character, too. In particular, the numerical exploration is performed using the binary system Achird to compute the positions of the equilibria and the eigenvalues of the characteristic equation. It is observed that the existence, location and number of equilibria of the problem depend on the values of the parameters of the problem. We have found both numerically and analytically that under constant P–R drag effect, collinear equilibrium solutions cease to exist. The linear stability of each equilibrium point is also studied and it is found that in the case where seven equilibria exist, the new point LN2 is always linearly stable while the other six are always linearly unstable. In the case where five equilibria exist, all of them are always linearly unstable due to P–R drag effect.