EQUILIBRIUM POINTS IN THE CR3BP OF THREE OBLATE BODIES UNDER THE EFFECTS OF CIRCUMBINARY DISC AND RADIATING PRIMARIES WITH POYNTING-ROBERTSON DRAG

Abstract

We study numerically the generalized planar photogravitational circular restricted three-body problem, where an infinitesimal body is moving under the Newtonian gravitational attraction of two bodies which are finite, moving in circles around their center of mass fixed at the origin of the coordinate system, where both bodies are situated on the horizontal 𝑥-axis. The third body 𝑚 is significantly smaller compared to the masses of the two bodies (primaries) where its influence on them can be neglected. The three participating bodies are modeled as oblate spheroids, under effect of radiation of the two main masses together with effective Poynting-Robertson drag and both of them are enclosed by a belt of homogeneous circular cluster of material points. In this paper, the existence and location of the equilibrium points and their linear stability are explored for various combinations of the model’s parameters. We observe that under constant P–R drag effect, collinear equilibrium solutions cease to exist but there are in the absence of the drag forces. We found that five or seven non-collinear equilibrium points may lie on the plane of primaries motion depends on the particular values of model’s parameters, and it is seen that the perturbing forces have significant effects on their positions and linear stability. In our model, the binary system Kruger 60 is used, and it is found that the positions of the equilibria and their stability are affected by these perturbing forces. In the case where seven critical points exist, all the equilibria are unstable except the equilibrium point (𝐿𝑛2) which is always linearly stable while in the case where five critical points exist, all the points are unstable due to the presence of P–R drag effect.