Combined effects of radiation and oblateness on the existence and stability of equilibrium points in the perturbed restricted four-body problem

Abstract

We study numerically the perturbed problem of four bodies, where an infinitesimal body is moving under the gravitational attraction of three primary bodies which move on circular orbits around their common centre of gravity, such that their configuration is always an equilateral triangle. The problem is perturbed in the sense that the dominant primary body m1 is a radiation source while the second primary m2 is an oblate spheroid, with masses of the two small primaries m2 and m3 taken to be equal. We investigate the effects of radiation and oblateness parameters on the existence and location of equilibrium points and their linear stability. The zero-velocity surfaces are also given. It is observed that under the perturbative effect of oblateness, collinear equilibrium points do not exist whereas the positions of the non-collinear equilibrium points are affected by the parameters. The stability of each points (Li, i = 1,, 8) is also studied.