ఆస్ట్రోఫిజిక్స్ & ఏరోస్పేస్ టెక్నాలజీ

Combined Effects of Radiation and Oblateness on the Existence and Stability of Equilibrium Points in the Perturbed Restricted Four-Body Problem

Abstract

Singh J and Vincent AE

We study numerically the perturbed problem of four bodies, where an infinitesimal body is moving under the Newtonian gravitational attraction of three much bigger bodies (called the primaries). The three bodies are moving in circles around their centre of mass fixed at the origin of the coordinate system, according to the solution of Lagrange where they are always at the apices of an equilateral triangle. The fourth body does not affect the motion of the primaries. The problem is perturbed in the sense that the dominant primary body m1 is a radiation source while the second smaller primary m2 is an oblate spheroid, with masses of the two small primaries m2 and m3 taken to be equal. The aim of this study is to investigate the effects of radiation and oblateness parameters on the existence and location of equilibrium points and their linear stability. It is observed that under the perturbative effect of oblateness, collinear equilibrium points do not exist (numerically and of course analytically) whereas the positions of the noncollinear equilibrium points are affected by the radiation and oblateness parameters. The stability of each equilibrium points ( Li,i = 1,...,6) is examined and we found that points Li,i = 1,...,6 are unstable while L7 and L8 are stable.