Stability of Triangular Equilibrium Points in BiER4BP under the Radiation and Oblateness Effect of Primaries Applied for Sun–Earth–Moon System

Abstract

The frame work of this study is the bi-elliptic restricted four body problem, where the largest primary \({{m}_{1}}\) is assumed to be a radiating body and the other two massive bodies \({{m}_{2}}\) and \({{m}_{3}}\) are assumed to be oblate spheroids. The problem is restricted in the sense that the fourth body is assumed to be of infinitesimal mass. The goal of the paper is to study the so-called equilibrium points by generalizing R3BP to a non-coherent but highly practical R4BP model. The location of the planar equilibrium points according to this model is numerically studied for Sun–Earth–Moon system. The position of the triangular equilibrium points are also obtained analytically and graphically compared with numerically obtained values. Both the graphical and analytical studies confirms the high dependence of the position of the triangular equilibrium points on radiation pressure, however the collinear points were found to be less affected. The collinear points were found to be more affected by the oblateness of the second primary. The triangular equilibrium points were found to be stable for the third and fourth order resonance cases when the mass ratio is less than equal to a critical mass ratio. This critical mass ratio is also found to be dependent on the radiation pressure and phase angle \({{\theta }_{0}}\). The transition curve in the (\(\mu - {{\epsilon }_{2}}\)) plane is plotted to find the value of \({{\epsilon }_{2}}\) for which the motion near triangular equilibrium points become unstable.