On the Stability of the Triangular Equilibrium Points in the Photogravitational R3BP with an Oblate Infinitesimal and Triaxial Primaries for the Binary Lalande 21258 System

Abstract

In the framework of the planar circular restricted three-body problem (R3BP), we explore the effects of oblateness of the infinitesimal mass body as well as radiation pressure and triaxiality of the two primaries on the position and stability of the triangular equilibrium points (TEPs). It is found that all the involved parameters affect the positions and stability of these points. Specifically, it has been shown that TEPs are stable for 0 < μ < μc and unstable for μc ≤ μ ≤ 1/2, where μc denotes the critical mass parameter which depends on system’s parameters. In addition, all the parameters of the bigger primary, except that of triaxiality, have destabilizing tendencies resulting in a decrease in the size of the region of stability. Finally, we justify the relevance of the model in astronomy by applying it to the binary Lalande 21258 system for which the equilibrium points have been seen to be unstable.