Effect of Oblateness of the Secondary up to J4 on L4,5 in the Photogravitaional ER3BP

In a synodic-pulsating dimensionless coordinate, with a luminous primary and an oblate secondary, we examine the effects of radiation pressure, oblateness (quadruple and octupolar i.e. ) and eccentricity of the orbits of the primaries on the triangular points in the ER3BP. have been shown to disturb the motion of an infinitesimal body and particularly has significant effects on a satellite’s secular perturbation and orbital precessions. The influence of these parameters on the triangular points of Zeta Cygni, 54 Piscium and Procyon A/B are highlighted in this study. Triangular points are stable in the range and their stability is affected by said parameters.

On the Stability ofL4,5in the Relativistic R3BP with Oblate Secondary and Radiating Primary

We consider a version of the relativistic restricted three-body problem (R3BP) which includes the effects of oblateness of the secondary and radiation of the primary. We determine the positions and analyze the stability of the triangular points. We find that these positions are affected by relativistic, oblateness, and radiation factors. It is also seen that both oblateness of the secondary and radiation of the primary reduce the size of stability region. Further, a numerical exploration computing the positions of the triangular points and the critical mass ratio of some binaries systems consisting of the Sun and its planets is given in the tables.