Exploring Effect of Perturbing Forces on Periodic Orbits in the Restricted Problem of Three Oblate Spheroids with Cluster of Material Points

This paper explores effect of perturbing forces on periodic orbits generated by the triangular equilibrium points of the restricted three-body problem taking into account small perturbations in the Coriolis and centrifugal forces when the infinitesimal mass is an oblate spheroid and the central binary is two radiating oblate stars surrounded by circular cluster of materials. We compute explicitly expressions for the frequency, angle of rotation of the principal axis, eccentricity and lengths of semi-major and minor axes of the orbits. Since some facts are not directly observable from the analytic solutions, numerical evidences are provided to analyze the structure and effect of each perturbing forces on the elements of the orbits. Among these, it is seen that the presence of cluster of materials reduces lengths of the semi-axes and is the only force that reduces the eccentricity while radiation pressure and oblateness of the primary star have same effect on the structure of the orbits. Our study has relevance in the long-term motion of planets in binary systems, where planets have masses infinitesimally small. A question of celestial mechanics is how long can the triangular equilibrium points keep the infinitesimal mass in orbit from escaping? The determination of ranges of semi-major axis taking into account the perturbing forces may help to know if body is likely to remain or escape. It is seen that under combined effect of radiation, perturbations, oblateness and cluster of materials, the period, angle of rotation, eccentricity and length of semi-major axis all increases. Consequently, the infinitesimal mass is likely to escape in this case. However, with increasing accumulation of materials, the departure of the infinitesimal mass in orbit away from the vicinity of triangular equilibrium points is unlikely as it will override other perturbing forces and reduce the length of the semi-major axis.