Divulging the effect of small perturbations in the Coriolis and centrifugal forces in the photogravitational version of autonomous restricted four‐body problem with oblate primary

Abstract

In the present problem, we have studied the effect of small perturbations in the Coriolis and centrifugal forces on the locations and stability of libration points by taking the smaller primary as radiating oblate spheroid in the restricted four‐body problem. We have supposed that all the primaries are set in an equilateral triangle configuration, moving in circular orbit around their common center of mass. We have observed that the oblateness and radiation of the third primary, and the effect of the small perturbation in centrifugal force have substantial influences on the locations of libration points but the effect of the small perturbation in the Coriolis force has no impact on their locations. However, the stability of the libration points is highly influenced by the effect of the small perturbation in the Coriolis force. Furthermore, it is obtained that the effect of the small perturbation in the centrifugal force has a substantial influence on the regions of possible motion. In addition, we have also discussed how the oblateness and radiation pressure of the third primary, and the small perturbations in the Coriolis and centrifugal forces influence geometry of the basins of convergence by using multivariate version of the Newton–Raphson iterative scheme.