On the photogravitational R4BP when the third primary is an oblate/prolate spheroid

Abstract

The present paper deals with the photogravitational restricted four-body problem, when the third primary placed at the triangular libration point of the restricted three-body problem is an oblate/prolate body. The third primary $m_{3}$ is not influencing the motion of the dominating primaries $m_{1}$ and $m_{2}$ . We have studied the motion of $m_{4}$ , moving under the influence of the three primaries $m_{i}, i=1,2,3$ , but the motion of the primaries is not being influenced by infinitesimal mass $m_{4}$ . The aim of this study is to find the locations of the libration points and their stability. We obtain three collinear and five non-collinear libration points when the third body is an oblate spheroid and source of radiation. The collinear libration points are unstable for all the mass parameter. The non-collinear libration points are stable for different mass parameters and oblateness factors. Further there exist 12 libration points, depending on the mass ratio of dominating primaries, the prolateness, and the radiation pressure of the third primary. We have drawn the zero velocity surface to determine the possible allowed boundary region. We observed that for increasing values of the oblateness coefficient $A$ , the corresponding possible boundary region increases where the particle can freely move from one side to another side. Further, for different values of the Jacobi constant $C$ , we can find the boundary region where the particle can move in the possible allowed partitions. The stability region of the libration points expanded due to the presence of the oblateness coefficient and various values of $C$ . We further apply these findings to the Sun–Jupiter–asteroid–spacecraft system.