On the R4BP when third primary is an oblate spheroid

Abstract

The present paper deals with the restricted four-body problem, when the third primary placed at the triangular libration point of the restricted three-body problem is an oblate 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 equilibrium points and their stability. We obtain three collinear and five non-collinear equilibrium points. The collinear equilibrium points are unstable for all the mass parameter. The non-collinear points are stable for different mass parameter and oblateness factor. Also, we have considered the autonomous coplanar circular restricted four-body problem with the infinitesimal mass as a low-thrust spacecraft. Artificial equilibrium points are created with the use of continuous low-thrust propulsion. The obtained results show that, in absence of thrust there are unstable equilibrium points close to the third primary. Also, using the constant low-thrust, the artificial equilibrium points can be generated, which move from the natural equilibrium points. Further, it is proved that in certain region closed to the third primary, these points are stable. We have drawn the zero velocity surfaces to determine the possible allowed boundary regions. We observed that for increasing values of oblateness coefficient A, the corresponding possible boundary regions increase where the particle can freely move from one side to another side. Further, for different values of Jacobi constant C, we can find the boundary region where the particle can move in possible allowed partitions. The stability regions of the equilibrium points expanded due to presence of oblateness coefficient and various values of C.