On the photogravitational R4BP when the third primary is a triaxial rigid body

Abstract

The present paper deals with the photogravitational restricted four-body problem, when the third primary is placed at the triangular libration point of the restricted three-body problem is a triaxial rigid 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 discuss their stability. We have obtained six non-collinear equilibrium points near the third body when the third body is a triaxial rigid body and a source of radiation. There exist at most ten non-collinear equilibrium points in total for this problem. However, the number of equilibrium points depends on the triaxiality parameters. Further, we have drawn the zero velocity surfaces to determine the possible allowed boundary regions. The stability of non-collinear equilibrium points for different mass parameters, radiation parameters and triaxiality of the third body is also studied. The stability regions of the equilibrium points were expanded due to the triaxiality of the third body and various values of the radiation parameter \(q\).