The analysis of the photogravitational R4BP under the combined effect of Stokes drag and oblateness within a frame of variable mass

In this paper, we have studied the existence, locations and stability of the equilibrium points as well as zero velocity curves (ZVCs) under the combined effect of oblateness, radiation pressure and the dissipative force (Stokes drag) in the restricted four-body problem (R4BP) with variable mass when the bigger primary (m 1) is a source of radiation and second primary (m 2) is an oblate or prolate spheroid. An equilateral triangle has been constructed by the three primaries and known as Lagrangian configuration. Jeans’ law and space time transformations of Meshcherskii have been used to derive the equations of motion of the infinitesimal body whose mass is varying. The dynamical behaviour of an infinitesimal body has been investigated under the influences of radiation pressure of bigger primary and oblateness of second primary with Stokes drag. The numerical investigation shows that all the equilibrium points are non-collinear and the collinear equilibrium points do not exist due to the presence of Stokes drag. The effect of parameters like oblateness A, radiation parameter q (0 < q < 1), α (0 < α ≤ 2.2), γ (0 < γ < 1) and dissipative constant k (0 < k < 1) have been investigated on the locations of equilibrium points and their stability. It is found that the regions of motion increase for the increasing values of the parameters A, q and α whereas these regions decrease for the increasing values of the dissipative constant k. We have also observed that all the equilibrium points are unstable for all values of the parameters used.