Effect of Stokes drag in the restricted four-body problem with variable mass

Abstract

The aim of this paper is to study the existence, locations and stability of the equilibrium points as well as zero velocity curves (ZVCs) under the effect of dissipative force (Stokes drag) in the restricted four-body problem (R4BP) with a variable mass. We have studied the dynamics of the infinitesimal body whose mass is variable and changing according to Jeans’ law. We have determined the equations of motion of the infinitesimal body by using the space time transformation of Meshcherskii when the change in mass is non-isotropic. We have determined the locations of equilibrium points in the special case of non-isotropic variation of mass under the effect of the dissipative force and found that all the equilibrium points are non-collinear. The effect of parameter k(0<k<1), which controls the dissipative force, on the locations of the libration points and their stability are investigated. It has been observed that the energy integral is time dependent due to the presence of the Stokes drag force. Further, it has been observed that all the equilibrium points are unstable for all values of the parameters used.