Stability and Zero Velocity Curves in the Perturbed Restricted Problem of 2

The present study investigates the existence and linear stability of the equilibrium points in the restricted problem of 2+2 bodies including the effect of small perturbations 61 and 62 in the Coriolis and centrifugal forces respectively. The less massive primary is considered as a straight segment and the more massive primary a point mass. The equations of motion of the infinitesimal bodies are derived. We obtain fourteen equilibrium points of the model, out of which six are collinear and rest non-collinear with the centers of the primaries. The position of the equilibrium points are affected by the small perturbation in centrifugal force, length and mass parameters, but there is no impact of small perturbation in Coriolis force on them. In addition, the obtained results are applied to Earth-22 Kalliope-dual satellite system. For this system, we calculate collinear and non-collinear equilibrium points and observed that the number of non-collinear equilibrium points depends on 62. Furthermore, for a set of values of the parameters 61 and 62, we have checked the stability of all the equilibrium points and concluded that all the equilibrium points are found to be unstable. The permissible regions of motion for the Earth-22 Kalliope-dual satellite system are also studied.