A Comparative study on generalized Manev potential and Newtonian potential in perturbed restricted four-body problem

The motion of a test particle within the context of the restricted four-body problem(R4BP) driven by a new kind of potential, called the generalized Manev potential, with perturbations in the Coriolis and centrifugal forces is considered in this study. The system possesses eight libration points which were distributed on its plane of motion in different manner from those of the usual Newtonian potential. Unlike the case of the perturbed R4BP under Newtonian potential, where two of these librations are stable, all of them are unstable in linear sense under Manev potential. We found that a gradual perturbation in the centrifugal force causes the trajectories of motion to drift inward but the Coriolis force was proven to have no effect on the location of the libration points of the system. Using first order Lyapunov characteristic exponents, the dynamical behavior of the system is found irregular. We experimented with a high velocity stellar system (82 G. Eridani) to establish the applicability of the model in astrophysics.