Restricted $2 + 2$ body problem with oblateness and straight segment

Abstract

The present study investigates the combined effects of the oblateness and straight segment on the positions and linear stability of the equilibrium points in the restricted $2+2$ body problem. The present model holds fourteen equilibrium points, out of which six are collinear with the centers of the primaries and the rest are non-collinear. It has been observed that the positions of all the equilibrium points are subsequently affected by the oblateness and length of the primary bodies. The linear stability of the equilibrium points is also presented by slightly perturbing the position of the equilibrium points. It is observed that for a considered set of parameters, all the fourteen equilibrium points are unstable. An application of the present model is also studied, for which the position and stability of the equilibrium points are investigated for the Earth-22 Kalliope-dual satellite system. It has been observed that for this system, all the equilibrium points are unstable except for two non-collinear equilibrium points that are found to be stable.