An insight on the restricted problem of 2 + 2 bodies with straight segment

Abstract

In the present paper, an effort to generalize the restricted problem of 2 + 2 bodies has been made by considering the primary bodies m1 and m2 to be a point mass and straight segment of length 2l, respectively. The motion of the two infinitesimal bodies mi, i = 3, 4 has been investigated, in which each mi, i = 3, 4 is moving in the gravitational field of mj, j = 1, 2, 3, 4 with i ≠ j. For the present problem, 14 equilibrium points are obtained, of which 6 are collinear and the rest are noncollinear. The length parameter l has a subsequent effect on the location of all the equilibrium points. Systematic stability analysis has been carried out by using the theory of perturbation. All the equilibrium points are found to be unstable.

Effect of the Planetesimal Belt on the Dynamics of the Restricted Problem of 2 + 2 Bodies

“…According to the formulation of the restricted 2 + 2 body problem given by [5,21,22], R2 + 2BP is characterized by three parameters, µ, µ 1 and µ 2 , which are the mass parameters of M 2 , P 1 , and P 2 , respectively. We consider a perturbed R2+2BP in the rotating coordinate system.…”