Effect of perturbations in the Coriolis and centrifugal forces in the Robe‐finite straight segment model with arbitrary density parameter

Abstract

The present article is a study of the effect of small perturbations ϵ and ϵ′ in the Coriolis and centrifugal forces, respectively, on the existence and stability of the equilibrium points in the Robe's restricted three‐body problem when the smaller primary is a finite straight segment. The effect of small perturbations in the centrifugal force has a substantial effect on the location of the equilibrium points, but a small perturbation in the Coriolis force has no impact on them. The present model has two collinear, two out‐of‐plane, and an infinite number of noncollinear equilibrium points. Furthermore, we have discussed the stability of the equilibrium points analytically. The collinear equilibrium points L1 and L2 are found to be conditionally stable for the parameters μ, k, l, ϵ, and ϵ′. It is perceived that, for any ϵ with ∣ϵ ∣ ≪ 1 and ϵ′ ≤ 0.2, L1 is stable, and for ϵ′ ≥ 0.23, it becomes unstable. Furthermore, for any ϵ with |ϵ| ≪ 1 and ϵ′ ≤ −0.025, L2 is stable, and for ϵ′ ≥ −0.024, it becomes unstable. The noncollinear and out‐of‐plane equilibrium points are always unstable.

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

“…They noticed the subsequent effect of the length parameter on the location and stability of the equilibrium points. In the continuation of their work, Kaur et al (2020) discussed the small perturbing effects of the Coriolis and centrifugal forces.…”