In this paper, the effect of small perturbations in the Coriolis and centrifugal forces on the existence and stability of the equilibrium point in the Robe’s restricted three-body problem (RR3BP) by taking the smaller primary as a finite straight segment is introduced. In the present structure the density rho1 of the fluid filled in the bigger primary of mass m1*and the density rho3 of the infinitesimal body of mass m3 are considered to be equal. It is worth mentioning that the location of the equilibrium point is affected by a small perturbation in the centrifugal force. The present model possesses one equilibrium point L1 which is collinear with the center of mass of the primaries. It lies towards the right or left of the center of the shell according as the perturbation pi2 in the centrifugal force is positive or negative. Further, the stability of L1 is analyzed. The range of stability is affected not only by the perturbations in the Coriolis and centrifugal forces but also by the length of the finite straight segment. For 0 < mu less than or equal to mu*, L1 is unstable whereas for mu* < mu < 1 it becomes stable. It is observed that the Coriolis force is a stabilizing force provided the centrifugal force is kept constant while the centrifugal force is a destabilizing force when the Coriolis force is kept constant.
Kaur, Bhavneet; Kumar, Dinesh; and Chauhan, Shipra
A Study of Small Perturbations in the Coriolis and Centrifugal Forces in RR3BP with Finite Straight Segment,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 15,
1, Article 6.
Available at: https://digitalcommons.pvamu.edu/aam/vol15/iss1/6