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Abstract

In this paper, the effect of viscous force on the linear stability of equilibrium points of the circular Robe’s restricted three-body problem (CRR3BP) with smaller primary as a finite straight segment is studied. The present model comprises of a bigger primary m*1 which is a rigid spherical shell filled with a homogeneous incompressible fluid of density ρ1 and the smaller primary m2 lies outside the shell. The infinitesimal mass m3 is a small solid sphere of density ρ3 moving inside m*1. The pertinent equations of motion of m3 are derived and solved for the equilibrium points. Routh-Hurwitz criterion is used to detect the stability of the obtained equilibrium points. The stability of the collinear equilibrium points has been studied systematically in the different regions for the various values of the parameters involved. These points are found to be conditionally stable, whereas the non-collinear and out-of-plane equilibrium points are always unstable for all the values of the parameters. We observed that viscosity has no effect on the location of equilibrium points. However, its effect along with the length parameter l is evident on the stability of equilibrium points.

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