Effects of viscosity and oblateness on the perturbed Robe’s problem with non-spherical primaries

Heading: 
Dynamics and Physics of Solar System Bodies
Kaur, B, Kumar, S, Aggarwal, R
Kinemat. fiz. nebesnyh tel (Online) 2022, 38(5):31-50
https://doi.org/10.15407/kfnt2022.05.031
Start Page: Dynamics and Physics of Solar System Bodies
Language: Ukrainian
Abstract: 

We here analyzed the effects of viscosity, oblateness of the primary m1, length parameter l, and perturbations in the Coriolis and centrifugal forces on the stability of the equilibrium points of the Robe’s problem. In the setting, it is assumed that the two primaries m1, an oblate spheroid of incompressible homogeneous viscous fluid of density ρ1 and m2, a finite straight segment of length 2l revolve around their common center of mass in circular orbits while third body m3 (a small solid sphere of density ρ3) moves inside m1. Two collinear {L1, L2} and infinite non-collinear equilibrium points are evaluated and found that the location of equilibrium points remain unaffected by viscosity. However, the effects of oblateness and perturbation in the centrifugal force are quite noticeable from the expressions of the equilibrium points. The stability criterion for L1 and are stated whereas the non-collinear equilibrium points are found to be unstable. It is observed that the viscosity has a substantial effect on the stability as it changes the nature of stability from marginal stability to asymptotic stability. The perturbations do not affect the stability of L1 but affect the stability of L2. Moreover, the effect of oblateness on the stability of the equilibrium points is quite evident. A very important observation of the study is that the oblateness parameter A neutralizes the effects of the length parameter l and perturbation ε2, on the stability of equilibrium point L1. The results obtained are applied on Earth-Moon, Jupiter-Amalthea, Jupiter-Ganymede systems (astrophysical problems) to predict the stability of L1.
Keywords: coriolis and centrifugal forces, finite straight segment, oblate spheroid, Robe’s restricted three-body problem, Viscosity

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