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Abstract

Associating the influences of viscosity and oblateness in the finite straight segment model of the Robe’s problem, the linear stability of the collinear and non-collinear equilibrium points for a small solid sphere m3 of density \rho3 are analyzed. This small solid sphere is moving inside the first primary m1 whose hydrostatic equilibrium figure is an oblate spheroid and it consists of an incompressible homogeneous fluid of density \rho1. The second primary m2 is a finite straight segment of length 2l. The existence of the equilibrium points is discussed after deriving the pertinent equations of motion of the small solid sphere. It is found that viscosity does not affect the location and number of equilibrium points but affects the stability as it converts the marginal stability to asymptotic stability. However, oblateness affects the locations of the equilibrium points. Applicability of the results of this study to an astrophysical problem is discussed and we have calculated a lower bound on ratio of orbital radius R and total mass M of primaries m1 and m2 of an astrophysical problem to which the results obtained may be applied. This ratio denoted by s is called as scaling factor.

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