Abstract
In studying the effects of radiation and oblateness of the primaries on the stability of collinear equilibrium points in the Robes restricted three-body problem we observed the variations of the density parameter k with the mass parameter μ for constant radiation and oblateness factors on the location and stability of the collin-ear points L1, L2and L3. It is also discovered that the collinear points are unstable for k > 0 and stable for k < 0.
Highlights
The classical Restricted Three-Body problem has been generalized in various forms ([1,11,13,12,5,6,7,10,14]) by incorporating perturbing parameters such as perturbations in Coriolis and centrifugal forces, radiation pressure forces, oblateness of the primaries, drag effects and so on.Robe [9] introduced a new kind of restricted three-body problem that incorporates the effect of buoyancy force
In studying the effects of radiation and oblateness of the primaries on the stability of collinear equilibrium points in the Robes restricted three-body problem we observed the variations of the density parameter k with the mass parameter μ for constant radiation and oblateness factors on the location and stability of the collinear points L1, L2 and L3
It is evident from Equations (9), (10) and (11) that the three physical parameters affect the location of collinear points
Summary
The classical Restricted Three-Body problem has been generalized in various forms ([1,11,13,12,5,6,7,10,14]) by incorporating perturbing parameters such as perturbations in Coriolis and centrifugal forces, radiation pressure forces, oblateness of the primaries, drag effects and so on. Shrivastava and Garain [12] studied the effect of small perturbations in the Coriolis and centrifugal forces on the location of equilibrium points in the Robes problem. Hallan and Rana [4] studied the effect of oblateness on the location and stability of equilibrium points in the Robes circular problem when the primary other than the elliptical shell is oblate spheroid and proved that the center of the first primary is always an equilibrium point for all values of the density parameter k and the mass parameter μ. We consider a rigid shell which is oblate spheroid and the second primary radiating to study the stability of collinear equilibrium points in Robes restricted three-body problem while observing the variation of the location of the collinear points with the density parameter k and the mass parameter μ
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