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Applied Mathematics and Nonlinear Sciences

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Available online: December 12, 2017

Investigation of the effect of albedo and oblateness on the circular restricted four variable body problem

Abdullah A Ansari
Volume 2 - Issue 2.     Year 2017.     Pages 529–542.

DOI: 10.21042/AMNS.2017.2.00044


This paper presents the motion of the infi nitesimal body in the circular restricted four body problem in which the masses of the primaries as well as the mass of the infi nitesimal body vary and also one of the primaries is taken as source of radiation pressure due to which albedo effects are produced by another two primaries and one primary is considered as oblate body which is placed at the triangular equilibrium point of the classical restricted three body problem. We have evaluated the equations of motion of the in finitesimal variable mass under the effect of these perturbations and also the variation of Jacobi Integral constant has been determined. We have studied numerically the equilibrium points, Poincare surface of sections and basins of attraction in five cases $($i. Third primary is placed at one of the triangular equilibrium points of the classical restricted three body problem, ii. Variation of masses, iii. Solar radiation pressure, iv. Albedo effect, v. Oblateness effect.$)$ by using Mathematica software. Finally, we have examined the stability of the equilibrium points and found that all the equilibrium points are unstable.

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Applied Mathematics, Nonlinear Sciences


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