Applied Mathematics and Nonlinear Sciences
Journal license

Journal

Applied Mathematics and Nonlinear Sciences


Volume
& Issue

Volume 2, Issue 2


Published
on

December 12, 2017


Pages

529-542


DOI

Article

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

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Authors

Abdullah A. Ansari Affiliation:
Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al Majma'ah 11932 Kingdom of Saudi Arabia


Abstract

The present paper investigates the motion of the variable infinitesimal body in circular restricted four variable bodies problem. We have constructed the equations of motion of the infinitesimal variable mass under the effect of source of radiation pressure due to which albedo effects are produced by another two primaries and one primary is considered as an oblate body which is placed at the triangular equilibrium point of the classical restricted three-body problem and also the variation of Jacobi Integral constant has been determined. We have studied numerically the equilibrium points, Poincaré 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.


Keywords

Albedo, Oblate body, Triangular equilibrium points, Stationary Points, Poincaré surface of sections, Basins of Attraction, 70F15, 85A20, 70F05


Citation

Ansari, A. A. (2017). Investigation of the effect of albedo and oblateness on the circular restricted four variable bodies problem. Applied Mathematics and Nonlinear Sciences, 2(2), 529–542. https://doi.org/10.21042/AMNS.2017.2.00044

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