Unveiling Perturbing Effects of PR Drag on Motion around Triangular Lagrangian Points of the Photogravitational Restricted Problem of Three Oblate Bodies
Current Journal of Applied Science and Technology,
Page 1031
DOI:
10.9734/cjast/2021/v40i131201
Abstract
The perturbing effects of the PoyntingRobertson drag on motion of an infinitesimal mass around triangular Lagrangian points of the circular restricted threebody problem under small perturbations in the Coriolis and centrifugal forces when the three bodies are oblate spheroids and the primaries are emitters of radiation pressure, is the focus of this paper. The equations governing the dynamical system have been derived and locations of triangular Lagrangian points are determined. It is seen that the locations are influenced by the perturbing forces of centrifugal perturbation and the oblateness, radiation pressure and, PR drag of the primaries. Using the software Mathematica, numerical analysis are carried out to demonstrate how the dynamical elements: mass ratio, oblateness, radiation pressure, PR drag and centrifugal perturbation influence the positions of triangular equilibrium points, zero velocity surfaces and the stability. Our investigation reveals that, though the radiation pressure, oblateness and centrifugal perturbation decrease region of stability when motion is stable, however, they are not the influential forces of instability but the PR drag. In the region when motion around the triangular points are stable an inclusion of the PR drag of the bigger primary even by an almost negligible value of 1.04548*10^{9 }overrides other effect and changes stability to instability. Hence, we conclude that the PR drag is a strong perturbing force which changes stability to instability and motion around triangular Lagrangian points remain unstable in the presence of the PR drag.
Keywords:
 Restricted threebody problem
 triangular lagrangian points
 radiation pressure
 oblateness
 PR drag
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References
Szebehely VG. Theory of orbits. Yale University, New Haven, Connecticut, Academic Press, NewYork and London, The Restricted Problem of Three Bodies; 1967.
Sharma RK, Subba Rao PV. Stationary solutions and their characteristic exponents in the restricted threebody problem when the more massive primary is an oblate spheroid. Celestial. Mechanics. 1976;13:137.
Singh J, Ishwar B. Stability of triangular points in the generalized photogravitational restricted threebody problem. Bulletin of the Astronomical Society of India. 1999;27:415.
Khanna M, Bhatnagar KB. Existence and stability of libration points in the restricted threebody problem when the smaller primary is a triaxial rigid body and the bigger one an oblate spheroid. International Journal of Pure and Applied. Mathematics. 1999;30;721.
AbdulRaheem A, Singh J. Combined effects of perturbations, radiation, and oblateness on the stability of equilibrium points in the restricted threebody problem. The Astronomical Journal. 2006;131:1880.
Singh J, Leke O. Stability of the photogravitational restricted threebody problem with variable masses. Astrophysics and Space Science. 2010;326:305.
Singh J, Leke O, Aishetu U. Analysis of the stability of triangular points in the perturbed photogravitational restricted threebody problem with variable masses. Astrophysics and Space Science. 2010;327:299.
Singh J, Leke O. Effects of oblateness, perturbations, radiation and varying masses on the stability of equilibrium points in the restricted threebody problem Astrophysics and Space Science. 2013;344:51.
Singh J, Haruna S. Equilibrium points and stability under effects of radiation and perturbing forces in the restricted problem of three oblate bodies. Astrophysics and Space Science. 2014;349:107.
Singh J, Amuda TO. Effects of poyntingrobertson (PR) drag, Radiation, and Oblateness on motion around the equilibrium points in the CR3BP. Journal of Dynamical Systems and Geometric Theories. 2017;15:177.
Schuerman DW. The restricted threebody problem including radiation pressure. Astrophysical Journal. 1980;238:337.
Murray CD. Dynamical effects of drag in the circular restricted threebody problem. Icarus. 1994;122:465.
Ragos O, Zafiropoulos FA. A numerical study of the influence of the study of the PoyntingRobertson effect on the equilibrium points of the photogravitational restricted threebody problem. Astronomy & Astrophysics. 1995;300:568.
Kushvah BS. The effect of radiation pressure on the equilibrium point in the generalized photogravitational restricted threebody problem. Astrophysics and Space Science. 2008;315:231.
Das MK, et al. On the out of plane equilibrium points in photogravitational restricted threebody problem. Journal of Astronomy and Astrophysics. 2009;30:177.
Singh J, Amuda TO. Stability analysis of triangular equilibrium points in the restricted threebody problem under effects o circumbinary disc, radiation and drag forces. Journal Astronomy and Astrophysics. 2019;40:5.
Bhatnagar KB, Hallan PP. The effect of perturbations in Coriolis and centrifugal forces on the linear stability of equilibrium points in the restricted problem of three bodies. Celestial Mechanics. 1978;18: 105.
Singh J, Leke O. Analytic and numerical treatment of motion of dust grain particle around triangular equilibrium points with postAGB binary star and disc. Advances in Space Research. 2014;54:1659.
Singh J, Abdulkarim A. Instability of triangular libration points in the perturbed photogravitational R3BP with PoyntingRobertson (PR) drag. Astrophysics and Space Science. 2014;351:473.
Luk’yanov LG. Particular solutions in the restricted problem of three bodies with variable masses. Astronomical Journal of Academy of Sciences of USSR. 1989;66:180.
Collins H. Interactional expertise as a third kind of knowledge. Phenomenology and the cognitive sciences. 2004;3:125.
Wolfram S. The Mathematica Book, 10th Ed. Wolfram Media, Campaigns; 2017.
SubbaRao PV, Sharma RK. A note on the stability of the triangular points of equilibrium in the restricted threebody. Astronomy and Astrodynamics. 1975;43:381.
Euaggelos E. Zotos. Fractal basins of attraction in the planar circular restricted threebody problem with oblateness and radiation pressure. Astrophysics and Space Science. 2016;361:181.

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