LIBRATION POINTS AND STABILITY OF AN OBLATE TEST PARTICLE IN THE SUNEARTH SYSTEM OF THE RESTRICTED THREEBODY PROBLEM
Journal of Applied Physical Science International, Volume 14, Issue 3,
Page 4268
DOI:
10.56557/japsi/2022/v14i38090
Abstract
This paper examines libration points and stability of a test particle having the shape of an oblate spheroid under the gravitational effect of a radiating first primary and an oblate shaped second primary using the model of the restricted threebody problem. The equations of motion have been stated and the libration points examined. It is seen that there exist a pair of triangular points which are defined by the radiation pressure force of the first primary, and oblateness of the second primary and the test particle. Further, there can be up to five collinear libration points in the presence of oblateness of either the second primary or the test particle. We examine the stability of the libration points and it is seen that the triangular points are linearly stable in the sense that the roots of the characteristic equation are all distinct imaginary roots, which produce bounded motion around the triangular points, while the collinear points are unstable due to the presence of a positive root. Further, we explore the periodic orbits around linearly stable triangular points and it was seen that the orbits are elliptic. The elements of the orbits, among which are the frequency, orientation, eccentricities, lengths of the semimajor and semiminor axis have all been obtained and are defined by the radiation pressure of the first primary and oblateness of the second primary and the test particle. These outcomes have been verified numerically when the radiating first primary is the Sun and the oblate second primary is the Earth.
 RTBP
 libration points
 radiation pressure
 oblateness, test particle
How to Cite
References
Murray C, Dermott S. Solar system dynamics. Cambridge: Cambridge University Press; 1999.
Radzievskii VV. The photogravitational restricted problems of threebodies. Astron J. 1950;27:2506.
Radzievskii VV. The photogravitational restricted problems of threebodies and coplanar solutions. Astron J. 1953;30:2659.
Singh J, Ishwar B. Stability of triangular points in the generalized photogravitational restricted threebody problem. Bull Astron Soc India. 1999;27:41524.
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. Int J Pure Appl Math. 1999;30: 72133.
Singh J, Taura JJ. Motion in the generalized restricted threebody problem. Astrophys Space Sci. 2013;343(1):95106. DOI: 10.1007/s1050901212250
Singh J, Leke O. Effects of oblateness, perturbations, radiation and varying masses on the stability of equilibrium points in the restricted threebody problem. Astrophys Space Sci. 2013;344(1):5161. DOI: 10.1007/s105090121324y
Javed MI, Imran M, Taqvi ZA. Existence and stability of the libration points in the restricted threebody problem when one of the primaries is an oblate spheroid. Int J Appl Math Mech. 2013;9:112.
Arif M. Motion around the equilibrium points in the planar magneticbinaries problem. Int J Appl Math Mech. 2013;9:98107.
Idrisi MJ. Existence and stability of the libration points in CR3BP when the smaller primary is an oblate spheroid. Astrophys Space Sci. 2014;354(2):31125. DOI: 10.1007/s1050901420317
Abouelmagd EI, Guirao JLG. On perturbed restricted threebody problem. Appl Math Nonlinear Sci. 2016;1:11839.
Pathak N, Abouelmagd EI, Thomas VO. On higher order resonant periodic orbits in the photo–gravitational planar restricted three–body problem with oblateness. J Astronaut Sci. 2019;66(4):475505. DOI: 10.1007/s4029501900178z
De S, Roychowdhury S, Banerjee R. BeyondNewtonian dynamics of a planar circular restricted threebody problem with Kerrlike primaries. Mon Not R Astron Soc. 2020; 501(1):71329. DOI: 10.1093/mnras/staa3733
Singh J, Richard TK. A study on the positions and velocity sensitivities in the restricted threebody problem with radiating and oblate primaries. New Astron. 2021;2021:101704.
Amuda TO, Leke O, AbdulRaheem A. Unveiling perturbing effects of PR drag on motion around triangular Lagrangian points of the photogravitational restricted problem of three oblate bodies. Curr J Appl Sci Technol. 2021;40:1031. DOI: 10.9734/cjast/2021/v40i131201
Leke O, John JT. On combined effects of radiation, perturbation, oblateness and disc on motion around collinear Lagrangian points of the restricted threebody problem. J Niger Assoc Math Phys. 2021;61:716.
Amuda TO, Singh J. Instability of triangular equilibrium points in the restricted threebody problem under effects of circumbinary disc, radiation and PR drag. Earth Moon Planets. 2022;126(1):1. DOI: 10.1007/s11038021095431
Vincent AE, Perdiou AE, Perdios EA. Existence and stability of equilibrium points in the R3BP with triaxialradiating primaries and an oblate massless body under the effect of the circumbinary disc. Front Astron Space Sci. 2022;9:872459. DOI: 10.3389/fspas.2022.877459
Alrebdi HI, Dubeibe FL, Zotos EE. On the equilibria of the restricted threebody problem with a triaxial rigid body, II: prolate primary. Results Phys. 2022;38:105623. DOI: 10.1016/j.rinp.2022.105623
Leke O, Singh J. Outofplane equilibrium points of extrasolar planets in the central binaries PSR B162026 and Kepler16 with cluster of material points and variable masses. New Astron. 2023;99:101958. DOI: 10.1016/j.newast.2022.101958
Wolfram S. The mathematica. 10th ed. Wolfram Campaigns; 2017.
Sharma RK. Linear Stability of triangular points in the generalized photogravitational restricted problem of three bodies. In: Fricke W, Teleki G, editors. Sun and planetary system. Dordrecht: Riedel. 1982;435.
SubbaRao PV, Sharma RK. A note on the stability of the triangular points of equilibrium in the restricted threebody. Astron Astrodynamics. 1975;43:38194.
Kunitsyn AL, Polyakhova EN. The restricted photogravitational threebody problem: A Modern State. Astron Astrophys Trans. 1995;6(4):28393. DOI: 10.1080/10556799508232073
AbdulRaheem A, Singh J. Combined effects of perturbations, radiation and oblateness on the stability of equilibrium points in the restricted threebody problem. Astron J. 2006; 131(3):18805. DOI: 10.1086/499300
Singh J, Leke O. Analytic and numerical treatment of motion of dust grain particle around triangular equilibrium points with postAGB binary star and disc. Adv Space Res. 2014;54(8):165977. DOI: 10.1016/j.asr.2014.06.031
AbdulRaheem A, Singh J. Combined effects of perturbations, radiation and oblateness on the periodic orbits in the restricted threebody problem. Astrophys Space Sci. 2008;317(12):913. DOI: 10.1007/s1050900898414
Singh J, Mrumun Begha JM. Periodic orbits in the generalized perturbed restricted threebody problem. Astrophys Space Sci. 2011; 332(2):31924. DOI: 10.1007/s1050901005451

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