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The Motion of Out-of-Plane Equilibrium Points in the Elliptic Restricted Three-Body Problem at <i>J<sub>4</sub></i>
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The Motion of Out-of-Plane Equilibrium Points in the Elliptic Restricted Three-Body Problem at J4

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Abstract:

We have investigated the motion of the out-of-plane equilibrium points within the framework of the Elliptic Restricted Three-Body Problem (ER3BP) at J4 of the smaller primary in the field of stellar binary systems: Xi- Bootis and Sirius around their common center of mass in elliptic orbits. The positions and stability of the out-of-plane equilibrium points are greatly affected on the premise of the oblateness at J4 of the smaller primary, semi-major axis and the eccentricity of their orbits. The positions L6, 7 of the infinitesimal body lie in the xz-plane almost directly above and below the center of each oblate primary. Numerically, we have computed the positions and stability of L6, 7 for the aforementioned binary systems and found that their positions are affected by the oblateness of the primaries, the semi-major axis and eccentricity of their orbits. It is observed that, for each set of values, there exist at least one complex root with positive real part and hence in Lyapunov sense, the stability of the out-of-plane equilibrium points are unstable.

Info:

Periodical:
International Frontier Science Letters (Volume 17)
Pages:
1-11
DOI:
https://doi.org/10.18052/www.scipress.com/IFSL.17.1
Citation:
J. Singh and T. K. Richard, "The Motion of Out-of-Plane Equilibrium Points in the Elliptic Restricted Three-Body Problem at J4", International Frontier Science Letters, Vol. 17, pp. 1-11, 2021
Online since:
April 2021
Authors:
Jagadish Singh, Tyokyaa K. Richard
Keywords:
ER3BP, Motion, Oblateness at J4, Out-of-Plane, Stability
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Distribution:
Open Access

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This work is licensed under a
Creative Commons Attribution 4.0 International License

References:

[1] J. Singh, A. Umar, On the stability of triangular equilibrium points in the elliptic R3BP under radiating and oblate primaries. Astrophys. Space Sci. 341(2012)349-358.

DOI: https://doi.org/10.1007/s10509-012-1109-3

[2] J. Singh, O. Leke, Equilibrium points and stability in the restricted three-body problem with oblateness and variable masses. Astrophys. Space Sci. 340(2012)27-41.

DOI: https://doi.org/10.1007/s10509-012-1029-2

[3] J. Singh, O. Leke,Analytic and numerical treatment of motion of dust grain particle around triangular equilibrium points with post-AGB binary star and disc. Advances in Space research. 54(2014)1659-1677.

DOI: https://doi.org/10.1016/j.asr.2014.06.031

[4] C. N. Douskos, V.V. Markellos, Out-of-Plane equilibrium points in the restricted three-body problem with oblateness. Astronomy and Astrophysics. 466(2006)357-362.

DOI: https://doi.org/10.1051/0004-6361:20053828

[5] P.V. Subbarao, R.K. Sharma, A note on the stability of the triangular points of equilibrium in the restricted three-body problem. Astron&Astrophys.43(1975)381-383.

[6] K.B. Bhatnagar, P.P. Hallan, Effect of perturbed potentials on the stability of libration points in the restricted problem. Celest. Mech. 20 (1979) 95-103.

DOI: https://doi.org/10.1007/bf01230231

[7] A.L. Kunitsyn, The stability of collinear libration points in the photogravitational three-body problem. J. Appl.Math. Mech. 65(2001)703.

DOI: https://doi.org/10.1016/s0021-8928(01)00075-2

[8] A. Abdulraheem,J. Singh, Combined effects of perturbations, radiation and oblateness on the periodic orbits in the restricted three-body problem, Astrophys. Space Sci. 317(2008)9-13.

DOI: https://doi.org/10.1007/s10509-008-9841-4

[9] J. Singh J.M. Begha, Periodic orbits in the generalized perturbed Restricted three-body problem. Astrophys. Space Sci. 332(2011)319-324.

DOI: https://doi.org/10.1007/s10509-010-0545-1

[10] J. Singh, A. Umar, On out of plane equilibrium points in the Elliptic restricted three-body problem with radiation and oblate primaries. Astrophys. Space Sci. 344(2013)13-19.

DOI: https://doi.org/10.1007/s10509-012-1292-2

[12] J. Singh, K.R. Tyokyaa, Stability of collinear points in the elliptic restricted three- body problem with oblateness up to zonal harmonic J4of both primaries. Eur. Phys. J. Plus. 132 (2017)330.

DOI: https://doi.org/10.1140/epjp/i2017-11604-8

[13] E.I. Abouelmagd, Existence and stability of triangular points in the restricted three-body problem. Astrophys. Space Sci. 342(2012)45-53.

DOI: https://doi.org/10.1007/s10509-012-1162-y

[14] M.K. Das, P. Narang, S. Mahajan, M. Yuasa, On out of plane equilibrium points in Photo-Gravitational restricted three-body problem Astrophys. Astr. 30(2009)177-185.

DOI: https://doi.org/10.1007/s12036-009-0009-6
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