THE STABILITY OF OUT-OF-PLANE EQUILIBRIUM POINTS IN THE ELLIPTIC RESTRICTED THREE-BODY PROBLEM AT J_4 OF THE BIGGER PRIMARY

Tyokyaa Kanshio Richard, T Danjuma, Funmilayo Balogun

Abstract


This paper examines the positions and stability of out-of-plane equilibrium points within the framework of the Elliptic Restricted Three-Body Problem (ER3BP) at  of the bigger primary in the field of stellar binary systems: HD188753 and Alpha Centauri around their common centre of mass in elliptic orbits. It is found that, the positions and stability of the out-of-plane equilibrium points are significantly affected by the oblateness, semi-major axis and the eccentricity of their orbits. The positions  of the infinitesimal body lie in the plane almost directly above and below the center of the bigger oblate primary. The effects of the perturbed parameters on the positions and stability are shown numerically for the aforementioned binary systems. The status of the out-of-plane equilibrium points as evidenced in most cases remain the same and are unstable even when only the bigger primary is viewed in the out-of-plane.   


Full Text:

PDF

References


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

Ammar, M.K. (2012). Third-order secular solution of the variational equations of motion of a satellite in orbit around a non-spherical planet. Astrophys. Space Sci. 340:43.

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

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

Sharma, R.K. (1987). The linear stability of libration points of the photogravitational restricted three-body problem when the smaller primary is an oblate spheroid. Astrophys. Space Sci. 135:271.

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

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

Singh J., Tyokyaa K.R., (2016). Stability of triangular points in the elliptic restricted three- body problem with oblateness up to zonal harmonic J_4 of both primaries. Eur. Phys. J. Plus, 131:365.

Singh J., Tyokyaa K.R., (2017). Stability of collinear points in the elliptic restricted three- body problem with oblateness up to zonal harmonic J_4 of both primaries. Eur. Phys. J. Plus, 132:330

Singh J., Amuda T.O., (2015). Out-of-Plane equilibrium points in the photogravitational circular restricted three-body problem with oblateness and P-R Drag. Astronomy and Astrophysics 36:291-305

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

Singh, J., Leke, O., (2014). 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: 1659-1677.

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

Tkhai, N.V. (2012). Stability of the collinear libration points of the photogravitational three-body problem with an internal fourth order resonance. J. Appl.Math. Mech. 76:441.

Tsirogiannis, G.A., Douskos, C.N., Perdios, E.A. (2006). Computation of the liapunov orbits in the photogravitational RTBP with oblateness. Astrophys. Space Sci. 305:389.

Tyokyaa, K. R., Yusuf A.B., (2016). Stability of triangular points in the elliptic restricted three-body problem with oblateness up to zonal harmonic J_4 of the bigger primary. Journal of the Nigerian Association of Mathematical Physics (ISSN: 1116-4336 (print)). VOL. 37: 371–378.

Tyokyaa K. R., Tikyaa E.V., Orverem M.J., (2017). Stability of triangular points in the elliptic restricted three-body problem with oblateness up to zonal harmonic J_4 of the Smaller primary. Journal of the Nigerian Association of Mathematical Physics (ISSN: 1116-4336 (print)). VOL. 42: 159–164.


Refbacks

  • There are currently no refbacks.




FEDERAL UNIVERSITY DUTSIN-MA, KATSINA STATE - Copyright 2020