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Influence of the Zonal Harmonics of the Primary on Collinear Points (L1,2,3) in the Photogravitational ER3BP
Current Issue
Volume 5, 2017
Issue 3 (June)
Pages: 12-18   |   Vol. 5, No. 3, June 2017   |   Follow on         
Paper in PDF Downloads: 28   Since Aug. 1, 2017 Views: 1240   Since Aug. 1, 2017
Authors
[1]
Jagadish Singh, Department of Mathematics, Faculty of Science, Ahmadu Bello University, Zaria, Nigeria.
[2]
Blessing Ashagwu, Department of Mathematics, Faculty of Science, Ahmadu Bello University, Zaria, Nigeria.
Abstract
We investigate in the framework of the elliptic restricted three-body problem (ER3BP), the influence of the zonal harmonics (J2 & J4) of the primary and the radiation pressure of the secondary in the neighbourhood of collinear libration point. The positions of the collinear points are affected by aforesaid perturbations. The changes in the locations of the points (L1,2,3) occur as a result of the perturbed oblateness. The positions do not move uniformly with increase in varying oblateness for the binary systems PSR J1903+0327. The collinear points as evidenced from the systems under consideration are unstable even with the introduction of oblateness up to zonal harmonics J4.
Keywords
Celestial Mechanics, ER3BP, Oblateness, Collinear Points
Reference
[1]
Euler, L., (1767). The motion in the rectilinear three-body problem. Nov. Comm. Petrop. (First Edition).
[2]
Routh, E. J., (1875). On Laplace’s three particle, with a supplement on the stability of steady motion. Proc. London Mathematical Society 6: 86.
[3]
Bhatnagar, K. B., and Hallan, P. P, (1978). “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 18: 105.
[4]
Kunitsyn, A. L., (2001). The stability of collinear libration points in the photogravitational three-body problem. J. Applied Mathematical Mechanics 65: 703.
[5]
Abdulraheem A. and Singh, J. (2008). Combined effects of perturbations, radiation and oblateness on the periodic orbits in the restricted three-body problem, Astrophysics and Space Science, 317: 9-13.
[6]
Singh, J. and Begha, J. M. (2011). Periodic orbits in the generalized perturbed restricted three-body problem. Astrophysics and Space Science, 332: 319-324.
[7]
Singh, J. and 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.
[8]
Szebehely, V. (1967b). Stability of the points of equilibrium in the restricted problem, Astronomical Journal, 72, 7 -9.
[9]
Sharma, R. K., (1982). “Linear Stability of triangular points in the generalized photogravitational restricted problem of three bodies”, In Sun and Planetary System. (Edited by Fricke, W., and Teleki, G.), Dordrecht: Riedel, 435.
[10]
Khanna, M. and Bhatnager, K. B., (1999). Existence and stability of libration points in the restricted three-body problem when the smaller primary is a triaxial rigid body and the bigger one an oblate spheroid. Indian Journal of pure and applied Mathematics, 30: 721- 733.
[11]
Sharma, R. K., Taqvi, Z. A., and Bhatnagar, K. B., (2001). “Existence and Stability of libration points in the restricted three-body when the primaries are Triaxial rigid bodies and source of radiation”, Indian Journal of Pure and Applied Mathematics, 32: 981-994.
[12]
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.
[13]
Abouelmagd, E. I. and El-Shaboury, S. M. (2012). Periodic orbits under combined effects of oblateness and radiation in the restricted problem of three bodies. Astrophysics and Space Science, 341: 331-341.
[14]
Kunitsyn, A. L., and Tureshbaev, A. T., (1985). “Stability of the coplanar libration points in the Photogravitational restricted three body problem”, Soviet Astron. Lett., 11: 391-392.
[15]
Tkhai, N. V. (2012). Stability of the collinear libration points of the photogravitational three-body problem with an internal fourth order resonance. J. Appllied Mathematical Mechanics 76: 441.
[16]
Singh, J. and Umar, A. (2013). Collinear equilibrium points in the elliptic R3BP with oblateness and radiation. Advances in Space Research, 52, 1489-1496.
[17]
Singh, J. and Umar, A. (2014). On motion around the collinear libration points in the elliptic restricted three-body problem with a bigger triaxial primary. New Astronomy, 29, 36-41.
[18]
Ammar, M. K., (2012). Third-order secular solution of the variational equations of motion of a satellite in orbit around a non-spherical planet. Astrophysics and Space Science. 340: 43.
[19]
Tsirogiannis, G. A., Douskos, C. N. and Perdios, E. A. (2006). Computation of the liapunov orbits in the photogravitational RTBP with oblateness. Astrophysics and Space Science, 305: 389.
[20]
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. Astrophysics and Space Science, 135: 271.
[21]
Singh, J. and Leke, O. (2012). Equilibrium points and stability in the restricted three-body problem with oblateness and variable masses. Astrophysics and Space Science, 340: 27-41.
[22]
J. Singh, B. Ashagwu, A. Umar, (2016). Influence of the Zonal harmonics of the primary on L4, 5 in the photographical ER3BP. International Frontial Sci. Letters, 10: 23-36.
[23]
Singh, J. and Umar, A. (2012). On the stability of triangular equilibrium points in the elliptic R3BP under radiating and oblate primaries. Astrophysics and Space Science, 341: 349-358.
[24]
AbdulRaheem, A. and Singh, J. (2006). Combined effects of perturbations, radiation and oblateness on the stability of libration points in the restricted three-body problem. Astronomical journal, 131: 1880-1885.
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