We investigate in the framework of the elliptic restricted three-body problem (ER3BP), the influence of the zonal harmonics (J_{2} and J_{4}) of the primary and the radiation pressure of the secondary on the positions and stability of the triangular equilibrium points. The triangular points of the problem are affected by the parameters involved in the systems’ dynamics. The positions change with increase in the zonal harmonics, eccentricity and radiation pressure. The triangular points remain stable in the interval 0<*μ*<*μ*_{c} as shown arbitrarily.

Periodical:

International Frontier Science Letters (Volume 10)

Pages:

23-36

Citation:

J. Singh et al., "Influence of the Zonal Harmonics of the Primary on L_{4,5} in the Photogravitational ER3BP", International Frontier Science Letters, Vol. 10, pp. 23-36, 2016

Online since:

Dec 2016

Authors:

Distribution:

Open Access

This work is licensed under a

Creative Commons Attribution 4.0 International License

References:

[1] A.L. Kunitsyn, A.T. Tureshbaev, The collinear libration points in the photogravitational three-body problem, Pisma v Astronomicheskii Zhurnal. 9(7) (1983) 432-435.

[2] J. Singh, B. Ishwar, Stability of collinear equilibrium points in the generalised photogravitational elliptic restricted three-body problem, Bull. Astron. Soc. India. 27 (1999) 415-424.

[3] S.K. Sahoo, B. Ishwar, Stability of collinear equilibrium points in the generalised photogravitational elliptic restricted three-body problem, Bull. Astron. Soc. India. 28 (2000) 579.

[4] A.L. Kunitsyn, The stability of collinear liberation points in the photogravitational three-body problem, Appl. Math. Mech. 65(4) (2001) 703.

[5] G.A. Tsirogiannis, C.N. Douskos, E.A. Perdios, Computation of the Liapunov orbits in the photogravitational RTBP with oblateness, Astrophys. Space Sci. 305(4) (2006) 389-398.

DOI: 10.1007/s10509-006-9171-3[6] S. Kumar, B. Ishwar, Location of equilibrium points in the generalised elliptic restricted three-body problem, Inter. J. Eng. Sci. Tech. 3(2) (2011) 157-162.

[7] M.V. Tkhai, Stability of the collinear libration points of the photogravitational three body problem with an internal fourth order resonance, J. Appl. Math. Mech. 76(4) (2012) 441-445.

DOI: 10.1016/j.jappmathmech.2012.09.011[8] C.R. Kumar, A. Narayan, Existence and stability of collinear equilibrium points in elliptical restricted three-body problem under the effects of photogravitional and oblateness primaries, Int. J. Pure and Appl. Math. 80(4) (2012) 477-494.

[9] J. Singh, A. Umar, On motion around the collinear libration points in the elliptic R3BP with a bigger triaxial primary, New Astronomy. 29 (2014) 36-41.

[10] J. Singh, A. Umar, Collinear equilibrium points in the elliptic R3BP with oblateness and radiation, Advances in Space Research. 52(8) (2013) 1489-1496.

DOI: 10.1016/j.asr.2013.07.027[11] J. Singh, A. Umar, Motion in the photogravitational elliptic restricted three-body problem under an oblate primary, Astron. J. 143 (2012) 109.

DOI: 10.1088/0004-6256/143/5/109[12] J. Singh, A Umar, On stability of triangular equilibrium points in the elliptic R3BP under radiating and oblate primaries, Astrophys. Space Sci. 341 (2012) 349.

DOI: 10.1007/s10509-012-1109-3[13] J. Singh, A. Umar, The influence of trixiality and oblateness on the triangular point of double pulsar in the ER3BP, Astrophys. Space Sci. 352 (2014) 429-436.

DOI: 10.1007/s10509-014-1930-y[14] V.V. Radzievsky, The restricted problem of three bodies taking account of light pressure, Astron. J. 27 (1950) 249.

[15] A. Umar, J. Singh, Periodic, Eccentricities and Axes around L4, 5 in the ER3BP under radiating and oblate primaries, International Journal of Astronomy and Astrophysics. 4 (2014) 668-682.

[16] J. Singh, J.J. Taura, Collinear libration points in the photogravitational CR3BP with Zonal Harmonics and a potential from a belt, International Journal of Astronomy and Astrophysics. 5 (2015) 155-165.

DOI: 10.4236/ijaa.2015.53020[17] R.K. Sharma, Z.A. Tagvi, K.B. Bhatnagar, Existence and stability of libration points in the restricted three-body problem when the primaries are triaxial rigid bodies, Celest. Mech. Dyn. Astron. 79(2) (2001) 119-133.

[18] A.L. Kunitsyn, The stability of triangular libration points in the photogravitational three-body problem. J. Appl. Math. Mech. 64 (2000) 757.

DOI: 10.1016/s0021-8928(00)00105-2[19] V. Kumar, R.K. Choudry, Nonlinear stability of the triangular libration points for the photo Gravitational elliptic restricted problem of three bodies, Celest. Mech. 48 (1987) 299.

[20] J.F.L. Simmons, A.J.C. McDonald, J.C. Brow, The restricted 3-body problem with radiation pressure, Celestial Mechanics. 35(2) (1985) 145-187.

DOI: 10.1007/bf01227667[21] G.G. Arutynyan, D.M. Sadrakyan, E.V. Chubaryan, Rotating white dwarfs in the general relativity theory, Astrophysics. 7(3) (1971) 274- 280.

[22] V.V. Papoyan, D.M. Sadrakyan, E.V. Chubaryan, Newtonian theory of rapidly rotating white dwarfs, Astrophysics. 7(1) (1971) 55-61.

DOI: 10.1007/bf01002622[23] W.G. Laarakkers, Quadrupole moments of rotating neutron stars, Astrophys. J. 512(1) (1999) 282-287.

[24] M. Shibata, Effects of the quadrupole moment of rapidly rotating neutron stars on the motion of the accretion disks, Prog. Theor. Phys. 99 (1998) 69-78.

[25] K. Boshkayev, H. Quevedo, R. Ruffini, Gravitational field of compact objects in general relativity, Phys. Rev. D. 86(6) (2012) ID 064043.

[26] J.S. Heyl, Gravitational radiation from strongly magnetized white dwarfs, Mon. Not. R. Astron. Soc. 317 (2000) 310-314.

DOI: 10.1046/j.1365-8711.2000.03533.x[27] P.V. Subba Rao, R.K. Sharma, Astral-t, Astrophys. 43 (1975) 381.

[28] A. Ellipe, S. Ferrer, On the equilibrium solutions in the circular planar restricted three rigid bodies problem, Celest. Mech. 37 (1985) 59-70.

[29] S.M. EL-Shaboury, The restricted problem of a tri-axial rigid body and two spherical bodies with variable masses, Astrophysics and space science. 186(2) (1991) 245-251.

DOI: 10.1007/bf02111199[30] R.K. Sharma, The linear stability of libration points in the generalised photogravitational restricted three-body problem when the smaller primary is an oblate spheroid, Astrophys. Space Sci. 135 (1987) 271-281.

[31] J. Singh, J.M. Begha, Stability of equilibrium points in the generalised perturbed restricted three-body problem, Astrophys. Space Sci. 331(2) (2011) 511-519.

[32] J. Singh, Motion around the out-of-plane equilibrium points of the perturbed restricted three-body problem, Astrophys. Space Sci. 342 (2012) 303- 308.

[33] A. Umar, J. Singh, Semi-analytic solutions for the triangular points of double white dwarfs in the ER3BP: Impact of the body's oblateness and the orbital eccentricity, Adv. Space Res. 55 (2015) 2584-2591.

[34] J. Singh, J.J. Taura, Effects of Zonal Harmonics and A Circular Cluster of Material Points on the Stability of Triangular Equilibrium Points in the R3BP, Astrophysics and Space Science. 350 (2014) 127-132.

[35] J. Singh, J.A. Omale, Robe's circular restricted three-body problem with zonal harmonics, Astrophys. Space Sci. 353(1) (2014) 89-96.

[36] E.L. Abouelmagd, S.M. EL-Shaboury, Periodic orbits under combined effects of oblateness and radiation in the restricted problem of three bodies, Astrophys. Space Sci. 341(2) (2012) 331-341.

DOI: 10.1007/s10509-012-1093-7[37] D.J. Champion et al., An eccentric Binary Millisecond pulsar in the Galactic plane, Science. 320 (2008) 1309-1312.

[38] J.M. Cordes et al., Arecibo Pulsar Survey Using ALFA. I. Survey Strategy and First Discoveries, The Astrophysical Journal. 637(1) (2006) 446.

[39] P.C.C. Freire et al., On the nature and evolution of the unique binary pulsar J1903+0327, Monthly Notices of the Royal Astronomical Society. 412(4) (2011) 2763-2780.