Stability of triangular equilibrium points in the Photogravitational elliptic restricted three body problem with Poynting-Robertson drag

Authors

  • Vivek Mishra B.R.A.Bihar University,Muzaffarpur
  • J.P. Sharma
  • Bhola Ishwar B.R.A.Bihar University,Muzaffarpur

DOI:

https://doi.org/10.14419/ijaa.v4i1.5834

Published:

2016-03-24

Keywords:

Triangular Points, Photogravitational, ERTBP, P-R Drag.

Abstract

We have examined the stability of triangular equilibrium points in photogravitational elliptic restricted three-body problem with Poynting-Robertson drag. We suppose that smaller primary is an oblate spheroid. We have taken bigger primary as radiating. We have found the location of triangular equilibrium points and characteristic equation of the problem. We conclude that triangular equilibrium points remain unstable, different from classical case.

References

[1] Broucke,R.,(1969): Stability of periodic orbits in the elliptic restricted three body problem, AIAA Journal, 7(6), 1003-1009 http://dx.doi.org/10.2514/3.5267.

[2] Chernikov Yu. A., (1970): The photogravitational restricted three body problems, Soviet Astronomy-AJ, 14(1), 176-181.

[3] Danby,J.M.A.,(1964): Stability of the triangular points in the elliptic restricted problem of three bodies, The Astronomical Journal,69(2), 165-172.http://dx.doi.org/10.1086/109254.

[4] Kushvah,B.S., Ishwar, B.,(2006): Linear stability of generalized photogravitational restricted three body problem with Poynting-Robertson drag,Journal of Dynamical system & Geometric Theories 4(1),79-86.

[5] Liou J. C., Zook, H.A. and Jackson, A.A. (1995b): Radiation pressure,Poynting-Robertson drag and solar wind drag in the restricted three body problem, Icarus 116,186-201. http://dx.doi.org/10.1006/icar.1995.1120.

[6] Murray,C.D.,(1994): Dynamical effects of drag in the circular restricted three body problem:Location and stability of the Lagrangian equilibrium points, Icarus 112,465-484. http://dx.doi.org/10.1006/icar.1994.1198.

[7] Narayan. A. and Kumar,C.R. (2011): Effects of photogravitational and oblateness on the triangular Lagrangian points in the elliptical restricted three body problem,Int.J.Pure and Appl.Math,68,201-224.

[8] Poynting, J.H., (1903): Radiation in the solar system: its effect on temperature and its pressure on small bodies, MNRAS, 64,525-552. http://dx.doi.org/10.1093/mnras/64.1.1a.

[9] Robertson.H.P. (1937): Dynamical effects of radiation in the solar system, MNRAS, 97, 423-438. http://dx.doi.org/10.1093/mnras/97.6.423.

[10] Schuerman, D. (1980): The restricted three body problem including radiation pressure, Astrophys. J., 238, 337–342 http://dx.doi.org/10.1086/157989.

[11] Sahoo, S.K.,Ishwar,B.,(2000): Stability of collinear equilibrium points in the generalized photogravitational elliptic restricted three body problem,Bulletin of the Astronomical Society of India 28,579-586.

[12] Singh, J. and Umar, A.(2012):Motion in the photogravitational elliptic restricted three body problem under an oblate primary, The Astronomical Journal, 143:109,(22pp).

[13] Wyatt S.P and Whipple F.L. (1950): The Poynting-Robertson effect on meteor orbits,American Astron.Soc.APJ.111,134-141. http://dx.doi.org/10.1086/145244.

[14] Zimovshchikov, A.S., Tkhai. (2004): Instability of libration points and resonance phenomena in the photogravitational elliptic restricted three body problem, V.N.: Sol. Syst. Res. 38, 155-164. http://dx.doi.org/10.1023/B:SOLS.0000022826.31475.a7.

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