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Stability of collinear points in the elliptic restricted three-body problem with oblateness up to zonal harmonic j4

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Abstract.

This paper investigates the positions and stability of the collinear equilibrium points \( L_{1,2,3}\) in the elliptic restricted three-body problem (ER3BP) with oblateness of the primaries up to zonal harmonic \(J_{4}\). It is found that their positions are affected by the oblateness of the primaries, eccentricity and the semi-major axis of the orbits, but its stability behavior remains unchanged and is unstable. Furthermore, numerical explorations are performed to show the effects of parameters involved on the position and stability of collinear points for the systems: HD188753 and Gliese 667.

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References

  1. K.B. Bhatnagar, P.P. Hallan, Celest. Mech. 20, 95 (1979)

    Article  ADS  Google Scholar 

  2. A.L. Kunitsyn, J. Appl. Math. Mech. 65, 703 (2001)

    Article  MathSciNet  Google Scholar 

  3. A. Abdulraheem, J. Singh, Astrophys. Space Sci. 317, 9 (2008)

    Article  ADS  Google Scholar 

  4. J. Singh, J.M. Begha, Astrophys. Space Sci. 332, 319 (2011)

    Article  ADS  Google Scholar 

  5. J. Singh, O. Leke, Adv. Space Res. 54, 1659 (2014)

    Article  ADS  Google Scholar 

  6. J. Singh, A. Umar, Astrophys. Space Sci. 341, 349 (2012)

    Article  ADS  Google Scholar 

  7. J. Singh, O. Leke, Astrophys. Space Sci. 340, 27 (2012)

    Article  ADS  Google Scholar 

  8. C.N. Douskos, V.V. Markellos, Astron. Astrophys. 466, 357 (2006)

    Article  ADS  Google Scholar 

  9. P.V. Subbarao, R.K. Sharma, Astron. Astrophys. 43, 381 (1975)

    ADS  Google Scholar 

  10. J. Singh, K.R. Tyokyaa, Eur. Phys. J. Plus 131, 365 (2016)

    Article  Google Scholar 

  11. E.J. Routh, Proc. London Math. Soc. 6, 86 (1875)

    ADS  Google Scholar 

  12. E.I. Abouelmagd, Astrophys. Space Sci. 342, 45 (2012)

    Article  ADS  Google Scholar 

  13. A.L. Kunitsyn, J. Appl. Math. Mech. 65, 703 (2001)

    Article  MathSciNet  Google Scholar 

  14. A.L. Kunitsyn, A.T. Tureshbaev, Sov. Astron. Lett. 11, 391 (1985)

    ADS  Google Scholar 

  15. N.V. Tkhai, J. Appl. Math. Mech. 76, 441 (2012)

    Article  MathSciNet  Google Scholar 

  16. J. Singh, A. Umar, Astrophys. Space Sci. 344, 13 (2013)

    Article  ADS  Google Scholar 

  17. M.K. Ammar, Astrophys. Space Sci. 340, 43 (2012)

    Article  ADS  Google Scholar 

  18. G.A. Tsirogiannis, C.N. Douskos, E.A. Perdios, Astrophys. Space Sci. 305, 389 (2006)

    Article  ADS  Google Scholar 

  19. R.K. Sharma, Astrophys. Space Sci. 135, 271 (1987)

    Article  ADS  Google Scholar 

  20. J. Singh, J.J. Taura, Astrophys. Space Sci. 350, 127 (2014)

    Article  ADS  Google Scholar 

  21. V.G. Szebehely, Theory of Orbits (Academic Press, New York, 1967)

  22. J. Singh, O. Leke, Astrophys. Space Sci. 344, 51 (2013)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Ahmadu Bello University, Zaria, Nigeria

    Jagadish Singh

  2. Department of Mathematical Sciences and IT, Faculty of Science, Federal University Dutsin-Ma, Dutsin-Ma, Katsina State, Nigeria

    Tyokyaa K. Richard

Authors
  1. Jagadish Singh
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  2. Tyokyaa K. Richard
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Correspondence to Tyokyaa K. Richard.

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Singh, J., Richard, T.K. Stability of collinear points in the elliptic restricted three-body problem with oblateness up to zonal harmonic j4 . Eur. Phys. J. Plus 132, 330 (2017). https://doi.org/10.1140/epjp/i2017-11604-8

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

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