Existence and linear stability of triangular points in the perturbed relativistic R3BP when the bigger primary is an oblate spheroid

  • Authors

    • Bello Nakone Usmanu Danfofiyo University,Sokoto
    • Jagadish Singh Ahmadu Bello UNIVERSITY,zARIA
    2016-05-09
    https://doi.org/10.14419/ijaa.v4i1.5893
  • Celestial Mechanics, Perturbation, Relativity, Triaxiality, R3BP.

  • We study the effects of oblateness and small perturbations in the Coriolis and centrifugal forces on the locations and stability of the triangular points in the relativistic R3BP. It is observed that the positions are affected by the oblateness, relativistic, and a small perturbation in the centrifugal force, but are unaffected by that of Coriolis force. It is also seen that the relativistic terms, oblateness, small perturbations in the centrifugal and Coriolis forces influence the critical mass ratio. It is also noticed that all the former three and the latter one possess destabilizing and stabilizing behavior respectively. However, the range of stability increases or decreases according to as p >0 or p<0 where p depends upon the relativistic, oblateness and small perturbations in the Coriolis and centrifugal forces.

  • References

    1. Szebehely V (1967), Theory of orbits. The restricted problem of three- bodies. Academic Press. New York.
    2. Wintner A (1941), The Analytical foundations of celestial mechanics, Princeton University Press, Princeton.
    3. Contopolous G (1976), the relativistic restricted three-body problem in D. Kotsakis (ed.) “In Memorian D. Eginitsâ€, Athens, 159.
    4. Szebehely V (1967), Stability of the points of equilibrium in the restricted problem, Atronomical Journal, 27, 7-9. http://dx.doi.org/10.1086/110195.
    5. Bhatnagar KB & Hallan PP (1978), Effect of perturbations in Coriolis and centrifugal forces on the stability of libration points in the restricted problem, Celestial Mechanics, 18,105-112. http://dx.doi.org/10.1007/BF01228710.
    6. AbdulRaheem a & Singh J (2006), Combined effects of perturbations, radiation and oblateness on the stability of equilibrium points in the restricted three-body problem, Atronomical Journal, 131, 1880-1885. http://dx.doi.org/10.1086/499300.
    7. Singh J & Begha JM (2011), Stability of equilibrium points in the generalized perturbed restricted three-body problem, Astrophysics & Space Science, 331, 511-519. http://dx.doi.org/10.1007/s10509-010-0464-1.
    8. Abouelmagd EI, Asiri HM & Sharaf MA (2013), The effect of oblateness in the perturbed restricted three-body problem,Meccanica 48, 2479-2490. http://dx.doi.org/10.1007/s11012-013-9762-3.
    9. Moulton FR (1914), an introduction to celestial Mechanics, 2nd Edition, Dover publications Inc. New York.
    10. SubbaRao PV & Sharma RK (1975), a note on the stability of the triangular points of equilibrium in the restricted three-body problem, Astrononomy & Astrophyics 43, 381-383.
    11. Elipe A & Ferrer S (1985), On the equilibrium solutions in the circular planar restricted three rigid bodies problem, Celestia[ Mechanics, 37, 50-70.
    12. Khanna M &Bhatnagar KB (1999), Existence and stability of libration points in the restricted three-body problem when the smaller primary is a triaxial rigid body, Indian Journal of Pure and Applied Mathematics, 29(10), 1011-1023.
    13. Singh J (2011), combined effects of perturbations, radiation, and oblateness on the nonlinear stability of triangular points in the restricted three-body problem, Astrophysics & Space Science, 332, 331-339. http://dx.doi.org/10.1007/s10509-010-0546-0.
    14. Sharma RK, Taqvi ZA &Bhatnagar KB (2001), Existence and stability of the libration points in the restricted three-body problem when the primaries are triaxial rigid bodies, Celestial Mechanics and Dynamical Astronomy, 79, 119-133. http://dx.doi.org/10.1023/A:1011168605411.
    15. Brumberg VA (1972), Relativistic Celestial Mechanics. Moscow, Nauka.
    16. Brumberg VA (1991), Essential Relativistic Celestial Mechanics, New York, Adam Hilger Ltd
    17. Bhatnagar KB & Hallan PP (1998), Existence and stability of L4, 5 in the relativistic restricted three-body problem. Celestial Mechanics and Dynamical Astronomy 69, 271-281. http://dx.doi.org/10.1023/A:1008271021060.
    18. Douskos CN & Perdios EA (2002), On the stability of equilibrium points in the relativistic three-body problem, Celestial Mechanics and Dynamical Astronomy, 82,317-321 http://dx.doi.org/10.1023/A:1015296327786.
    19. Katour DA, Abd El-Salam, FA &Shaker MO (2014), Relativistic restricted three-body problem with oblateness and photo-gravitational corrections to triangular equilibrium points. Astrophysics &Space Science, 351(1), 143-149. http://dx.doi.org/10.1007/s10509-014-1826-x.
    20. Singh J & Bello N (2014), Effect of radiation pressure on the stability of L4, 5 in relativistic R3BP. Astrophysics & Space Science, 351(2), 483-490 http://dx.doi.org/10.1007/s10509-014-1858-2.
    21. Singh J & Bello N (2014), Motion around L4 in the perturbed relativistic R3BP, Astrophysics & Space Science, 351(2), 491-497. http://dx.doi.org/10.1007/s10509-014-1870-6.
    22. [Singh J, Bello N (2014) ,Effect of perturbations in the Coriolis and centrifugal forces on the stability of L4 in the relativistic R3BP,Journal of Astrophysics and Astronomy,35 (4) 701-713.
    23. McCuskey SW (1963), Introduction to celestial mechanics, Addison, Wesley.

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    Nakone, B., & Singh, J. (2016). Existence and linear stability of triangular points in the perturbed relativistic R3BP when the bigger primary is an oblate spheroid. International Journal of Advanced Astronomy, 4(1), 49-56. https://doi.org/10.14419/ijaa.v4i1.5893