Existence and stability of triangular points in the relativistic R3BP when the bigger primary is a triaxial rigid body and a source of radiation

  • Authors

    • Jagadish Singh Ahmadu Bello UNIVERSITY,zARIA
    • Bello Nakone Usmanu Danfofiyo University,Sokoto
    2016-05-09
    https://doi.org/10.14419/ijaa.v4i1.5711
  • Celestial Mechanics, Radiation, Triaxiality, Relativity, R3BP.

  • Abstract

    We study the effect of triaxiality and radiation of the bigger primary on the positions and stability of the triangular points in the relativistic R3BP. It is found that the locations of the triangular points are affected by the relativistic terms apart the radiation force and the triaxiality of the bigger primary. It is also seen that for these points, the range of stability region increases or decreases according as without which depends upon the relativistic terms, the radiation and triaxiality coefficient is greater than or less than zero. A practical application of this model could be the study of the motion of a dust grain particle near the Sun-Earth system. A practical application of this model could be the study of the motion of a dust grain particle near the Sun-Earth system.

  • 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 (2002), rder and Chaos in Dynamical Astronomy. Springer, Berlin.
    4. SubbaRao PV&Sharma RK (1975), a note on the stability of the triangular points of equilibrium in the restricted three-body problem, Astronomy & Astrophysics 43, 381-383.
    5. AbdulRaheem A & Singh J (2006), Combined effects of perturbations,radiation and oblateness on the stability of equilibrium points in the restricted three-body problem, Astronomical Journal,131,1880-1885 http://dx.doi.org/10.1086/499300.
    6. Sharma RK (1987), The linear stability of libration points of the photogravitational restricted three-body problem when the smaller primary is an oblate spheroid, Astrophysics & Space Science, 135, 271-281 http://dx.doi.org/10.1007/BF00641562.
    7. Idrisi M J, Imran M& Taqvi Z A(2013), Existence and stability of libration points in the restricted three-body problem when one of the primaries is an oblate spheroid, International Journal of Applied Mathematics and Mechanics, 9(17), 1-12 .
    8. El-Shaboury SM (1991), The libration points of a triaxial satellite in the photogravitational restricted problem of three bodies, Indian Journal of Pure and Applied Mathematics, 22(8), 703-712 .
    9. Sharma RK, Taqvi ZA& Bhatnagar KB(2001), Existence and stability of the libration points in the restricted three-body problem the when the primaries are triaxial rigid bodies, Indian Journal of Pure and Applied Mathematics, 32(7), 944-981 .
    10. Sharma RK ,Taqvi ZA&Bhatnagar K B (2001), Existence and stability of the libration points in the restricted three-body problem when the bigger primary is a triaxial rigid body and source of radiation, Indian Journal of Pure and Applied Mathematics, 32(2) 255-266
    11. 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 and the bigger one an oblate spheroid, Indian Journal of Pure and Applide Mathematics, 30 (7), 721-733
    12. Singh J (2013), the equilibrium points in the perturbed R3BP with triaxial and luminous primaries. Astrophysics &Space Science, 346, 41-50 http://dx.doi.org/10.1007/s10509-013-1420-7.
    13. De Sitter W (1916), On Einstein’s theory of gravitation and its astronomical consequences, Monthly Notes of Royal Astronomical Society, 76, 699-728. http://dx.doi.org/10.1093/mnras/76.9.699.
    14. Kottler F (1922), Gravitation Und Relativitats theorie. Encykl. Math. Wiss 6 (2), No 22a.
    15. Chazy J (1928), La theorie de la relativite et la mecanique celeste vol.1, Paris Gauthier- villars .
    16. Chazy J (1930), La theorie de la relativite et la mecanique celeste vol.1, Paris Gauthier- villars.
    17. Eddington AS & Clark GL (1938), The problem of n bodies in general relativity theory, Proceeding of Royal Society of America,166, 465 http://dx.doi.org/10.1098/rspa.1938.0104.
    18. Brumberg V A (1972), Relativistic Celestial Mechanics. Nauka, Moscow
    19. Brumberg VA (1991), Essential Relativistic Celestial Mechanics. New York Adam Hilger.
    20. Bhatnagar K B & Hallan PP (1998), Existence and stability of L4,5 in the relativistic restricted three-body problem, Celestial Mechanics and Dynamica Astronomy. 69(3), 271-281. http://dx.doi.org/10.1023/A:1008271021060.
    21. Douskos C N & Perdios E A (2002), on the stability of equilibrium points in the relativistic three-body problem, Celestial Mechanics and Dynamical Astroonomy, 82, 317-321. http://dx.doi.org/10.1023/A:1015296327786.
    22. Abd El-Salam F a & Abd El-Bar S E (2014), On the triangular equilibrium points in the photogravitional relativistic restricted three-body problem, Astrophysics & Space Science, 349, 125-135. http://dx.doi.org/10.1007/s10509-013-1629-5.
    23. Katour D A, Abd El-Salam F A& 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.
    24. 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.
    25. 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.
    26. McCuskey S W (1963), Introduction to celestial mechanics, Addison-Wesley.
    27. Radzievskii VV (1950), The restricted problem of three odies taking account of light pressure,Astronomical Journal,250-256.

  • Downloads

  • How to Cite

    Singh, J., & Nakone, B. (2016). Existence and stability of triangular points in the relativistic R3BP when the bigger primary is a triaxial rigid body and a source of radiation. International Journal of Advanced Astronomy, 4(1), 43-48. https://doi.org/10.14419/ijaa.v4i1.5711

    Received date: 2015-12-29

    Accepted date: 2016-01-28

    Published date: 2016-05-09