Pulsating curves of zero velocity for infinitesimal mass around oblate and triaxial rigid body of triangular equilibrium points in elliptical restricted three body problem

  • Authors

    • Nutan Singh Bhilai Institute of Technology, Durg
    • A. Narayan
    2017-02-17
    https://doi.org/10.14419/ijaa.v5i1.7025
  • Er3bp, Triaxiality, Dynamical System, Zero Velocity Curve, Triangular Points.
  • Abstract

    This paper explore pulsating Curves of zero velocityof the infinitesimal mass around the triangular equilibrium points with oblate and triaxial rigid body in the elliptical restricted three body problem(ER3BP).

  • References

    1. [1] Danby JMA (1964), Stability of the triangular points in the elliptical restricted problem of three bodies, Astronomical Journal, 69,166-174.

      [2] Bennet A (1965), Characteristic exponents of the five equilibrium solutions in the EllipticallyRestricted Problem, ICARUS 4, 177-187.https://doi.org/10.1016/0019-1035(65)90060-6.

      [3] Szebehely V (1975), Stability of the points of equilibrium in restricted problem, Astronomical Journal, 72, 7-9.https://doi.org/10.1086/110195.

      [4] Szebehely V (1967), Theory of Orbits, Academic press, New-York.

      [5] Markeev A P (1978), Libration points in celestial mechanics and cosmic dynamics, NAUKA Moscow, 312.

      [6] Grebnikov E A (1964), On the stability of the Lagrangian triangle solutions of the restricted elliptic three body problem, Soviet Astronomy,8, No.3, 567-578.

      [7] Grebnikov E A (1986), the methods of Averaging Applications, NAUKA, Moscow Revised.

      [8] Gyorgyey J (1985), on the non-linear motions around the elliptical restricted problem of three bodies, Celestial Mechanics and Dynamical Astronomy, 36, No.3, 281-285.https://doi.org/10.1007/BF01230741.

      [9] KumarV &ChoudharyRK (1990), Non-linear stability of the triangular libration points for the photogravitationalelliptic restrictedproblem of three bodies, Celestial Mechanics and Dynamical Astronomy, 48, No.4, 299-317.https://doi.org/10.1007/BF00049387.

      [10] Kumar S &Ishwar B (2009), Solutions of Generalized Photogravitational Elliptical Restricted ThreeBody Problem, AIP Conf.Proc, 1146,456.https://doi.org/10.1063/1.3183564.

      [11] MarkellosV V, PerdiosE &LabrapoulouP(1992), Linear stability of the triangular equilibrium points in the photogravitationalelliptic restrictedthree body problem, Astrophysics and Space Science ,194, 207-214.https://doi.org/10.1007/BF00643991.

      [12] ZimvoschikovA S &Thkai V N (2004), Instability of libration points and resonance phenomena in the photogravitationalellipticalrestricted three bodyproblem, Solar system research, 38(2), 155-163.https://doi.org/10.1023/B:SOLS.0000022826.31475.a7.

      [13] AmmarMK (2008), The effect of solar radiation pressure on the Lagrangian points in the elliptical restricted three body problem, Astrophysics and Space Science, 313 , 393-408.https://doi.org/10.1007/s10509-007-9709-z.

      [14] Singh, J &Aishetu U (2012a), Motion in the photogravitationalellipticrestrictedthree body problem under an oblate primary, Astronomical Journal, 143, No.5, 109.https://doi.org/10.1088/0004-6256/143/5/109.

      [15] Singh J &Aishetu U (2012b), On the stability of triangular points in the ellipticrestrictedthree bodies under the radiating and oblate Primaries, Astrophysics and Space Science ,341, 349-358.https://doi.org/10.1007/s10509-012-1109-3.

      [16] Narayan a&Usha T (2014), Stability of triangular equilibrium points in the elliptic restricted problem of three bodies with radiation and triaxial primaries, Astrophysics and Space Science, 351(1), 135-142.https://doi.org/10.1007/s10509-014-1818-x.

      [17] UshaT, NarayanA&Ishwar B (2014), Effects of radiation and triaxiality of primaries on triangular equilibrium points in elliptic restricted three body problem, Astrophysics and Space Science, 349(1), 151-164.https://doi.org/10.1007/s10509-013-1655-3.

      [18] F aAbd El-Salam (2015), Stability of Triangular equilibrium points in the elliptic restricted three body problem with oblate and triaxial Primaries, AstrophysSpaceSci, 357:15.https://doi.org/10.1007/s10509-015-2308-5.

      [19] IshwarB &Elipe A (2001), Secular Solutions at Triangular Equilibrium Point in the Generalized Photogravitational Restricted ThreeBody Problem, Astrophysics and Space Science, 277, No.3, 437-446.https://doi.org/10.1023/A:1012528929233.

      [20] Subbarao PV & Sharma R K (1975), A Note on the Stability of the Triangular points of Equilibrium in the Restricted-Three body problem, Astronomy and Astrophysics, 43,381-383.

      [21] KhannaM &Bhatnagar K B (1998), Existence and Stability of the 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.

  • Downloads

  • How to Cite

    Singh, N., & Narayan, A. (2017). Pulsating curves of zero velocity for infinitesimal mass around oblate and triaxial rigid body of triangular equilibrium points in elliptical restricted three body problem. International Journal of Advanced Astronomy, 5(1), 29-37. https://doi.org/10.14419/ijaa.v5i1.7025

    Received date: 2016-11-29

    Accepted date: 2017-01-01

    Published date: 2017-02-17