Effect of elliptic angle φ on the existence and stability of libration points in restricted three-body problem in earth-moon system considering earth as an ellipsoid

  • Authors

    • M Javed Idrisi School of Physical and Molecular SciencesDepartment of MathematicsAl-Falah UniversityFaridabad (Haryana) - 121004
    • Muhammad Amjad School of Physical and Molecular SciencesDepartment of MathematicsAl-Falah UniversityFaridabad (Haryana) - 121004
    2015-10-09
    https://doi.org/10.14419/ijaa.v3i2.5313
  • Restricted Three-Body Problem, Libration Points, Linear Stability, Elliptic Integrals, Newton-Raphson Method.

  • This paper deals with the existence and the stability of the earth-moon libration points in the restricted three-body problem. In this paper we have considered the bigger primary as an ellipsoid while the smaller one as a point-mass. This is observed that the collinear and non-collinear libration points exist only in the interval 0Ëš<φ < 45Ëš. There exist three collinear libration points and the non-collinear libration points are forming a right triangle with the primaries. Further observed that the libration points either collinear or non-collinear all are unstable in 0Ëš<φ < 45Ëš.

  • References

    1. [1] Abouelmagd, E. I., Asiri, H. M., Sharaf, M. A., 2013. “The effect of oblateness in the perturbed restricted three-body problemâ€, Meccanica, vol. 48 (10), p. 2479-2490.http://dx.doi.org/10.1007/s11012-013-9762-3.

      [2] Byrd, P. F. & Friedman, M. D., 1954. “Handbook of Elliptic Integrals for Engineers and Physicistsâ€, Springer-Verlag, Germany, p. 4-5.http://dx.doi.org/10.1007/978-3-642-52803-3.

      [3] Idrisi, M. Javed, Taqvi, Z. A., 2013. “Restricted three-body problem when one of the primaries is an ellipsoidâ€, Astrophysics and Space Science, vol. 348 (1), p. 41-56.http://dx.doi.org/10.1007/s10509-013-1534-y.

      [4] Idrisi, M. Javed, Taqvi, Z. A., 2014. “Existence and stability of the non-collinear libration points in the restricted three body problem when both the primaries are ellipsoidâ€, Astrophysics and Space Science, vol. 350 (1), p. 133-141.http://dx.doi.org/10.1007/s10509-013-1718-5.

      [5] Idrisi, M. Javed, 2014. “Existence and stability of libration points in CR3BP when the smaller primary is an oblate spheroidâ€, Astrophysics and Space Science, http://dx.doi.org/10.1007/s10509-014-2031-7.

      [6] Khanna, M. & Bhatnagar, K. B., 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 spheroidâ€, Indian Journal of Pure and Applied Mathematics, vol. 30 (7), p. 721-733.

      [7] Kumari, Reena, Kushvah, Badam Singh, 2014. “Stability regions of equilibrium points in restricted four-body problem with oblateness effectsâ€, Astrophysics and Space Science, vol. 349 (2), p. 693-704.http://dx.doi.org/10.1007/s10509-013-1689-6.

      [8] Narayan, A., Kumar, C. Ramesh, 2011, “Effects of photogravitational and oblateness on the triangular lagrangian points in the elliptical restricted three body problemâ€, International Journal of Pure and Applied Mathematics, vol. 68(2), p. 201-224.

      [9] Raheem, Abdul Razzaq Abdul, Singh, Jagdish, 2006, “Combined effects of perturbations, radiation and oblateness on the stability of equilibrium points in the restricted three-body problemâ€, The Astronomical Journal, vol. 131, p. 1880-1885.http://dx.doi.org/10.1086/499300.

      [10] Singh, Jagdish, Taura, J. J., 2013. “Motion in the generalized restricted three-body problemâ€, Astrophysics and Space Science, vol. 343 (1), p. 95-106.http://dx.doi.org/10.1007/s10509-012-1225-0.

      [11] Szebehely, Victor, 1967. “Theory of Orbits, The restricted problem of three bodiesâ€, Academic Press, New York and London.

  • Downloads

  • How to Cite

    Idrisi, M. J., & Amjad, M. (2015). Effect of elliptic angle φ on the existence and stability of libration points in restricted three-body problem in earth-moon system considering earth as an ellipsoid. International Journal of Advanced Astronomy, 3(2), 87-96. https://doi.org/10.14419/ijaa.v3i2.5313