Location of triangular equilibrium points in the perturbed CR3BP with laser radiation pressure and oblateness

  • Authors

    • Nabawia Khalifa 1 Department of Basic Science, Deanship of Preparatory Year, University of Hail, Hail, KSA2 Sun and Space researches lab, National Institute of Astronomy and Geophysics (NRIAG), Helwan Egypt.
    2018-04-30
    https://doi.org/10.14419/ijaa.v6i1.9641
  • Perturbed CR3BP- Laser Radiation Pressure-Triangular Points.

  • Abstract

    This paper represents a semi-analytical study of the effect of ground-based laser radiation pressure on the location of triangular points in the framework of the planar circular restricted three-body problem (CR3BP). The formulation includes both the effects of oblateness of J2 in addition to laser radiation pressure, where laser’s disturbing function expanded in Legendre polynomials up to the first order. Earth-Moon system is considered in which a laser station is located on Earth and sends laser beams toward the infinitesimal body. The model takes into account the effect of Earth's atmosphere on laser beam propagation. The numerical application emphasis that the location of the triangular points affected by the considered perturbations.

  • References

    1. [1] Danby J M A (1996). Fundamentals of Celestial Mechanicsâ€, New York: Macmillan.

      [2] Szebehely, V. (1967) Theory of Orbits: The Restricted Problem of Three Bodies. Academic Press, New York.

      [3] Bocalletti D and Pucacco G (1996) Theory of Orbits 1: Integrable Systems and Non-Perturbative Methods.Springer. https://doi.org/10.1007/978-3-662-03319-7.

      [4] Simmons J F L, McDonald A J C, and Brown J C. (1985) THE RESTRICTED 3-BODY PROBLEM WITH RADIATION PRESSUREâ€, Celestial Mechanics, vol. 35, 145-187. https://doi.org/10.1007/BF01227667.

      [5] Chernikov Y.A. (1970) The Photogravitational Restricted Three-body Problem. Soviety Astronomy Astrophysics, vol. 14, no. 1, pp. 176 -181.

      [6] Radzievskii V.V. (1950) the restricted problem of three-bodies taking account of light pressure. Astronomy Journal volume 27, 250–256.

      [7] Elbaz I Abouelmagd and Juan L.G. Guirao (2016) on the perturbed restricted three-body problem. Applied Mathematics and Nonlinear science 1(1), 123 – 144. https://doi.org/10.21042/AMNS.2016.1.00010.

      [8] K. Zahra, M. Radwan and M.E. Awadc (2016). On the location of triangular points of the elliptic restricted three-body problem with triaxial and oblate primaries. Journal of nonlinear and differential equations, Vol. 4, No. 13, 609 – 617. https://doi.org/10.12988/nade.2016.6863.

      [9] Ibnu Nurul Huda and Budi Dermawan (2016) The locations of triangular equilibrium points in elliptic restricted three-body problem under the oblateness and radiation Effects. Journal of Physics: Conference Series Volume 771, Number 1. https://doi.org/10.1088/1742-6596/771/1/012052.

      [10] Jagadish Singh (2013). The equilibrium points in the perturbed R3BP with triaxial and luminous primaries, Astrophys Space Sci, Vol. 346, 41 – 50. https://doi.org/10.1007/s10509-013-1420-7.

      [11] Kumar R C and Narayan A (2012). Existence and stability of collinear equilibrium points in elliptic restricted three body problem under the effect of photo gravitational and oblateness primariesâ€, International Journal of Pure and Applied Mathematics Volume 80, 477-494.

      [12] Singh J and Umar (2012) Motion in the Photogravitational Elliptic Restricted Three-Body Problem under an Oblate Primary. The Astronomical Journal, 143, 109-131. https://doi.org/10.1088/0004-6256/143/5/109.

      [13] Nabawia S. Khalifa (2009). Effect of an Artificial Radiant Force on the Spacecraft’s Orbit. Phd. Thesis, Cairo university.

      [14] El-Saftawy, M.I., Abd El-Hameed, Afaf M., Khalifa, N.S. (2007). Analytical Studies of Laser Beam Propagation through the Atmosphere. Proceeding of 6th International Conference on Laser Science and Applications (ICLAS-07), Cairo, Egypt.

      [15] Danielson, E., Levin, J., Abrams, E. (2003). Meteorology, second edâ€, McGraw-Hill Companies.

      [16] Prilutsky O.F. and Fomenkova M.N. (1990). Appendix laser beam scattering in the atmosphere. Science & Global Security Volme 2, 79 – 86. https://doi.org/10.1080/08929889008426349.

      [17] Escobal, P.R. (1965). Methods of Orbit Determination. John Wiley and Sons Inc., New York, London, Sydney.

  • Downloads

  • How to Cite

    Khalifa, N. (2018). Location of triangular equilibrium points in the perturbed CR3BP with laser radiation pressure and oblateness. International Journal of Advanced Astronomy, 6(1), 8-11. https://doi.org/10.14419/ijaa.v6i1.9641

    Received date: 2018-02-20

    Accepted date: 2018-03-29

    Published date: 2018-04-30