Trajectories of the infinitesimal mass around the triangular equilibrium points in elliptical restricted three bodies problem under oblate and radiating primaries for the binary systems

  • Authors

    • Nutan Singh
    • Ashutosh Narayan Bhilai Institute of Technology, Durg
    • B. Ishwar
    2015-10-23
    https://doi.org/10.14419/ijaa.v3i2.5304
  • Radiation Pressure, Triangular Points, Oblateness Parameters, Trajectory of Infinitesimal Stability.

  • Abstract

    This paper describes the trajectory of the infinitesimal mass around L4 of the triangular equilibrium points for the binary systems in the elliptical restricted three body’s problem (ERTBP), where both oblate primaries are radiating. The solutions for the perturbed motion in the vicinity of L4 is given by u(f) and v(f) function .The stability of the infinitesimal mass around the triangular points is also studied by plotting u(f) and v(f) curve. It is found that radiation pressure, oblateness and eccentricity show a significant effect on the trajectory and stability of the infinitesimal mass around the triangular equilibrium points. Simulation technique has been used to design the trajectory of the binary systems (Achird, Luyten, α Cen AB, Kruger-60 and Xi-Bootis).

  • References

    1. [1] Ammar MK (2008), the effect of solar radiation pressure on the Lagrangian points in the elliptical restricted three body problem, Astrophysics & Space Science, 313, 393-408. http://dx.doi.org/10.1007/s10509-007-9709-z.

      [2] Danby, JMA (1964), Stability of the triangular points in the elliptic restricted problem of three bodies, Astronomical Journal, 69, 165-172. http://dx.doi.org/10.1086/109254.

      [3] Erdi B (2009), A parametric study of stability and resonance around L4 in the elliptical restricted three body problem, Celestial Mechanics and Dynamical Astronomy, 104,145- 158 http://dx.doi.org/10.1007/s10569-009-9197-2.

      [4] Grebenikov EA (1964), On the stability of the Lagrangian Triangular Solutions of the Restricted Elliptic Three Body problem, Soviet Astronomy, 8(3), 451-459.

      [5] Gyorgyey J (1985), on the nonlinear stability of motions around the elliptical restricted problem of three bodies, Celestial Mechanics and Dynamical Astronomy, 36(3), 281-285. http://dx.doi.org/10.1007/BF01230741.

      [6] Halan PP & Rana N (2001), The Existence and stability of equilibrium points in the Robe's restricted three body problem, Celestial Mechanics and Dynamical Astronomy, 79, 145-155. http://dx.doi.org/10.1023/A:1011173320720.

      [7] Kumar S & Ishwar B (2011) Location of collinear equilibrium points in the generalized photogravitational elliptical restricted three body problem, Int. Journal of Sciience & Technology, 3(2), 157-162.

      [8] Kumar V & Choudhary RK (1986), On the stability of the triangular libration points for the photogravitational circular restricted problem of three bodies when both of the attracting bodies are radiating as well, Celestial Mechanics, 40(2), 155-170 http://dx.doi.org/10.1007/BF01230257.

      [9] Markeev AP (1978), Libration points in celestial Mechanics and Cosmodynamics, nauka, Moscow, Russia.

      [10] Markellos VV, Perdios E & Labropoulou P (1992), Linear stability of the triangular equilibrium points in the phptogravitational elliptical restricted three body problem, Astrophysics & Space Science, 194, 207- 213. http://dx.doi.org/10.1007/BF00643991.

      [11] Narayan, A & Singh.N (2014a), Motion and stability of triangular equilibrium points in elliptical restricted three body problem under the radiating primaries , Astrophysics & Space Science, 352 (1) , 57-70. http://dx.doi.org/10.1007/s10509-014-1903-1.

      [12] Narayan, A., Singh.N. (2014c), Resonance stability of triangular equilibrium points in elliptical restricted three body problem under the radiating primaries, Astrophysics & Space Science, 353 (2) 441-455. http://dx.doi.org/10.1007/s10509-014-2085-6.

      [13] Narayan, A & Singh N (2014b), Stability of triangular lagrangian points in elliptical restricted three body problem under the radiating binary systems, Astrophysics & Space Science, 353 (2) 457-464. http://dx.doi.org/10.1007/s10509-014-2014-8.

      [14] Roberts G (2002), linear stability of the elliptic Lagrangian triangle solution in the three body problem, Differential equation, 182, 191-218.

      [15] Selaru D & Cucu-Dumitrescu C (1995), Infinitesimal orbit around Lagrange points in the elliptic restricted three body problem , Celestial Mechanics and Dynamical Astronomy, 61(4), 333- 346. http://dx.doi.org/10.1007/BF00049514.

      [16] Sharma, R.K., W.Frucke, G.Teleki. (1982), Sun and platenary system, Reidel Publishing company, 435.

      [17] Singh J & Umar A (2012a), Motion in the photogravitational elliptic restricted three-body problem under an oblate primary, Astronomical Journal, 143, 109. http://dx.doi.org/10.1088/0004-6256/143/5/109.

      [18] Singh J & Umar A, (2012b), on the stability of triangular equilibrium points in the elliptic R3BP under radiating and oblate primaries, Astrophysics & Space Science, 341, 349. http://dx.doi.org/10.1007/s10509-012-1109-3.

      [19] Subbarao,P.V.,Sharma R.K.: 1975, A note on the stability of the triangular points of the equilibrium in the restricted three body problem, Astron. Astrophys., 43.

      [20] Szebebely V (1967), Stability of the points of equilibrium in the restricted problem, Astronomical Journal, 72, 7-9. http://dx.doi.org/10.1086/110195.

      [21] Zimvoschikov AS & Thakai VN (2004), Instability of libration points and resonance phenomena in the photogravitational in the elliptical restricted three body problem, Solar System Research, 38 (2), 155-163. http://dx.doi.org/10.1023/B:SOLS.0000022826.31475.a7.

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  • How to Cite

    Singh, N., Narayan, A., & Ishwar, B. (2015). Trajectories of the infinitesimal mass around the triangular equilibrium points in elliptical restricted three bodies problem under oblate and radiating primaries for the binary systems. International Journal of Advanced Astronomy, 3(2), 107-116. https://doi.org/10.14419/ijaa.v3i2.5304

    Received date: 2015-09-09

    Accepted date: 2015-10-11

    Published date: 2015-10-23