Characteristics exponents of the triangular solution in the elliptical restricted three-body problem under radiating and triaxial primaries

 
 
 
  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract


    This Paper deals with the effects of the radiation pressure and triaxiality of primaries on the stability of infinitesimal motion about triangular equilibrium points [ , ] in the elliptical restricted three body problem (ER3EB) around binary system. For determining the characteristic exponents of variational equations with periodic coefficient, we have used analytical method, described by Bennet in [3, 4]. This analytical method is based on Floquet’s theory. The stability of equilibrium points has been discussed under the assumption thatboth the primaries are radiating and triaxial. For this we have drawn transition cureves in μ-e plane. And it is seen that system is stable outside the transition curves, while system is Unstable within the transition curves.


  • Keywords


    ER3BP; Dynamical System Libration Points; Flouqet Theory.

  • References


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

      [2] Alfriend, K.T., Rand, R. H.: Stability of the triangular points in the elliptic restricted problem of three bodies. AIAAJ 6, 1024(1969)https://doi.org/10.2514/3.5270.

      [3] Bennet, A.: In Astrodynamicssecialist Conference. Monetary, California. 101 (1965)

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

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

      [6] Deprit, A., Rom, A.: Characteristics exponents at L4 in the elliptic restricted problem. Astron. Astrphysc.5, 416-425(1970)

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

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

      [9] Kumar, S., Ishwar B.: Location of collinear equilibrium points in the generalized photogravitational elliptic restricted three body problem. Int.J.Eng. Sci. Tech.3 (2), 157-162 (2011)https://doi.org/10.4314/ijest.v3i2.68143.

      [10] Kumar, V., Choudhary , R. K.,Non-linear stability of the triangular libration points for the photogravitational elliptic restricted problem of three bodies, Celestial Mechanics and Dynamical Astronomy,48, No.4, 299-317(1990)https://doi.org/10.1007/BF00049387.

      [11] Markellos, V. V., Perdios, E., Labrapoulou, P., Linear stability of the triangular equilibrium points in the photogravitational elliptic restricted three body problem, Astrophysics and Space Science ,194, 207-214(1992)https://doi.org/10.1007/BF00643991.

      [12] Moulton, F.R.: On the stability of direct and retrograde orbits. Astron. Soc. 75, 40-57 (1914)https://doi.org/10.1093/mnras/75.2.40.

      [13] Narayan, A., Kumar, C.R. Effects of photogravitational and oblateness on the Triangular Lagrangian points in the Elliptical Restricted three body problem, Indian Journal of Pure and Applied Mathematics,68, No.2, 201-224(2011)

      [14] Narayan, A., Singh, N.: Motion and stability of triangular equilibrium points in elliptical restricted three body problem under the radiating primaries. Astrophys. Space Sci.352 (1), 57-70 (2014)https://doi.org/10.1007/s10509-014-1903-1.

      [15] Narayan, A., Usha, T., 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(2014)https://doi.org/10.1007/s10509-014-1818-x.

      [16] Narayan,A., Singh, N.: Stability of triangular points in elliptical restricted three body problem under the radiating binary system . Astrophys. Space Sci. doi: 10.1007/s 10509-014-2014-8

      [17] Narayan,A., Pandey, K.K and Shrivastava,S.K.: Effects of radiation and triaxiality of triangular equilibrium points in elliptical restricted three body problem. International Journal of Advanced Astronomy 3(2), 97-106 (2015).https://doi.org/10.14419/ijaa.v3i2.5302.

      [18] Singh, J., Aishetu, U., Motion in the photogravitational elliptic restricted three body problem under an oblate primary, Astronomical Journal, 143, No.5, 109(22pp)(2012)

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

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

      [21] Usha, T., Narayan, A., Ishwar, B., 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(2014)https://doi.org/10.1007/s10509-013-1655-3.

      [22] Zimvoschikov, A.S., Thkai, V.N., Instability of libration points and resonance phenomena in the photogravitational elliptical restricted three body problem, Solar system research, 38, No.2, 155-163(2004).https://doi.org/10.1023/B:SOLS.0000022826.31475.a7.


 

View

Download

Article ID: 7114
 
DOI: 10.14419/ijaa.v5i1.7114




Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.