Abstract
This paper studies the stability of Triangular Lagrangian points in the model of elliptical restricted three body problem, under the assumption that both the primaries are radiating. The model proposed is applicable to the well known binary systems Achird, Luyten, αCen AB, Kruger-60, Xi-Bootis. Conditional stability of the motion around the triangular points exists for 0≤μ≤μ∗, where μ is the mass ratio. The method of averaging due to Grebenikov has been exploited throughout the analysis of stability of the system. The critical mass ratio depends on the combined effects of radiation of both the primaries and eccentricity of this orbit. It is found by adopting the simulation technique that the range of stability decreases as the radiation pressure parameter increases.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ammar, M.K.: Astrophys. Space Sci. 313, 393–408 (2008)
Bennet, A.: Icarus 4, 177–187 (1965)
Conxita, P.: Celest. Mech. Dyn. Astron. 61, 315–331 (1995)
Danby, J.: Astron. J. 69, 165–172 (1964)
Erdi, B.: Celest. Mech. Dyn. Astron. 104, 145–158 (2009)
Floria, L.: Monografsen. Mat. Caracia De Galdeano 31, 135–144 (2004)
Grebenikov, E.A.: The Methods of Averaging Applications. Nauka, Moscow (1986). Revised
Gyorgyey, J.: Celest. Mech. Dyn. Astron. 36(3), 281–285 (1985)
Halan, P.P., Rana, N.: Celest. Mech. Dyn. Astron. 79, 145–155 (2001)
Khasan, S.N.: Cosm. Res. 34(2), 146–151 (1996a)
Khasan, S.N.: Cosm. Res. 34(5), 299–317 (1996b)
Kumar, S., Ishwar, B.: AIP Conf. Proc., vol. 1146, p. 456 (2009)
Kumar, S., Ishwar, B.: Int. J. Eng. Sci. Tech. 3(2), 157–162 (2011)
Kumar, V., Choudhary, R.K.: Celest. Mech. Dyn. Astron. 48(4), 299–317 (1990)
Markeev, A.P.: J. Appl. Math. Mech. 33, 105–110 (1966)
Markeev, A.P.: Astron. Lett. 31(5), 300–356 (2005)
Markellos, V.V., Perdios, E., Labropoulou, P.: Astrophys. Space Sci. 194, 207–213 (1992)
Narayan, A., Singh, N.: Astrophys. Space Sci. (2014). doi:10.1007/s10509-014-1903-1
Narayan, A., Usha, T.: Astrophys. Space Sci. (2014). doi:10.1007/s10509-014-1818-x
Rabe, E.: In: Recent Advances in Dynamical Astronomy, pp. 155–160 (1973)
Roberts, G.: Differ. Equ. 182, 191–218 (2002)
Selaru, D., Cucu-Dumitreacu, C.: Celest. Mech. Dyn. Astron. 61(4), 333–346 (1995)
Singh, J., Umar, A.: Astron. J. 143, 109 (2012a)
Singh, J., Umar, A.: Astrophys. Space Sci. 341, 349 (2012b)
Szebebely, V.: Theory of Orbits. Academic Press, New York (1967)
Usha, T., Narayan, A., Ishwar, B.: Astrophys. Space Sci. 349, 151–164 (2014)
Zimvoschikov, A.S., Thakai, V.N.: Sol. Syst. Res. 38(2), 155–163 (2004)
Acknowledgements
The authors acknowledge and are grateful to the reviewer; his comments have greatly improved the paper.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Narayan, A., Singh, N. Stability of triangular lagrangian points in elliptical restricted three body problem under the radiating binary systems. Astrophys Space Sci 353, 457–464 (2014). https://doi.org/10.1007/s10509-014-2014-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10509-014-2014-8