Abstract
This paper examines the effect of a constant κ of a particular integral of the Gylden-Meshcherskii problem on the stability of the triangular points in the restricted three-body problem under the influence of small perturbations in the Coriolis and centrifugal forces, together with the effects of radiation pressure of the bigger primary, when the masses of the primaries vary in accordance with the unified Meshcherskii law. The triangular points of the autonomized system are found to be conditionally stable due to κ. We observed further that the stabilizing or destabilizing tendency of the Coriolis and centrifugal forces is controlled by κ, while the destabilizing effects of the radiation pressure remain unchanged but can be made strong or weak due to κ. The condition that the region of stability is increasing, decreasing or does not exist depend on this constant. The motion around the triangular points L 4,5 varying with time is studied using the Lyapunov Characteristic Numbers, and are found to be generally unstable.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
AbdulRaheem, A., Singh, J.: Astron. J. 131, 1880 (2006)
Bekov, A.A.: Sov. Astron. 32, 106 (1988)
Bekov, A.A.: Sov. Astron. 35, 103 (1991)
Bekov, A.A., Beysekov, A.N., Aldibaeva, L.T.: Astron. Astrophys. Trans. 24, 311 (2005)
Bhatnagar, K.B., Hallan, P.P.: Celest. Mech. 18, 105 (1978)
Bhatnagar, K.B., Chawla, J.M.: Indian J. Pure Appl. Math. 10, 1443 (1979)
Chetaev, N.G.: Stability of motion GITTL. Moscow (1952)
Devi, G.S., Singh, R.: Bull. Astron. Soc. India 22, 433 (1994)
El-Shaboury, S.M.: Astrophys. Space Sci. 174, 151 (1990)
Gasanov, S.A.: Astron. Lett. 34, 179 (2008)
Gel’fgat, B.E.: Modern Problems of Celestial Mechanics and Astrodynamics, p. 7. Nauka, Moscow (1973)
Gylden, H.: Astron. Nachr. 109, 1 (1884)
Lu, T.-W.: Publ. Purple Mt. Obs. 9, 290 (1990)
Luk’yanov, L.G.: Sov. Astron. 32, 682 (1988)
Luk’yanov, L.G.: Sov. Astron. 33, 92 (1989)
Luk’yanov, L.G.: Sov. Astron. 34, 87 (1990)
Lyapunov, A.M.: A General Problem of Stability of Motion. Acad. Sci. USSR, Moscow (1956)
Meshcherskii, I.V.: Works on the Mechanics of Bodies of Variable mass. GITTL, Moscow (1952)
MaLklin, J.G.: Theory of the Stability of Motion, (Editorial) Moscow (2004)
Orlov, A.A.: Astron. J. Acad. Sci. Mosc. 16, 52 (1939)
Poincaré, H.: Leçons sur les Hypothèsis Cosmogoniques (1911)
Radzievskii, V.V.: Astron. J. 27, 249 (1950)
Radzievskii, V.V.: Astron. Zh. 30, 225 (1953)
Singh, J., Ishwar, B.: Celest. Mech. 32, 297 (1984)
Singh, J., Ishwar, B.: Celest. Mech. 35, 201 (1985)
Singh, J., Ishwar, B.: Bull. Astron. Soc. India 27, 415 (1999)
Singh, J.: Astrophys. Space Sci. 321, 127 (2009)
Singh, J., Oni, L.: Astrophys. Space Sci. 326, 305 (2010)
Szebehely, V.G.: Theory of Orbits. Academic Press, New York (1967a)
Szebehely, V.: Astron. J. 72, 7 (1967b)
Wintner, A.: The Analytical Foundations of Celestial Mechanics, pp. 372–373. Princeton University Press, New Jersey (1941)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Singh, J., Leke, O. & Aishetu, U. Analysis on the stability of triangular points in the perturbed photogravitational restricted three-body problem with variable masses. Astrophys Space Sci 327, 299–308 (2010). https://doi.org/10.1007/s10509-010-0339-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10509-010-0339-5