Abstract
This paper investigates the stability of equilibrium points in the restricted three-body problem, in which the masses of the luminous primaries vary isotropically in accordance with the unified Meshcherskii law, and their motion takes place within the framework of the Gylden–Meshcherskii problem. For the autonomized system, it is found that collinear and coplanar points are unstable, while the triangular points are conditionally stable. It is also observed that, in the triangular case, the presence of a constant κ, of a particular integral of the Gylden–Meshcherskii problem, makes the destabilizing tendency of the radiation pressures strong. The stability of equilibrium points varying with time is tested using the Lyapunov Characteristic Numbers (LCN). It is seen that the range of stability or instability depends on the parameter κ. The motion around the equilibrium points L i (i=1,2,…,7) for the restricted three-body problem with variable masses is in general unstable.
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References
AbdulRaheem, A., Singh, J.: Astron. J. 131, 1880 (2006)
Bekov, A.A.: Astron. Z. 65, 202 (1988)
Chetaev, N.G.: Stability of Motion. GITTL, Moscow (1955)
Gasanov, S.A.: Astron. Lett. 34, 179 (2008)
Gel’fgat, B.E.: Modern Problems of Celestial Mechanics and Astrodynamics. Nauka, Moscow (1973), p. 7
Gylden, H.: Astron. Nachr. 109, 1 (1884)
Jeans, J.H.: Astronomy and Cosmogony. Cambridge University Press, Cambridge (1928)
Lu, T.-W.: Publ. Purple Mt. Obs. 9, 290 (1990)
Luk’yanov, L.G.: Astron. Z. 66, 180 (1989)
Luk’yanov, L.G.: Astron. Z. 67, 167 (1990)
Lyapunov, A.M.: A General Problem of Stability of Motion. Acad. Sci. USSR, Moscow (1956)
Maklin, J.G.: Theory of the Stability of Motion. Editorial URSS, Moscow (2004)
Meshcherskii, I.V.: Studies on the Mechanics of Bodies of Variable Mass. GITTL, Moscow (1949)
Meshcherskii, I.V.: Works on the Mechanics of Bodies of Variable Mass. GITTL, Moscow (1952)
Minglibaev, M.J.: Questions of Celestial Mechanics and Stellar Dynamics. Nauka Kazakh SSR, Alma-Ata (1990), p. 36
Orlov, A.A.: Astron. J. Acad. Sci. Moscow 16, 52 (1939)
Poincaré, H.: Leçons sur les Hypothésis Cosmogoniques (1911)
Radzievskii, V.V.: Astron. J. 27, 249 (1950)
Radzievskii, V.V.: Astron. Z. 30, 225 (1953)
Singh, J.: Indian J. Pure Appl. Math. 32, 335 (2003)
Singh, J.: Astrophys. Space Sci. 321, 127 (2009)
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)
Szebehely, V.: Theory of Orbits: The Restricted Problem of Three Bodies. Academic Press, San Diego (1967a)
Szebehely, V.: Astron. J. 72, 7 (1967b)
Tran, T.L.: Agriensis. Sect. Math. 26, 87 (1999)
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Singh, J., Leke, O. Stability of the photogravitational restricted three-body problem with variable masses. Astrophys Space Sci 326, 305–314 (2010). https://doi.org/10.1007/s10509-009-0253-x
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DOI: https://doi.org/10.1007/s10509-009-0253-x