Abstract
In the previously published (1977a) Part I of the paper, the author has constructed a formal long-periodic solution for the case of 1:1 resonance in the restricted problem of three bodies. Here the accuracy of the solution is carried fromO(m) toO(m 3/2), wherem is the mass parameter of the system.
Asymptotic approximations for the period of the motion are obtained for the case of small oscillations about the Lagrangian pointL 4, in agreement with the classical theory, and for the vicinity of a logarithmic singularity on themean separatrix, passing throughL 3. The regularizing function ψ(λ), which removes the singularities of the Poincaré type, is extended to all orders, and the result is used to prove the periodicity of the solution.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Brown, E. W.: 1911,Monthly Notices Roy. Astron. Soc. 71, 438.
Deprit, A. and Henrard, J.: 1970, in G. E. O. Giacaglia (ed.),Periodic Orbits, Stability, and Resonances, D. Reidel Publ. Co., Dordrecht, p. 1.
Garfinkel, B.: 1973,Celest. Mech. 8, 25 (Paper VII).
Garfinkel, B.: 1976,Celest. Mech. 13, 229 (Paper X).
Garfinkel, B.: 1977a,Astron. J. 82, 368 (Paper XI).
Garfinkel, B.: 1977b,Bull. Am. Astron. Soc. 9, 437 (abstract).
Garfinkel, B., Jupp, A. H., and Williams, C. A.: 1971,Astron. J. 76, 157 (Paper II).
Hori, G.: 1966,Publ. Astron. Soc. Japan 18, 287.
Iszak, I.: 1962, S.A.O. Special Report 90.
Jupp, A.H.: 1968, Private communication.
Jupp, A. H.: 1973,Celest. Mech. 8, 213.
Poincaré, H.: 1893,Les Méthodes Nouvelle de la Mécanique Céleste 2, 206, Dover (1957).
Szebehely, V.: 1967,Theory of Orbits, Academic Press.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Garfinkel, B. Theory of the Trojan asteroids Part II. Celestial Mechanics 18, 259–275 (1978). https://doi.org/10.1007/BF01230167
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01230167