Abstract
The stability of satellites in spin-orbit resonances is investigated in the light of perturbation theory. By means of KAM theory we construct invariant surfaces trapping the periodic orbit associated to the resonance in a finite region of the phase space. In the last part of the work we study the probability of capture in a resonance, providing an explicit application to Mercury.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arnold V.I., Proof of a Theorem by A.N, Kolmogorov on the invariance of quasi- periodic motions under small perturbations of the Hamiltonian, Russ. Math. Surveys 18, 9 (1963)
Celletti A., Analysis of resonances in the spin-orbit problem in Celestial Mechanics: The synchronous resonance (Part I), J. of Appl. Math, and Phys. (ZAMP) 41, 174 (1990)
Celletti A., Analysis of resonances in the spin-orbit problem in Celestial Mechanics: Higher order resonances and some numerical experiments (Part II), J. of Appl. Math, and Phys. (ZAMP) 41, 453 (1990)
Celletti A., Chierchia L., Construction of analytic KAM surfaces and effective stability bounds, Commun. Math. Phys. 118, 119 (1988)
Celletti A., Falcolini C., work in progress
Danby J.M.A., Fundamentals of Celestial Mechanics Macmillan, New York (1962)
De La Llave R., Rana D., Accurate strategies for KAM bounds and their implementation, preprint
Goldreich P., Peale S., Spin-orbit coupling in the solar system Astron. J. 71, 425 (1966)
Greene J.M., A method for determining a stochastic transition J. of Math. Phys. 20, 1183 (1979)
Henrard J., Spin-orbit resonance and the adiabatic invariant in: "Resonances in the Motion of Planets, Satellites and Asteroids", S. Ferraz-Mello and W. Sessin eds., Sao Paulo, 19 (1985)
Kolmogorov A.N., On the conservation of conditionally periodic motions under small perturbation of the Hamiltonian, Dokl. Akad. Nauk. SSR 98, 469 (1954)
Mather J.N., Nonexistence of invariant circles. Erg. theory and dynam. systems 4, 301 (1984)
Moser J., On invariant curves of area-preserving mappings of an annulus Nach. Akad. Wiss. Göttingen, Math. Phys. Kl. II 1, 1 (1962)
Wisdom J., Chaotic behaviour in the solar system Proc. R. Soc. Lond. A413, 109 (1987)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Plenum Press, New York
About this chapter
Cite this chapter
Celletti, A. (1991). Stability of Satellites in Spin-Orbit Resonances and Capture Probabilities. In: Roy, A.E. (eds) Predictability, Stability, and Chaos in N-Body Dynamical Systems. NATO ASI Series, vol 272. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-5997-5_28
Download citation
DOI: https://doi.org/10.1007/978-1-4684-5997-5_28
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4684-5999-9
Online ISBN: 978-1-4684-5997-5
eBook Packages: Springer Book Archive