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Frequency Map and Global Dynamics in Planetary systems: Short Period Dynamics

Published online by Cambridge University Press:  26 May 2016

Philippe Robutel  and
Jacques Laskar
Philippe Robutel
Affiliation:
Astronomie et Systèmes Dynamiques, IMC, CNRS UMR 8028, 77 av Denfert-Rochereau, 75014, Paris, France
Jacques Laskar
Affiliation:
Astronomie et Systèmes Dynamiques, IMC, CNRS UMR 8028, 77 av Denfert-Rochereau, 75014, Paris, France

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Frequency Map Analysis (FMA) (Laskar, 1990, 1999) is a refined numerical method based on Fourier techniques which provide a clear representation of the global dynamics of multi-dimensional systems, which is very effective for systems of 3 degrees of freedom and more, and was applied to a large class of dynamical systems. FMA requires only a very short integration time to obtain a measure of the diffusion of the trajectories, and allows to identify easily the location of the main resonances. Using this method, we have performed a complete analysis of massless particles in the Solar System (Robutel & Laskar 2001), from Mercury to the outer parts of the Kuiper belt (90 AU), for all values of the eccentricities, and several values for the inclinations. This provides a complete dynamical map of the Solar System, which is, in this first step, restricted to mean motion resonances. The dynamics of a planetary system which all the bodies have no zero mass can be studied with the same methods: an application to the JupiterSaturn system can be fined in (Robutel & Laskar 2002). We present here the application of this method to the understanding of the dynamics of the newly discovered v-Andromedae system.

Type
Part II: Progress in the theory of planet formation
Information
Symposium - International Astronomical Union , Volume 202: Planetary Systems in the Universe – Observation, Formation and Evolution , 2004 , pp. 235 - 237
Copyright
Copyright © Astronomical Society of the Pacific 2004 

References

Butler, P., Marcy, G., Fischer, D., Brown, T., Contos, A., Korzennik, S., Nisenson, P., & Noyes, R. 1999, ApJ, 526, 916.Google Scholar
Laskar, J. 1990, Icarus, 88, 266.Google Scholar
Laskar, J. 1999, in NATO ASI Hamiltonian Systems with Three or More Degrees of Freedom, Kluwer, Dordrecht, 134.CrossRefGoogle Scholar
Lissauer, J. 1999, Nature, 398, 659.Google Scholar
Robutel, P., & Laskar, J. 2001, Icarus, 152, 4.Google Scholar
Robutel, P., & Laskar, J. 2002, Dynamics of Natural and Artificial Celestial Bodies. Proceedings of the US/European Celestial Mechanics Workshop, held in Poznan, Poland, 3-7 July 2000, Pretka-Ziomek, H., Wnuk, E., Seidelmann, P. K., and Richardson, D. Eds., Kluwer Academic Publishers, p. 253.Google Scholar