Abstract
The determination of the maximum Lyapunov exponents in the 2/1 and 3/2 Jovian resonances (Ferraz-Mello 1994) suggested that the chaotic diffusion in the 2/1 resonance may be much faster than in the 3/2. As this fact could explain why the primordial population of the 2/1 resonance was removed (forming the Hecuba gap) and the 3/2-population was kept (Hilda group), we have decided to evaluate the diffusion speed for a large number of initial conditions using the frequency map analysis of Laskar (1988) (see also: Laskar 1996), adapted for the particular problem of Jovian resonances (Nesvorý and Ferraz-Mello 1997a). The ‘diffusion maps’ were also computed for the 4/3 Jovian resonance as it is, due to its similarity to the 3/2 resonance, a potential candidate for stable motion.
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References
Bowell, E., Muinonen, K. and Wasserman, L. H. (1994) A public-domain asteroid orbit database, Asteroids, Comets, Meteors, editors: A. Milani et al., Kluwer, Dordrecht, pp. 477–481
Ferraz-Mello, S. (1994) Dynamics of the asteroidal 2/1 resonance, Astron. J. 108, pp. 2330–2337
Ferraz-Mello, S. and Michtchenko, T. A. (1997) Orbital evolution of asteroids in the Hecuba gap, The Dynamical Behavior of Our Planetary System, editors: R. Dvorak et al., Kluwer, Dordrecht
Henrard, J. (1990) A semi-numerical perturbation method for separable hamiltonian systems, Celest. Mech. 49, pp. 43–68
Henrard, J., Watanabe, N. and Moons, M. (1995) A bridge between secondary and secular resonances inside the Hecuba gap, Icarus 115, pp. 336–346
Laskar, J. (1988) Secular evolution of the solar system over 10 million years, Astron. A stroph ys. 198, pp. 341–362
Laskar, J. (1996) Introduction to frequency map analysis, Proceedings of the NATO Advanced Study Institute 3DHAM95, Kluwer, Dordrecht, in press
Michtchenko, T. A. and Feraz-Mello, S. (1997) Escape of asteroids from the Hecuba gap, Planetary and Space Science, submitted
Morbidelli, A. (1996) The Kirkwood gap at the 2/1 commensurability with Jupiter: new numerical results, Astron. J. 111, pp. 2453–2461
Morbidelli, A. and Moons, M. (1993) Secular resonances in mean motion commensurabilities: the 2/1 and 3/2 cases, Icarus 102, pp. 316–332
Nesvorný, D. and Ferraz-Mello, S. (1997a) Chaotic diffusion in the 2/1 asteroidal resonance, Astron. Astrophys. 320, pp. 672–680
Nesvorný, D. and Ferraz-Mello, S. (1997b) On the asteroidal population of the first-order jovian resonances, Icarus, in press
Quinlan, G. D. and Tremaine, S. (1990) Symmetric multistep methods for the numerical integration of planetary orbits, Astron. J. 100, pp. 1694–1700
Quinn, T. R., Tremaine, S. and Duncan, M. (1991) A three million year integration of the Earth’s orbit, Astron. J. 101, pp. 2287–2305
Šidlichovský, M. and Nesvorný, D. (1997) Frequency modified Fourier transform and its application to asteroids, Cel. Mech. and Dyn. Astron. 65, pp. 137–148
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© 1999 Springer Science+Business Media Dordrecht
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Nesvorný, D., Ferraz-Mello, S. (1999). Chaotic Diffusion in the 2/1, 3/2 and 4/3 Jovian Resonances. In: Steves, B.A., Roy, A.E. (eds) The Dynamics of Small Bodies in the Solar System. NATO ASI Series, vol 522. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9221-5_4
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DOI: https://doi.org/10.1007/978-94-015-9221-5_4
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