Abstract
The effects of the “great inequality” (the quasi-resonance between Jupiter and Saturn) on the motion in the 2/1 mean motion resonance with Jupiter (the Hecuba gap) is investigated. We confirm the proposition made by Ferraz-Mello and collaborators that the great inequality generates secondary resonances which are likely to produce the slow diffusion observed in numerical investigations. We identify, in the restricted three body problem, the frequencies responsible for these secondary resonances.
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References
Ferraz-Mello, S.: 1994, ‘Dynamics of the asteroidal 2/1 resonance’, Astron. J., 108, 2330 – 2337.
Ferraz-Mello, S. and Klafke, J.: 1991, ‘A model for the study of very-highj eccentricity asteroidalmotion: the 3/1 resonance’. In Predictability, Stability and Chaos in N-Body Dynamical Systems ( Roy ed.), pages 177 – 184, Plenum Press, New-york.
Ferraz-Mello, S., Klafke, J., Michtchenko, T., and Nesvorny, N.: 1996, ‘Chaotic transitions in resonant asteroidal dynamics’, Celest. Mech., 64, 93 – 105.
Ferraz-Mello, S. and Michtchenko, T.: 1997, ‘Orbital evolution of asteroids in the Hecuba gap’. In The Dynamical Behaviour of our Planetary System ( Dvorak and Henrard eds.), pages 377 – 384, Kluwer A.P., Dordrecht.
Froeschlé, C. and Lega, E.: 1996, ‘On the measure of the structure around the last KAM torus before and after its break-up’, Celest. Mech., 64, 21 – 31.
Froeschlé, C. and Scholl, H.: 1976, ‘On the dynamical topology of the Kirkwood gaps’, Astron. Astrophys., 43, 389 - 393.
Giffen, R.: 1973, ‘A study of commensurable motion in the asteroid belt’, Astron. Astrophys., 23, 387 – 403.
Henrard, J., Watanabe, N., and Moons, M.: 1995, ‘A bridge between secondary and secularresonances inside the Hecuba gap’, Icarus, 115, 336 – 346.
Laskar, J.: 1993, ‘Frequency analysis for multi-dimensional systems; global dynamics and diffusion’, Physica D, 67, 257 – 281.
Lemaître, A. and Henrard, J.: 1990, ‘On the origin of chaotic behaviour in the 2/1 Kirkwood gap’, Icarus, 83, 391 – 409.
Levison, H. and Duncan, M.: 1994, ‘The long term dynamical behaviour of short-period comets’, Icarus, 108, 18 – 36.
Michtchenko, T. and Ferraz-Mello, S.: 1997, ‘Escape of asteroids from the Hecuba gap’. In Asteroids, Comets and Meteors 1996, in print.
Moons, M.: 1994, ‘Extended Schubart averaging’, Celest. Mech., 60, 173 – 286.
Moons, M.: 1997, ‘Review of the dynamics in the Kirkwood gaps’, Celest. Mech., 65, 175 – 204.
Moons, M. and Morbidelli, A.: 1995, ‘Secular resonances in mean motion commensurabilities: the 4/1,3/1,5/2 and 7/3 cases’, Icarus, 114, 33 – 50.
Morbidelli, A.: 1996, ‘The Kirkwood gap at the 2/1 commensurability with Jupiter: New numerical results’, Astron. J., 111, 2453 – 2461.
Morbidelli, A. and Moons, M.: 1993, ‘Secular resonances in mean motion commensurabilities: the 2/1 and 3/2 cases’, Icarus, 102, 316 – 332.
Morbidelli, A. and Moons, M.: 1995, ‘Numerical evidence on the chaotic nature of the 3:1 mean motion commensurability’, Icarus, 115, 60 – 65.
Wisdom, J.: 1985, ‘A perturbative treatment of motion near the 3/1 commensurability’, Icarus, 63, 272 – 289.
Wisdom, J.: 1987, ‘Urey prize lecture: Chaotic dynamics in the Solar system’, Icarus, 72, 241 – 275.
Nesvornÿ, D. and Ferraz-Mello, S.: 1997, ‘On the asteroidal population of the first-order jovian resonances’, Icarus, in print.
Wisdom, J.: 1983, ‘Chaotic behaviour and the origin of the 3/1 Kirkwood gap’, Icarus, 56, 51 – 74
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© 1998 Springer Science+Business Media Dordrecht
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Henrard, J. (1998). The Effect of the Great Inequality on the Hecuba GAP. In: Yabushita, S., Henrard, J. (eds) Dynamics of Comets and Asteroids and Their Role in Earth History. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1321-4_14
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DOI: https://doi.org/10.1007/978-94-017-1321-4_14
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5081-6
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