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Kirkwood Gaps and Resonant Groups

Published online by Cambridge University Press:  19 July 2016

Sylvio Ferraz-Mello*
Affiliation:
Instituto Astronômico e Geofísico, Universidade de São Paulo, Caixa Postal 9638, São Paulo, SP, Brasil. E-mail SYLVIO@IAG.USP.ANSP.BR

Abstract

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This paper is a short review of the dynamics of the asteroidal resonances as currently determined from maps and simulations over 106 – 107 years. The main recent results concern the extensive exploration of the phase space to determine domains of initial conditions leading to close approaches to the inner planets, the topological dynamics of the planar Sun-Jupiter-asteroid problem at very high eccentricities and the differences amongst 2/1 and 3/2 resonances able to explain the existence of a gap in the asteroidal belt at the 2/1 resonance and of a group of asteroids in the 3/2 resonance. Current results point to a confirmation of Wisdom's theory for the formation of the gaps by gravitational evolution and scattering by the inner planets.

Type
Dynamics
Copyright
Copyright © Kluwer 1994 

References

Efemeridi Malikh Planet na 1994 god (EMP 1994), Inst. Teoret. Astron., St. Peterburg, Russia (1993).Google Scholar
Ferraz-Mello, S.: 1988, “The high-eccentricity libration of the Hildas”. Astron. J. 96, 400408.Google Scholar
Ferraz-Mello, S.: 1994, “The convergence domain of the Laplacian expansion of the disturbing function”. Celest. Mech. Dyn. Astron. 58.Google Scholar
Ferraz-Mello, S. and Klafke, J.C.: 1991, “A model for the study of very-high-eccentricity asteroidal motion. The 3: 1 resonance”. In Predictability, Stability and Chaos in N-Body Dynamical Systems (Roy, A. E., ed.), Plenum Press, New York, 177184.Google Scholar
Franklin, F., Lecar, M. and Murison, M.: 1993, “Chaotic orbits and long-term stability: an example from asteroids of the Hilda group”. Astron. J. 105, 23362343.Google Scholar
Froeschlé, C. and Greenberg, R.: 1989, “Mean-motion resonances”. In Asteroids II (Binzel, R. P. et al., eds.), Univ. Arizona Press, Tucson, 827844.Google Scholar
Froeschlé, C. and Scholl, H.: 1976, “On the dynamical topology of the Kirkwood gaps”. Astron. Astrophys. 48, 389393.Google Scholar
Froeschlé, C. and Scholl, H.: 1981, “The stochasticity of peculiar orbits in the 2/1 Kirkwood gap”. Astron. Astrophys. 93, 6266.Google Scholar
Froeschlé, Ch. and Scholl, H.: 1986, “The secular resonance ν6 in the asteroidal belt”. Astron. Astrophys. 166, 326332.Google Scholar
Giffen, R.: 1973, “A study of commensurable motion in the asteroidal belt”. Astron. Astrophys. 23, 387403.Google Scholar
Hadjidemetriou, J.: 1992, “The elliptic restricted problem at the 3: 1 resonance”. Celest. Mech. Dyn. Astron. 53, 151183.Google Scholar
Henrard, J.: 1988, “Resonances in the planar restricted elliptic problem”. In Long-term Dynamical Behaviour of Natural and Artificial N-Body Systems (Roy, A. E., ed.), Plenum Press, New York, 405425.Google Scholar
Henrard, J. and Caranicolas, N.: 1990, “Motion near the 3/1 resonance of the planar elliptic restricted three body problem”. Celest. Mech. Dynam. Astron. 47, 99121.Google Scholar
Henrard, J. and Lemaître, A.: 1987, “A perturbative treatment of the 2/1 jovian resonance”. Icarus 69, 266279.Google Scholar
Ipatov, S.I.: 1990, “Variations in orbital eccentricities of asteroids near the 5: 2 resonance”. Sov. Astron. Letters 15, 324328.Google Scholar
Ipatov, S.I.: 1992, “Evolution of asteroidal orbits at the 5: 2 resonances”. Icarus 95, 100114; 97, 309.Google Scholar
Klafke, J.C., Ferraz-Mello, S. and Michtchenko, T.: 1992 “Very-high-eccentricity librations at some higher-order resonances”. In IAU Symposium 152 (Ferraz-Mello, S., ed.), Kluwer, Dordrecht, 153158.Google Scholar
Lemaître, A. and Henrard, J.: 1988, “The 3/2 resonance”. Celest. Mech. 43, 9198.Google Scholar
Lemaître, A. and Henrard, J.: 1990, “Origin of the chaotic behaviour in the 2/1 Kirkwood gap”. Icarus 83, 391409.CrossRefGoogle Scholar
Michtchenko, T.A.: 1993, Dr. Thesis, University of São Paulo.Google Scholar
Michtchenko, T.A. and Ferraz-Mello, S.: 1993, “The high-eccentricity libration of the Hildas. II. Synthetic-theory approach”. Celest. Mech. Dynam. Astron. 56, 121129.CrossRefGoogle Scholar
Milani, A., Carpino, M., Hahn, G. and Nobili, A.M.: 1989, “Project Spaceguard: Dynamics of planet-crossing asteroids. Classes of Orbital Behaviour”. Icarus 78, 212269.Google Scholar
Moons, M. and Morbidelli, A.: 1993, “The main mean-motion commensurabilities in the planar circular and elliptical problem”. Celest. Mech. Dynam. Astron. 57, 99108.Google Scholar
Morbidelli, A. and Moons, M.: 1993, “Secular resonances in mean-motion commensurabilities. The 2/1 and 3/2 cases”. Icarus 102, 316332.Google Scholar
Murray, C.D.: 1986, “Structure of the 2: 1 and 3: 2 Jovian Resonances”. Icarus 65, 7082.Google Scholar
Ries, J.G.: 1993, “Numerical exploration of the 4: 3 resonance in the Elliptic Restricted Problem”. Bull. Amer. Astron. Soc. (in press). Google Scholar
Saha, P.: 1992, “Simulating the 3: 1 Kirkwood gap”. Icarus, 100, 434439.CrossRefGoogle Scholar
Scholl, H. and Froeschlé, C.: 1974, “Asteroidal motion at the 3/1 commensurability”. Astron. Astrophys. 33, 455458.Google Scholar
Scholl, H. and Froeschlé, C.: 1975, “Asteroidal motion at the 5/2, 7/3 and 2/1 resonances”. Astron. Astrophys. 42, 457463.Google Scholar
Scholl, H. and Froeschlé, Ch.: 1991, “The ν6 secular resonance region near 2 AU: A possible source of meteorites”. Astron. Astrophys. 245, 316336.Google Scholar
Schubart, J.: 1990, “The low-eccentricity gap at the Hilda group of asteroids”. In Asteroids, Comets, Meteors III (Lagerqvist, C.-I. et al., eds.), Reprocentralen HSC, Uppsala, 171174.Google Scholar
Schweizer, F.: 1969, “Resonant asteroids in the Kirkwood gaps and statistical explanation of the gap”. Astron. J. 74, 779788.Google Scholar
Šidlichovský, M.: 1993, “Chaotic behaviour of trajectories for the fourth and third order asteroidal resonances”. Celest. Mech. Dyn. Astron. 56, 143152.Google Scholar
Šidlichovský, M. and Melendo, B.: 1986, “Mapping for the 5/2 asteroidal commensurability”. Bull. Astron. Inst. Czechoslov. 37, 6580.Google Scholar
Wiggins, S.: 1990, Chaotic Transport in Dynamical Systems, Springer-Verlag, New York.Google Scholar
Wisdom, J.: 1982, “The origin of Kirkwood gaps: A mapping for asteroidal motion near the 3/1 commensurability”. Astron. J. 85, 11221133.CrossRefGoogle Scholar
Wisdom, J.: 1983, “Chaotic behaviour and the origin of the 3/1 Kirkwood gap”. Icarus 56, 5174.CrossRefGoogle Scholar
Wisdom, J.: 1985, “A perturbative treatment of motion near the 3/1 commensurability”. Icarus 63, 279282.Google Scholar
Wisdom, J.: 1987, “Chaotic dynamics in the Solar System”. Icarus 72, 241275.Google Scholar
Yokoyama, T. and Balthazar, J.M.: 1992, “Application of Wisdom's perturbative method for 5: 2 and 7: 3 resonances”. Icarus, 99, 175190.Google Scholar
Yoshikawa, M.: 1990, “Motions of asteroids at the Kirkwood gaps. I. On the 3: 1 resonance with Jupiter”. Icarus 87, 78102.CrossRefGoogle Scholar
Yoshikawa, M.: 1991, “Motions of asteroids at the Kirkwood gaps. II. On the 5: 2, 7: 3 and 2: 1 resonances with Jupiter”. Icarus 92, 94117.CrossRefGoogle Scholar