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The Locations of Secular Resonances and the Evolution of Small Solar System Bodies

Published online by Cambridge University Press:  07 August 2017

Ch Froeschle ,
P. Farinella ,
C. Froeschle ,
Z. Knežević  and
A. Milani
Ch Froeschle
Affiliation:
Observatoire de la Côte d'Azur, B.P. 139, F-06003 Nice Cedex, France
P. Farinella
Affiliation:
Dipartimento di Matematica, Università di Pisa, Via Buonarroti 2, 56127 Pisa, Italy
C. Froeschle
Affiliation:
Observatoire de la Côte d'Azur, B.P. 139, F-06003 Nice Cedex, France
Z. Knežević
Affiliation:
Astronomska Opservatorija, Volgina 7, 11050 Beograd, Yugoslavia
A. Milani
Affiliation:
Dipartimento di Matematica, Università di Pisa, Via Buonarroti 2, 56127 Pisa, Italy

Abstract

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Generalizing the secular perturbation theory of Milani and Knežević (1990), we have determined in the a — e — I proper elements space the locations of the secular resonances between the precession rates of the longitudes of perihelion and node of a small body and the corresponding eigenfrequencies of the secular perturbations of the four outer planets. We discuss some implications of the results for the dynamical evolution of small solar system bodies. In particular, our findings include: (i) the fact that the g = g 6 resonance in the inner asteroid belt lies closer than previously assumed to the Flora region, providing a plausible dynamical route to inject asteroid fragments into planet-crossing orbits; (ii) the possible presence of some low-inclination “stable islands” between the orbits of the outer planets; (iii) the fact that none of the secular resonances considered in this work exists for semimajor axes > 50 AU, so that these resonances do not provide a mechanism for transporting inwards possible Kuiper–belt comets.

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