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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 = g6 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.

Type
Part III - The Asteroidal Belt
Information
Symposium - International Astronomical Union , Volume 152: Chaos, Resonance and Collective Dynamical Phenomena in the Solar System , 1992 , pp. 123 - 132
Copyright
Copyright © Kluwer 1992 

References

Brouwer, D. and Van Woerkom, A. J. J. (1950). ‘The secular variations of the orbital elements of the principal planets’, Astron. Papers U.S. Naval Obs. Naut. Almanac Off. 13, 81–107.Google Scholar
Farinella, P., Gonczi, R., Froeschlé, Ch., and Froeschlé, C. (1991) ‘Injecting asteroids fragments into resonances’, presented at the Asteroids Comets Meteors 1991 conference, Flagstaff, June 1991.Google Scholar
Franklin, F., Lecar, M. and Soper, P. (1989) ‘On the original distribution of the asteroids. II. Do stable orbits exist between Jupiter and Saturn?’, Icarus 79, 223–227.CrossRefGoogle Scholar
Froeschlé, Ch., and Scholl, H. (1991) ‘The effect of secular resonances in the asteroid region between 2.1 and 2.4 AU‘, presented at the Asteroids Comets Meteors 1991 conference, Flagstaff, June 1991.Google Scholar
Gladman, B., and Duncan, M. (1990) ‘On the fates of minor bodies in the outer solar system’, Astron. J. 100, 1680–1693.CrossRefGoogle Scholar
Heppenheimer, T.A. 1979 ‘Reduction to proper elements for the entire solar system’, Celest. Mech. 20, 231–241.CrossRefGoogle Scholar
Kneževicć, Z. 1989 ‘Asteroid long-periodic perturbations: The second order Hamiltonian’, Celest. Mech. 46, 147–158.CrossRefGoogle Scholar
Knežević, Z., Milani, A., Farinella, P., Froeschlé, Ch., and Froeschlé, C. (1991) ‘Secular resonances from 2 to 50 AU‘, Icarus, in press.CrossRefGoogle Scholar
Levinson, H. F. (1991) ‘The long-term dynamical behaviour of small bodies in the Kuiper Belt’, Astron. J. 102, 787–794.CrossRefGoogle Scholar
Milani, A. and Knežević, Z. (1990) ‘Secular perturbation theory and computation of asteroid proper elements’, Celest. Mech. 49, 247–411.CrossRefGoogle Scholar
Milani, A. and Knežević, Z. (1991) ‘Asteroid proper elements and secular resonances’, Icarus, submitted.CrossRefGoogle Scholar
Morbidelli, A. and Henrard, J. (1991) ‘Secular resonances in the asteroid belt: Theoretical perturbation approach and the problem of their location’, Celest. Mech., in press.CrossRefGoogle Scholar
Nobili, A.M., Milani, A. and Carpino, M. (1989) ‘Fundamental frequencies and small divisors in the orbits of the outer planets’, Astron. Astrophys. 210, 313–336.Google Scholar
Rickman, H. and Froeschlé, C. (1979) ‘Orbital evolution of short period comets treated as a Markov process’, Astron. J. 84, 1910–1917.CrossRefGoogle Scholar
Scholl, H. and Froeschlé, Ch. (1991) ‘The v 6 secular resonance region near 2 AU: A possible source of meteorites’, Astron. Astrophys. 245, 316–321.Google Scholar
Torbett, M.V., and Smoluchowski, R. (1990) ‘Chaotic motion in a primordial comet disk beyond Neptune and comet influx to the Solar System’, Nature 345, 49–51.CrossRefGoogle Scholar
Weibel, N.M., Kaula, W.M. and Newmann, W. I. (1990), ‘A computer search for stable orbits between Jupiter and Saturn’, Icarus 83, 382–392.CrossRefGoogle Scholar
Williams, J.G. (1969) ‘Secular perturbations in the Solar System’, Ph. D. Dissertation, Univ. of California, Los Angeles.Google Scholar
Williams, J.G. and Faulkner, J. (1981) ‘The positions of secular resonances surfaces’, Icarus 46, 390–399.CrossRefGoogle Scholar