Title:
The location of secular resonances close to the 2/1 commensurability
Authors:
Morbidelli, A.; Scholl, H.; Froeschle, Ch.
Affiliation:
AAObservatoire de la Cote d'Azur, Nice, France ABObservatoire de la Cote
d'Azur, Nice, France
ACObservatoire de la Cote d'Azur, Nice, France
Journal:
Astronomy and Astrophysics (ISSN 0004-6361), vol. 278, no. 2, p. 644-653
(A&A Homepage)
Publication Date:
11/1993
Category:
Astrophysics
Origin:
STI
NASA/STI Keywords:
ASTEROID BELTS, ASTEROIDS, CELESTIAL MECHANICS, FOURIER SERIES, SECULAR
VARIATIONS, SOLAR SYSTEM, ALGORITHMS, ECCENTRICITY, HAMILTONIAN
FUNCTIONS
Bibliographic Code:
1993A&A...278..644M
Abstract
This paper is devoted to the problem of the location of secular resonances
close to a mean motion commensurability in the main
asteroid belt. This is quite a difficult problem because of the presence
of several resonances in the same part of the phase space,
which makes it a dynamical system with strongly coupled degrees of
freedom. Therefore, we apply here the perturbation method
of 'successive elimination of harmonics' in order to find out in the
regular regions the proper frequencies of the system and,
consequently, locate the secular resonances. In particular, we concentrate
on the location of the nu6 resonance close to the 2/1
commensurability, since this is related to the existence of the upper
bound of the distribution of the inclinations of the asteroids
between 3.0 and 3.2 A.U.. We confirm that, as suspected, the nu6 resonance
is at a larger inclination than the main asteroid
population. Our theoretical findings are confirmed by several numerical
integrations, with initial conditions systematically chosen
on a suitable grid.