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.