The location of secular resonances close to the 2/1 commensurability

Details The location of secular resonances close to the 2/1 commensurability The location of secular resonances close to the 2/1 commensurability

Nov 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993a%26a...278..644m&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 278, no. 2, p. 644-653

Astronomy and Astrophysics

Astrophysics

1

Asteroid Belts, Asteroids, Celestial Mechanics, Fourier Series, Secular Variations, Solar System, Algorithms, Eccentricity, Hamiltonian Functions

Scientific paper

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.

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