Secular resonances in the asteroid belt - Theoretical perturbation approach and the problem of their location

Details Secular resonances in the asteroid belt - Theoretical perturbation approach and the problem of their location Secular resonances in the asteroid belt - Theoretical perturbation approach and the problem of their location

Jun 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991cemda..51..131m&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 51, no. 2, 1991, p. 131-167. Research supported by CEC.

Statistics

Computation

24

Asteroid Belts, Orbital Mechanics, Orbital Resonances (Celestial Mechanics), Perturbation Theory, Approximation, Computational Astrophysics, Hamiltonian Functions, Perihelions

Scientific paper

In this paper a theoretical perturbation approach to the problem of the dynamics in secular resonance is exposed. This approach avoids any expansion of the main term of the Hamiltonian (linear term in the masses) with respect to the eccentricity or the inclination of the asteroid, in order to achieve results valid for any value of these variables. Moreover suitable action-angle variables are introduced to take properly into account the dynamics related to the motion of the argument of perihelion of the asteroid, which is relevant at high inclination. A class of secular resonances wider than that usually considered is found. An explicit computation of the location of the main secular resonances, estimating also the contribution of the quadratic term in the masses by means of classical series expansion, is reported in the last sections. The accuracy of computations obtained by series expansion is discussed in the paper.

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