Comparative study of the asteroidal motion in the 3:2 and 2:1 resonances with Jupiter. I. Planar model.

Abstract

The long-period behavior of the asteroids in the 3:2 and 2:1 resonances with Jupiter is investigated by integrating numerically the equations of motion of the planar three-body system. The results of the numerical integration procedure were submitted to a low-pass filtering and the decimation parameter was chosen in accordance with the filter. The behaviour of the most important physical quantities which describe the orbital evolution in the resonance were Fourier analysed. The topology of phase space was studied by constructing the surfaces of section. The structure of the phase space in the 3:2 and 2:1 resonances showed the presence of both regular and chaotic motion. Regular motion shows a great variety of orbital behaviour. Chaotic motion occurs because of: (1) the proximity of the resonance border; (2) the presence of secondary resonances (when the one fundamental frequency enters into resonance with the other frequencies and creates a pattern of islands inside the primary resonance); (3) the proximity of the chaotic region emanating from the boundary of corotations. The location of the main secondary resonances was computed on the (a_0_,e_0_)-plane. The results obtained with our numerical technique were compared to similar results previously obtained with either analytical or semi-numerical models by several authors.