Dynamical study of the Hilda asteroids - I. Resonant orbital motion of the PLS objects from the Palomar-Leiden Survey

Schubart's model of a planar, elliptic restricted three-body problem is used to study the orbital motion of the Hilda asteroids from the Palomar-Leiden Survey. The 3:2 resonant coupling to Jupiter of some of these small asteroids are found to be stable. However, some of the small asteroids with absolute magnitude g>15 have large amplitude of variation in their orbital elements in one libration period. Since the lifetime scales against catastrophic collision of the Hilda asteroids are estimated to be several times larger than those of the main belt objects, a significant portion of these resonant asteroids could be the original members of the Hilda group. From this point of view, it is suggested that such 'size-dependence' of resonant orbital motions might be the result of the cosmogonic effects of jet stream accretion.