Mean motion resonances in the trans-Neptunian region I. The 2 : 3 resonance with Neptune

The stability of the 2:3 mean motion resonance with Neptune is systematical ly explored and compared to the observed resonant population, It is shown t hat orbits with small and moderate amplitudes of the resonant angle are sta ble over the age of the Solar System, The observed resonant population is d istributed within the stability limits, There exists an interval of large r esonant amplitudes, where orbits are marginally unstable, Resonant objects starting in this interval may leave the resonance by slow increase of their resonant amplitudes on a time scale of several billion years, These object s eventually attain Neptune-crossing trajectories and contribute to the flu x of Jupiter-family comets, The number of objects leaking from the 2:3 reso nance per time interval is calibrated by the number of objects needed to ke ep the Jupiter-family comets population in steady state. This allows us to compute the upper limit of the number of resonant objects with cometary siz e, The effects of collisions and mutual gravitational scattering are discus sed in this context. (C) 2000 Academic Press.