Mean Motion Resonances in the Trans-neptunian RegionI. The 2:3 Resonance with Neptune

The stability of the 2:3 mean motion resonance with Neptune is systematically explored and compared to the observed resonant population. It is shown that orbits with small and moderate amplitudes of the resonant angle are stable over the age of the Solar System. The observed resonant population is distributed within the stability limits. There exists an interval of large resonant 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 objects eventually attain Neptune–crossing trajectories and contribute to the flux of Jupiter–family comets. The number of objects leaking from the 2:3 resonance per time interval is calibrated by the number of objects needed to keep the Jupiter–family comets population in steady state. This allows us to compute the upper limit of the number of resonant objects with cometary size. The effects of collisions and mutual gravitational scattering are discussed in this context. c © 2000 Academic Press