Migration timescale thresholds for resonant capture in the Plutino problem

Dynamic autoresonance theory is applied to the problem of thresholds on migration timescales for capture into resonances in the planar-restricted three-body problem with m(1) >> m(2) >> m(0) and slowly migrating masses m(1,2). The thresholds are found analytically, scale as (m(2)/m(1))(-4/3), and yield an order of magnitude longer timescales required for capture of m(0) into 2 : 1 outer resonance as compared with 3 : 2 and other resonances. The difference is due to the rotation of the primary mass m(1), affecting the 2 : 1 resonance only. This could explain the observed small abundance of Kuiper Belt objects in the 2 : 1 resonance and could define accurate bounds on the timescales involved in the early evolution of the solar system.