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.