Migration Timescale Thresholds for Resonant Capture in the Plutino Problem

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Abstract
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 m1 m2 m0 and slowly migrating masses m1, 2. The thresholds are found analytically, scale as (m2/m1)-4/3, and yield an order of magnitude longer timescales required for capture of m0 into 2 : 1 outer resonance as compared with 3 : 2 and other resonances. The difference is due to the rotation of the primary mass m1, 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.