  The spatial distribution of Kuiper belt objects (KBOs) in 2:1 exterior
resonance with Neptune constrains that planet's migration history. Numerical
simulations demonstrate that fast planetary migration generates a larger
population of KBOs trailing rather than leading Neptune in orbital longitude.
This asymmetry corresponds to a greater proportion of objects caught into
asymmetric resonance such that their resonance angles librate about values > pi
(trailing) as opposed to < pi (leading). We provide, for the first time, an
explanation of this phenomenon, using physical, analytic, and semi-analytic
arguments. Central to our understanding is how planetary migration shifts the
equilibrium points of the superposed direct and indirect potentials. Large
capture asymmetries appear for exponential timescales of migration shorter than
10 Myr. The observed distribution of 2:1 KBOs (2 trailing and 7 leading)
excludes migration timescales < 1 Myr with 99.65% confidence.
