  A migrating planet can capture planetesimals into mean motion resonances.
However, resonant trapping can be prevented when the drift or migration rate is
sufficiently high. Using a simple Hamiltonian system for first and second order
resonances, we explore how the capture probability depends on the order of the
resonance, drift rate and initial particle eccentricity. We present scaling
factors as a function of the planet mass and resonance strength to estimate the
planetary migration rate above which the capture probability drops to less than
1/2. Applying our framework to multiple extra solar planetary systems that have
two planets locked in resonance, we estimate lower limits for the outer
planet's migration rate allowing resonance capture of the inner planet. Mean
motion resonances are comprised of multiple resonant subterms. We find that the
corotation subterm can reduce the probability of capture when the planet
eccentricity is above a critical value. We present factors that can be used to
estimate this critical planet eccentricity. Applying our framework to the
migration of Neptune, we find that Neptune's eccentricity is near the critical
value that would make its 2:1 resonance fail to capture twotinos. The capture
probability is affected by the separation between resonant subterms and so is
also a function of the precession rates of the longitudes of periapse of both
planet and particle near resonance.
