  The early stages of dynamical evolution of planetary systems are often shaped
by dissipative processes that drive orbital migration. In multi-planet systems,
convergent amassing of orbits inevitably leads to encounters with rational
period ratios, which may result in establishment of mean motion resonances. The
success or failure of resonant capture yields exceedingly different subsequent
evolutions, and thus plays a central role in determining the ensuing orbital
architecture of planetary systems. In this work, we employ an integrable
Hamiltonian formalism for first order planetary resonances that allows both
secondary bodies to have finite masses and eccentricities, and construct a
comprehensive theory for resonant capture. Particularly, we derive conditions
under which orbital evolution lies within the adiabatic regime, and provide a
generalized criterion for guaranteed resonant locking as well as a procedure
for calculating capture probabilities when capture is not certain.
Subsequently, we utilize the developed analytical model to examine the
evolution of Jupiter and Saturn within the protosolar nebula, and investigate
the origins of the dominantly non-resonant orbital distribution of sub-Jovian
extrasolar planets. Our calculations show that the commonly observed extrasolar
orbital structure can be understood if planet pairs encounter mean motion
commensurabilities on slightly eccentric (e~0.02) orbits. Accordingly, we
speculate that resonant capture among low-mass planets is typically rendered
unsuccessful due to subtle axial asymmetries inherent to the global structure
of protoplanetary disks.
