Transformation of Trojans into Quasi-Satellites During Planetary   Migration and Their Subsequent Close-Encounters with the Host Planet
  We use numerical integrations to investigate the dynamical evolution of resonant Trojan and quasi-satellite companions during the late stages of migration of the giant planets Jupiter, Saturn, Uranus, and Neptune. Our migration simulations begin with Jupiter and Saturn on orbits already well separated from their mutual 2:1 mean-motion resonance. Neptune and Uranus are decoupled from each other and have orbital eccentricities damped to near their current values. From this point we adopt a planet migration model in which the migration speed decreases exponentially with a characteristic timescale tau (the e-folding time). We perform a series of numerical simulations, each involving the migrating giant planets plus test particle Trojans and quasi-satellites. We find that the libration frequencies of Trojans are similar to those of quasi-satellites. This similarity enables a dynamical exchange of objects back and forth between the Trojan and quasi-satellite resonances during planetary migration. Furthermore, under the influence of these secondary resonances quasi-satellites can have their libration amplitudes enlarged until they undergo a close-encounter with their host planet and escape from the resonance. High-resolution simulations of this escape process reveal that ~80% of Jovian quasi-satellites experience one or more close-encounters within Jupiter's Hill radius (R_H) as they are forced out of the quasi-satellite resonance. As many as ~20% come within R_H/4 and ~2.5% come within R_H/10. Close-encounters of escaping quasi-satellites occur near or even below the 2-body escape velocity from the host planet. 
Stephen J. Kortenkamp and Emily C. S. Joseph
astro-ph.EP