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We use numerical integrations to investigate the dynamical evolution ofresonant Trojan and quasi-satellite companions during the late stages ofmigration of the giant planets Jupiter, Saturn, Uranus, and Neptune. Ourmigration simulations begin with Jupiter and Saturn on orbits already wellseparated from their mutual 2:1 mean-motion resonance. Neptune and Uranus aredecoupled from each other and have orbital eccentricities damped to near theircurrent values. From this point we adopt a planet migration model in which themigration speed decreases exponentially with a characteristic timescale tau(the e-folding time). We perform a series of numerical simulations, eachinvolving the migrating giant planets plus test particle Trojans andquasi-satellites. We find that the libration frequencies of Trojans are similarto those of quasi-satellites. This similarity enables a dynamical exchange ofobjects back and forth between the Trojan and quasi-satellite resonances duringplanetary migration. Furthermore, under the influence of these secondaryresonances quasi-satellites can have their libration amplitudes enlarged untilthey undergo a close-encounter with their host planet and escape from theresonance. High-resolution simulations of this escape process reveal that ~80%of Jovian quasi-satellites experience one or more close-encounters withinJupiter's Hill radius (R_H) as they are forced out of the quasi-satelliteresonance. 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 the2-body escape velocity from the host planet.

Transformation of Trojans into Quasi-Satellites During Planetary Migration and Their Subsequent Close-Encounters with the Host Planet