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0 2 x 107 4 x 107 6 x 107 8 x 107 1 x 108 time t (years)

0 2 x 107 4 x 107 6 x 107 8 x 107 1 x 108 time t (years)

Fig. 6.6 Numerical modelling of the migration of the Solar System's giant planets. The dashed lines represent the positions of resonances with Neptune (After Hahn and Malhotra, 2005)

inside Uranus, and that their orbits crossed. Their formation in a denser zone of the protoplanetary disk would therefore have been faster than originally expected. This resolves a problem, because the formation of the cores of these two planets seemed to require longer than the lifetime of the disk of gas. Even if Uranus and Neptune had significant cores of ice, their gaseous envelopes prove that their cores formed before the gaseous disk dissipated.

During this migration, the planets drove the Kuiper-Belt objects outwards, forcing them into resonances with Neptune. The migration was sufficiently slow for the Kuiper-Belt objects to remain trapped in the resonances and for their eccentricities to increase, eventually leading to the current configuration.

This phenomenon of migration was undoubtedly operative in the circumplane-tary disks around the giant planets. This is suggested by the existence of several systems of satellite that are in resonance, in particular, the Galilean satellites of Jupiter. The satellites migrated until they became trapped in what is known as a mean-motion resonance. Once trapped, the orbits could continue to migrate, preserving the resonant relationship.

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