The existence of the Oort comet cloud, the Kuiper belt, and plausible inefficiencies in planetary core formation all suggest that there was once a residual planetesimal disk of mass D10È100 in the vicin-Mî ty of the giant planets following their formation. Since removal of this disk requires an exchange of orbital energy and angular momentum with the planets, signiÐcant planetary migration can ensue. The planet migration phenomenon is examined numerically by evolving the orbits of the giant planets while they are embedded in a planetesimal disk having a mass of We Ðnd that Saturn, M D \ 10È200 M^. Uranus, and Neptune evolve radially outward as they scatter the planetesimals, while JupiterÏs orbit shrinks as it ejects mass. Higher mass disks result in more rapid and extensive planet migration. If orbital expansion and resonance trapping by Neptune are invoked to explain the eccentricities of Pluto and its cohort of Kuiper belt objects at NeptuneÏs 3 : 2 mean motion resonance, then our simulations suggest that a disk mass of order is required to expand NeptuneÏs orbit by *a D 7 AU, in M D D 50 Mô rder to pump up Plutino eccentricities to e D 0.3. Such planet migration implies that the solar system was more compact in the past, with the initial Jupiter-Neptune separation having been smaller by about 30%.We discuss the fate of the remnants of the primordial planetesimal disk. We point out that most of the planetesimal disk beyond NeptuneÏs 2 :1 resonance should reside in nearly circular, low-inclination orbits, unless there are (or were) additional, unseen, distant perturbers. The planetesimal disk is also the source of the Oort cloud of comets. Using the results of our simulations together with a simple treatment of Oort cloud dynamics, we estimate that D12 of disk material was initially deposited in the Oort Mĉ loud, of which D4 will persist over the age of the solar system. The majority of these comets orig-Mî nated from the Saturn-Neptune region of the solar nebula.

Nbody simulations are used to examine the consequences of Neptune's outward migration into the Kuiper Belt, with the simulated endstates being compared rigorously and quantitatively to the observations. These simulations confirm the findings of Chiang et al. (2003), who showed that Neptune's migration into a previously stirred-up Kuiper Belt can account for the Kuiper Belt Objects (KBOs) known to librate at Neptune's 5:2 resonance. We also find that capture is possible at many other weak, high-order mean motion resonances, such as the

A model that computes the secular evolution of a gravitating disk-planet system is developed. The disk is treated as a set of gravitating rings, with the rings'/planets' time-evolution governed by the classical Laplace-Lagrange solution for secular evolution but modified to account for the disk's finite thickness h. This system's Lagrange planetary equations yield a particular class of spiral wave solutions, usually denoted as apsidal density waves and nodal bending waves. There are two varieties of apsidal waves:long waves and short waves. Planets typically launch long density waves at the disk's nearer edge or else at a secular resonance in the disk, and these waves ultimately reflect downstream at a more distant disk edge or else at a Q-barrier in the disk, whereupon they return as short density waves. Planets also launch nodal bending waves, and these have the property that they can stall in the disk, that is, their group velocity plummets to zero upon approaching a disk region too thick to support the continued propagation of bending waves. The rings model is used to compute the secular evolution of a Kuiper Belt having a variety of masses, and it is shown that the early massive Belt was very susceptible to the propagation of low-amplitude apsidal and nodal waves launched by the giant planets.Comment: 45 pages, 6 figure

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