gravitational attraction assists with both collecting and binding the grains and the process becomes known as accretion. When the grains become macroscopic, the accretion can be modeled more easily, and many investigators have studied the various mechanisms that lead to growth from macroscopic grains to planetesimals. The role of resonances and the ability of resonances to lead to characteristic sizes of planetesimals have been investigated with inconclusive results by many people. The current state of the art in this modeling is the work by Weidenschilling (1997), who finds that resonances are unimportant but predicts characteristic sizes on the order of 100 meters, the size at which the planetesimal has a sufficiently large ratio of mass to cross section that it decouples from the effects of gaseous drag.
The planetesimals that have grown large enough to escape the effects of gaseous drag can be modeled with purely gravitational physics. The results are somewhat sensitive to the assumed starting conditions, but in the vicinity of Jupiter and Saturn most planetesimals are either incorporated into Jupiter and Saturn or ejected entirely from the solar system by encounters with those bodies. In the vicinity of Uranus and Neptune, many planetesimals are still captured into the two planets or ejected from the solar system, but there is also a significant likelihood of a gentle ejection from the planetary region outward for thousands of astronomical units, i.e., to distances that are a significant fraction of interstellar distances, where the planetesimals are still gravitationally bound to the protosun in a very extended disk. Comprehensive models have not been calculated, but the studies thus far indicate that this is the dominant source of comets in the Oort Cloud.
Since the relative numbers of planetesimals at the distances of the different giant protoplanets are not well known, the relative contributions to the Oort Cloud from various regions of the protoplanetary disk also are not well known. The efficiency is much higher near proto-Uranus and proto-Neptune than near proto-Jupiter and proto-Saturn, but it is unclear whether higher relative numbers of planetesimals near proto-Jupiter and proto-Saturn might have counteracted this effect. As originally explained by Oort (1950), many dynamical simulations have shown that the effects of passing stars, galactic tides, and passages through molecular clouds convert this disk into a roughly spherical distribution that is now know as the Oort Cloud. Beyond Neptune, the process of formation of planetesimals proceeded more slowly owing to the lower densities and lower velocities. The formation of a planet was inhibited because the slow accretion to planetesimals used up all the material before one planetesimal became large enough that its gravitational cross section greatly exceeded its geometrical cross section and approached the scale of the mean separation between planetesimals. Most of these planetesimals are still present today in what is now called the Kuiper Belt, although the inner parts of this belt, say from 40 to 50 AU, have been considerably depleted by subsequent planetary perturbations.
The time scale for formation of large (tens of kilometers) comets in the Uranus-Neptune region is on the order of 106 years, that for ejection to the Oort disk is probably up to an order of magnitude longer, and the time scale to convert the Oort Cloud from a disk to a sphere is on the order of 109 years. It should be noted that one expects mixing of planetesimals from one part of the protoplanetary disk to another during the stage at which the planets accrete, although the simulations are not yet accurate enough to determine how much mixing occurs. Today the orbits of comets in both the Kuiper Belt and the Oort Cloud are nearly circular, with orbital periods in the Oort Cloud being the longest at about 106 years.
The comets that are seen today in the inner solar system have been delivered from both the Oort Cloud and the Kuiper Belt much more recently than the epoch of formation. Comets entering the inner solar system for the first time from the Oort Cloud can be recognized with high confidence from their orbits, the orbit having been perturbed by some passing star or possibly by a chance encounter between two comets. On the basis of an analysis of their orbits, it is possible to identify those comets that more likely came from the Oort Cloud and ones that more likely came from the Kuiper Belt, but for any individual comet we cannot be sure from which of these two reservoirs it came. Researchers also know of seven Centaurs, bodies orbiting roughly between Jupiter and Neptune, one of which is known to show cometary outgassing. These are transition objects between short-period comets and Kuiper Belt objects, although again researchers do not know confidently in individual cases whether the Centaur is arriving from the Kuiper Belt or is being ejected back toward the Kuiper Belt.