Terrestrial planet and asteroid formation in the presence of giant planets- I. Relative velocities of planetesimals subject to Jupiter and Saturn perturbations

We investigate the orbital evolution of 10(13)- to 10(25)-g planetesimals n ear 1 AU and in the asteroid belt (near 2.6 AU) prior to the stage of evolu tion when the mutual perturbations between the planetesimals become importa nt. We include nebular gas drag and the effects of Jupiter and Saturn at th eir present masses and in their present orbits. Gas drag introduces a size- dependent phasing of the secular perturbations, which leads to a pronounced dip in encounter velocities (V-enc) between bodies of similar mass. Planet esimals of identical mass have V-enc similar to 1 and similar to 10 m s(-1) (near 1 and 2.6 AU, respectively) while bodies differing by similar to 10 in mass have V-enc similar to 10 and similar to 100 m s(-1) (near 1 and 2.6 AU, respectively). Under these conditions, growth, rather than erosion, wi ll occur only by collisions of bodies of nearly the same mass. There will b e essentially no gravitational focusing between bodies less than 10(22) to 10(25) g, allowing growth of planetary embryos in the terrestrial planet re gion to proceed in a slower nonrunaway fashion. The environment in the aste roid belt will be even more forbidding and it is uncertain whether even the severely depleted present asteroid belt could form under these conditions. The perturbations of Jupiter acid Saturn are quite sensitive to their semi- major axes and decrease when the planets' heliocentric distances are increa sed to allow for protoplanet migration. It is possible, though not clearly demonstrated, that this could produce a depleted asteroid belt but permit f ormation of a system of terrestrial planet embryos on a similar to 10(6)-ye ar timescale, initially by nonrunaway growth and transitioning to runaway g rowth after similar to 10(5) years. The calculations reported here are valid under the condition that the relat ive velocities of the bodies are determined only by Jupiter and Saturn pert urbations and by gas drag, with no mutual perturbations between planetesima ls. If, while subject to these conditions, the bodies become large enough f or their mutual perturbations to influence their velocity and size evolutio n significantly, the problem becomes much more complex. This problem is und er investigation. (C) 2000 Academic Press.