Terrestrial Planet and Asteroid Formation in the Presence of Giant Planets: I. Relative Velocities of Planetesimals Subject to Jupiter and Saturn Perturbations
✍ Scribed by Stephen J. Kortenkamp; George W. Wetherill
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 442 KB
- Volume
- 143
- Category
- Article
- ISSN
- 0019-1035
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✦ Synopsis
We investigate the orbital evolution of 10 13 -to 10 25 -g planetesimals near 1 AU and in the asteroid belt (near 2.6 AU) prior to the stage of evolution when the mutual perturbations between the planetesimals become important. We include nebular gas drag and the effects of Jupiter and Saturn at their 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. Planetesimals of identical mass have V enc ∼1 and ∼10 m s -1 (near 1 and 2.6 AU, respectively) while bodies differing by ∼10 in mass have V enc ∼10 and ∼100 m s -1 (near 1 and 2.6 AU, respectively). Under these conditions, growth, rather than erosion, will occur only by collisions of bodies of nearly the same mass. There will be essentially no gravitational focusing between bodies less than 10 22 to 10 25 g, allowing growth of planetary embryos in the terrestrial planet region to proceed in a slower nonrunaway fashion. The environment in the asteroid 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 and Saturn are quite sensitive to their semi-major axes and decrease when the planets' heliocentric distances are increased to allow for protoplanet migration. It is possible, though not clearly demonstrated, that this could produce a depleted asteroid belt but permit formation of a system of terrestrial planet embryos on a ∼10 6 -year timescale, initially by nonrunaway growth and transitioning to runaway growth after ∼10 5 years.
The calculations reported here are valid under the condition that the relative velocities of the bodies are determined only by Jupiter and Saturn perturbations and by gas drag, with no mutual perturbations between planetesimals. If, while subject to these conditions, the bodies become large enough for their mutual perturbations to influence their velocity and size evolution significantly, the problem becomes much more complex. This problem is under investigation.