Planetary Sciences American and Soviet Research/Proceedings from the U.S.-U.S.S.R. Workshop on Planetary Sciences (1991) / Chapter Skim
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8. Formation of the Terrestrial Planets from Planetesimals
8. Formation of the Terrestrial Planets from Planetesimals
Pages 98-115
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From page 98... ...
Numerical simulations of this final merger showed that this stage of accumulation was marked by giant impacts (1027 - 1028 g) that could be responsible for providing the angular momentum of the Earth-Moon system, removal of Mercury's silicate mantle, and the removal of primordial planetary atmospheres (Hartmann and Davis 1975; Cameron and Ward 1976; Wetherill 1985~.
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From page 99... ...
Other possibly important physical phenomena, such as gravitational resonances between the terrestrial planet embryos have not yet been considered. INTRODUCTION This article will describe recent and current development of theories in which the terrestrial planets formed by the accumulation of much smaller (one- to 10-kilometer diameter)
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From page 100... ...
Agglomeration under these conditions requires processes such as physical "stickiness," the imbedding of high-velocity projectiles into porous targets, or physical coherence of splash products following impact. Despite serious efforts to experimentally or theoretically treat this stage of planetary growth, our poor understanding of physical conditions in the solar nebula and other physical properties of these primordial aggregates make it very difficult.
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From page 101... ...
Safronov (1962) made a major contribution to this problem by recognition that this relative velocity is not a free parameter, but is determined by the mass distribution of bodies.
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From page 102... ...
1983) complemented the work of Safronov and his colleagues by including the effects of gas drag, but did not include collisional damping.
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From page 103... ...
For an initial swarm of planetesimals of equal or nearly equal mass, the mass distribution will quickly disperse as a result of stochastic differences in the collision rate and thereby the growth rate of a large number of small bodies. As a result of the equipartition of energy terms, this will quickly lead to a velocity dispersion, whereby the larger bodies have velocities, relative to a circular orbit, significantly lower than that of the more numerous smaller bodies of the swarm.
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From page 104... ...
This runaway body will quickly capture all the residual material in the original accumulation zone, specified in this case to be 0.02 AU in width. The orbit of the runaway body will be nearly circular, and it will be able
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From page 105... ...
Depending on the initial surface density, runaway growth of this kind can be expected to produce approximately 30 to 200 bodies in the terrestrial planet region with sizes ranging from that of the Moon to that of Mars. There are a number of important physical processes that have not been included in this simplified model.
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From page 106... ...
All of these simulations are in some sense "Monte Carlo" calculations, because even in the less demanding two-dimensional case, a complete numerical integration of several hundred bodies for the required number of orbital periods is computationally prohibitive. Even if such calculations were possible, the intrinsically chaotic nature of orbital evolution dominated by close encounters causes the final outcome to be so exquisite sensitive to the initial conditions that the final outcome is essentially stochastic.
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From page 107... ...
In both the two- and three-dimensional calculations, the physical processes considered are mutual gravitational perturbations, physical collisions, and mergers, and in some cases collisional fragmentations and tidal disruption (Wetherill 1986, 1988~. In the work cited above it was necessary to initially confine the initial swarm to a region smaller than the space presently occupied by the observed terrestrial planets.
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From page 108... ...
Subject to uncertainties associated with hypotheses of the kind discussed above, the published simulations of the final stages of planetary growth, show that an initial collection of several hundred embryos spontaneously evolve into two to five bodies in the general mass range of the present terrestrial planets. In some cases the size and distribution of the final bodies resemble rather remarkably those observed in the present solar system (Wetherill 1985~.
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From page 109... ...
The studies of terrestrial planet growth discussed earlier in which the only physical processes included are collisions and merger, are clearly inadequate to cause an extended swarm of embryos to evolve into the present compact group of terrestrial planets. Accomplishment of this will require inclusion of additional physical processes.
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From page 110... ...
In Figure S the point marked "initial swarm" corresponds to the specific energy and angular momentum of an extended swarm of runaway planetesimals extending from 0.45 to Z35 AU, with a surface density falling off as 1/a. The size of the runaway embryos is prescribed by the condition
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From page 111... ...
The crosses are simulations in which mass, angular momentum, and negative energy are lost by means of the resonances shown in Figure 3. The solid squares represent simulations in which angular momentum and losses result from inclusion of spiral density wave damping, as described by Ward (1986, 1988~.
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From page 112... ...
The initial surface density can be adjusted to match the present total mass of the terrestrial planets, without disturbing the agreement with the observed energy and angular momentum. Similar agreement has been obtained in calculations in which both the gas and embryo surface densities varied as a-3t2, instead of a-i as used for the
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From page 113... ...
Therefore, all of the effects related to such giant impacts, formation of the Moon, fragmentation of smaller planets, and impact loss of atmospheres are to be expected for terrestrial planet systems arising from the more extended initial embryo swarms of the kind considered here. Furthermore, the inward radial migration associated with density wave drag, as well as the acceleration in eccentricity caused by the resonances, augment the tendency for a widespread provenance of the embryos responsible for the chemical composition of the final planets.
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From page 114... ...
1794. Uber den Unsprung der van PallasGefundenen und anderer ihr ahnlicher Eisen massen.
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From page 115... ...
1986. Accumulation of the terrestrial planets and implications concerning lunar origin.
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