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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11. Late Stages of Accumulation and Early Evolution of the Planets
11. Late Stages of Accumulation and Early Evolution of the Planets
Pages 143-162
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From page 143... ...
VITYAZEV AND G.V. PECHERNIKOVA Schmidt Institute of the Physics of the Earth ABSTRACT This article briefly discusses recently developed solutions of problems that were traditionally considered fundamental in classical solar system cosmogony: determination of planetary orbit distribution patterns, values for mean eccentricity and orbital inclinations of the planets, and rotation periods and rotation axis inclinations of the planets.
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From page 144... ...
produced a satisfactory picture of circumsolar disk formation, or a reliable estimate of its mass M and characteristic initial dimensions R*
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From page 145... ...
in low-mass, circumstellar gaseous disks. The solid line indicates models of disks near FS class stem: 1: m/k = 1; 2: m/k = 1/2; 3: m/1: = 1/4; the dashed line indicates models of disks near GO class stem: 4: m/k = 1; 5: m/k =1/2; 6: m/k =1/4; the dotted and dashed line shows disks near GS class stars: 7: m/k = 1; 8: m/k = 1/2; 9: my = 1/4; the straight lines are critical density distributions for the corresponding classes of stars: 10: °.Cr(FS)
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From page 146... ...
This excess may be related to diffusion spread of the planetesimal swarm during planet accumulation. Therefore, present planetary system dimensions may
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From page 147... ...
PI^NETESIMAL MASS SPECTRUM N(M,T) AND MATTER REDISTRIBUTION After dust settles on the central plane and dust clusters are formed due to gravitational instability, there occurs the growth and compacting of some clusters, and the breakdown and absorption of others.
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From page 148... ...
R2/TE(m) , e is the eccentricity, rE is the characteristic Chandrasekhar relaxation time scale, AR = eR.
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From page 149... ...
where Te, Tg and Ts are correspondingly the characteristic Chandrasekhar relaxation time scales, gas deceleration and the characteristic time scale between collisions, ,0~1 = 0.05 - 0.13 (Safronov 1969; Stewart and Kaula 1980) , p2 = 0.5 (Safronov 1~9)
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From page 150... ...
R ~ v(`t~JR/vk, (11) The characteristic mixing time scale for R in this zone virtually coincides with the characteristic time scale for the transfer of regular energy motion to chaotic energy motion, and the characteristic time scale for energy exchange between bodies.
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From page 151... ...
~. The circles and dots indicate the results of numerical simulation of the process of terrestrial planet accumulation (Ipatov 1987; Wetherill 1985~.
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From page 152... ...
The theory that was developed not only explains the physical meaning of the Titius-Bode law, but also provides a satisfactory estimate of parameter b. The partial overlapping of zones,
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From page 153... ...
An estimate of the number of forming planets can easily be generated from (19) for a preplanetary disk with moderate mass and distribution BARD according to the standard or MK-models with pre-assigned outer and inner boundaries: N— l n(R*
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From page 154... ...
TIME SCALE FOR THE REMOVAL OF GAS FROM THE TERRESTRIAL PLANET ZONE It is easy to demonstrate that if gas with a density of at least 10-2 of the original amount remains during the formation of meteorite parent bodies in the preplanetary disk between the asteroid belt and the Sun, then
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From page 156... ...
The reasoning was that prior to that time nontransparency of the swarm of bodies was still sufficiently high, while less matter would have been irradiated at a later stage than the 5-10% that has been discovered experimentally,. The conclusion then follows that there was virtually no gas as early as the primary stage of terrestrial planet accumulation.
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From page 157... ...
went into forming the terrestrial planets had already passed the swarm through repeated metamorphism and melting, both at the surface and in the cores of bodies analogous to parent bodies of meteorites. INITIAL EARTH TEMPERATURE AND ENERGY SOURCES If we take into account the collisions of accreting planets with 1000kilometer bodies, we conclude that there were extremely heated interiors, beginning with protoplanetary masses ~ 10-M.
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From page 158... ...
HEAT MASS TRANSFER PROCESSES Heat-mass transfer calculations in planetary evolution models are current~ made using various procedures to parameterize the entire system of viscous liquid hydrodynamic equations for a binary or even singlecomponent medium. This issue was explored (Safronov and Vityazev 1986; Vityazev et al.
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From page 159... ...
. In the order of magnitude, velocity v, relaxation time scale T
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From page 160... ...
Complications with an estimate of the characteristic time scales for separation are, first of all, related to highly ambiguous data on numerical viscosity values for matter in the interiors. Variations in the temperature and content of fluids on the order of several percent, close to liquidus-solidus curves, alter viscosity numerical values by orders of magnitude.
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From page 161... ...
At the same time, if we are to make significant progress in this area, we will need to conduct experimental studies on localized matter separation and labor-intensive numerical modeling to simulate large-scale processes of fractioning and differentiation of the matter of planetary cores. REFERENCES Cassen, P.M., and A
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From page 162... ...
AS USSR Publ. Earth Physics 6:5-24.
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