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1.
A simulation of collisional and gravitational interaction in the early solar system generates planets ～500 km in diameter from an initial swarm of kilometer-sized planetesimals, such as might have resulted from gravitational instabilities in the solar nebula. The model treats collisions according to experimental and theoretical impact results (such as rebound, cratering, and catastrophic fragmentation) for a variety of materials whose parameters span plausible values for early solid objects. Ad hoc sticking mechanisms are avoided. The small planets form in ～104 yr, during which time most of the mass of the system continues to reside in particles near the original size. The relative random velocities remain of the order of a kilometer-sized body's escape velocity, with random velocities of the largest objects somewhat depressed because of damping by the bulk of the material. The simulation is terminated when the largest objects' random motion is of smaller dimension than their collision cross sections, so that the “particle-in-a-box” statistical methods of the model break down. The few 500-km planets, in a swarm still dominated by kilometer-scale planetesimals, may act as “seeds” for the subsequent, gradual, accretional growth into full-sized planets. 相似文献
2.
S.J. Weidenschilling 《Icarus》1976,27(1):161-170
Some aspects and consequences of the theory of gravitational accretion of the terrestrial planets are examined. The concept of a “closed feeding zone” is somewhat unrealistic, but provides a lower bound on the accretion time. Safronov's relative velocity relation for planetesimals is not entirely consistent with the feeding zone model. A velocity relation which includes an initial velocity component is suggested. The orbital parameters of the planetesimals and the dimensions of the feeding zone are related to their relative velocities. The assumption of an initial velocity does not seriously change the accretion time.Mercury, Venus, and the Earth have accretion times on the order of 108yr. Mars requires well over 109yr to accrete by the same assumptions. Currently available data do not rule out a late formation of Mars, but the lunar cratering history makes it unlikely. If Mars is as old as the Earth, nongravitational forces or a violation of the feeding zone concept is required. One such possibility is the removal of matter from the zone of Mars by Jupiter's influence. The final sweeping up by Mars after this event would result in the scattering of a considerable mass among the other terrestrial planets. The late postaccretional bombardments infrerred for the Moon and Mercury may have had this source. 相似文献
3.
A model for Galilean satellite formation was analyzed in which the satellites accrete in the presence of a dense, gaseous disk-shaped nebula and rapidly form optically thick, gravitationally bound primordial atmospheres. Upper-bound temperatures expected during accretion lead to partially differentiated structures for both Ganymede and Callisto, although with Ganymede much more differentiated than Callisto. When allowance is made for the aerodynamic breaking of infalling planetesimal fragments, lower surface temperatures result, and the amount of partial differentiation of Callisto is small, possibly approaching zero for a narrow size distribution of infalling planetesimals. The model is chosen to be consistent with the observed densities of the Galilean satellites and our current understanding of Jupiter formation. The retention of ices more volatile than H2O is considered but not modeled in detail. A nominal nebula of ～0.1 Jupiter masses is constructed by consideration of likely surface density profiles and existing Jupiter collapse calculations. This nebula is optically thick (even if grain opacity is ignored) in both radial and vertical directions and has a temperature profile T ～ 3600 (RJ/R), where RJ is Jupiter's radius and R is the radial distance in the disk midplane. Satellites accrete very rapidly (dynamical time scales being 102–104 years) and their optically thick gaseous envelopes are unable to eliminate the heat of accretion by radiation. Water-saturated, convective, adiabatic envelopes form, through which planetesimals fall, break up, and partially disseminate their mass. The resulting satellite surface temperatures during accretion are calculated. Possible implications of these models for the subsequent evolution of Ganymede and Callisto are explored and it is suggested that the extensive differentiation undergone by Ganymede may provide the right environment for subsequent resurfacing, whereas the relative lack of extensive differentiation for Callisto may explain the inferred absence of endogenic tectonism. 相似文献
4.
The temporal evolutions of the planetesimals scattered from the Jupiter zone for different masses of the proto-Jupiter [(a) 0.1 and (b) 1.0 of the present mass] are investigated. Due to the combined effects of the orbital evolution of the planetesimals and the elimination of these projectiles either via impact capture or injection into escape velocity by the outer planets, the whole scattering process lasts about 108 yr for case (a) and about 107 yr for case (b). The longer time scale may be a good estimate for the accretion time interval of Jupiter while the shorter one (107) gives the upper time limit of the late heavy-bombardment epoch of the terrestrial planets due to planetesimals scattered from the Jupiter zone. The limiting value of the encounter velocity U at the end of the scattering process is ≈0.6. Consideration of the collisional interaction of these projectiles with the asteroids indicates that the corresponding bombardment effect could be rather appreciable. Also, the asteroids on the inner edge of the main asteroid belt would have been bombarded more severely than those on the outer edge. From this point of view, the structure of the asteroidal belt could be affected significantly not only by Jupiter's gravitational perturbation effect but also by its early scattering process. 相似文献
5.
We have calculated formation of gas giant planets based on the standard core accretion model including effects of fragmentation and planetary envelope. The accretion process is found to proceed as follows. As a result of runaway growth of planetesimals with initial radii of ∼10 km, planetary embryos with a mass of ∼1027 g (∼ Mars mass) are found to form in ∼105 years at Jupiter's position (5.2 AU), assuming a large enough value of the surface density of solid material (25 g/cm2) in the accretion disk at that distance. Strong gravitational perturbations between the runaway planetary embryos and the remaining planetesimals cause the random velocities of the planetesimals to become large enough for collisions between small planetesimals to lead to their catastrophic disruption. This produces a large number of fragments. At the same time, the planetary embryos have envelopes, that reduce energies of fragments by gas drag and capture them. The large radius of the envelope increases the collision rate between them, resulting in rapid growth of the planetary embryos. By the combined effects of fragmentation and planetary envelope, the largest planetary embryo with 21M⊕ forms at 5.2 AU in 3.8×106 years. The planetary embryo is massive enough to start a rapid gas accretion and forms a gas giant planet. 相似文献
6.
Richard Greenberg Stuart J. Weidenschilling Clark R. Chapman Donald R. Davis 《Icarus》1984,59(1):87-113
Numerical simulations of planet growth in the outer solar system shows thatgrwoth of Uranus and Neptune occurs in reasonably short time, well below the actual age of the system, without the need for ad hoc assumptions about excess mass or artificially low relative velocities among the icy planetesimals. Low velocities, which speed accretion, are a natural consequence of the non-power-law size distribution of planetesimals, just as in our earlier simulations of terrestial planet growth. Initial planetesimals of size ～ 100 km, predicted by formal expressions for gravitational instability in a thin disk of solid material, failed to produce sufficient debris in the size range 1 to 10 km to account for population of the Oort cloud with comet-sized bodies. However, our model of nonhomologous settling of grains to the midplane of the solar system shows that gravitational clumping did not wait until all solid material had settled to the midplane, as had been assumed in earlier models. Rather, the clumping occurred in successive portions of the material that reached the midplane, producing “initial” planetesimals probably of comet-like sizes. Models of subsequent collisional evolution show that such an initial size distribution, similar to known comets, would have been required in order to have an adequate comet-like size distribution available to feed the Oort cloud as the other planets reach full size. Comets are probably unaltered remnants of the initial population of planetesimals in the outer solar system, not fragments of larger bodies. 相似文献
7.
E. L. Ruskol 《Solar System Research》2006,40(6):456-461
The properties of gas-dust disks that surrounded Jupiter and Saturn during the final stage of their formation are analyzed. The sizes of the disks are determined by the total planetocentric angular momentum of the matter accreted by planets and correspond to the sizes of the orbits of their largest satellites. The mass of the solid component of disks is limited from below by the total mass of the Galilean satellites of Jupiter (no less than 4 × 1026 g) and the mass of the largest Saturnian satellites (1.4 × 1026 g), whereas the mass of the gaseous component is limited from above by the amount of hydrogen and helium that could have been later lost by the disks. Our analysis of the known mechanisms of dissipation of gas showed that its simultaneous content in the disks relative to the solid component was much lower than the corresponding gas-to-solid ratio in the Sun. A certain amount of solid compounds (including ice) could have been brought into the disks with planetesimals, which had undergone mutual collisions in the neighborhood of giant planets and served as germs of satellites. The bulk of solid matter appears to have been captured into disks when the latter were crossed by smaller and intermediate-sized planetesimals, which then became parts of the satellites. 相似文献
8.
A two-stage growth of the giant planets, Jupiter and Saturn, is considered, which is different from the model of contraction of large gaseous protoplanets. In the first stage, within a time of ～3 × 107 years in Jupiter's zone and ～2 × 108 years in Saturn's zone, a nucleus forms from condensed (solid) material having the mass, ～1028 g, necessary for the beginning of acceleration. The second stage may gravitating body, and a relatively slow accretion begins until the mass of the planet reaches ～10 m⊕. Then a rapid accretion begins with the critical radius less than the radius of the Hill lobe, so that the classical formulae for the rate of accretion may be applied. At a mass m > m1 ≈ 50 m⊕ accretion proceeds slower than it would according to these formulae. When the planet sweeps out all the gas from its nearest zone of feeding (m = m2 ≈ 130 m⊕), the width of the exhausted zone being of the whole zone of the planet) growth is provided the slow diffusion of gas from the rest of the zone (time scale increases to 105?106 years and more). The process is terminated by the dissipation of the remnants of gas. In Saturn's zone m1 > m2 ≈ 30 m⊕. The initial mass of the gas in Jupiter's zone is estimated. Before the beginning of the rapid accretion about 90% of the gas should have been lost from the solar system, and in the planet's zone less than two Jupiter masses remain. The highest temperature of Jupiter's surface, ≈5000°K, is reached at the stage of rapid accretion, m < 100 m⊕, when the luminosity of the planet reaches 3 × 10?3 L⊙. This favors an effective heating of the inner parts of the accretionary disk and the dissipation of gas from the disk. The accretion of Saturn produced a temperature rise up to 2000?2400° K (at m ≈ 20?25 m⊕) and a luminosity up to 10?4 L⊙. 相似文献
9.
Anthropic selection of a Solar System with a high Al/Al ratio: Implications and a possible mechanism
Since our technological civilisation depends on our planet's properties, anthropic selection can explain the close match between the high 26Al/27Al ratios in the earliest Solar System solids, which are difficult to produce in models of star-formation, and the limiting value required to cause (the widely observed) thermal processing of planetesimals. We suggest that volatile loss on heating of planetesimals favours future development of technological civilisations in Solar Systems with elevated concentrations of 26Al. 相似文献
10.
When Jupiter was on the order of three to ten Earth masses in size, there undoubtedly was a considerably larger mass of condensed matter in its zone, since Jupiter would have perturbed most of it to other parts of the solar system. Monte Carlo studies indicate a significant portion would have crossed the Earth's orbit. If the Earth and Moon had not yet fully formed, the probability of Earth-zone planetesimals being hit by this Jupiter-scattered material was high. Further Monte Carlo models of these collisions and their products indicate a significant portion of matter was heated to melting, even if less than 5% of the relative kinetic energy went into heat. The models include capture probabilities by an embryo Earth and a protolunar swarm. Because heat energy is correlated with comminution energy, and because the capture probability of the swarm is mass-dependent while the embryo's is not, the protolunar material suffered much higher heating on the average than did the proto-Earth material. 相似文献
11.
S.J. Weidenschilling 《Icarus》1980,44(1):172-189
The behavior of solid particles in a low-mass solar nebula during settling to the central plane and the formation of planetesimals is examined. Gravitational instability in a dust layer and collisional accretion are considered as possible mechanisms of planetesimal formation. Non-Keplerian rotation of the nebula results in shear between the gas and a dust layer. This shear produces turbulence within the layer which inhibits gravitational instability, unless the mean particle size exceeds a critical value, ～1 cm at 1 AU. The size requirement is less stringent at larger heliocentric distances, suggesting a possible difference in planetesimal formation mechanisms between the inner and outer nebula. Coagulation of grains during settling is expected in the solar nebula environment. Van der Waals forces appear adequate to produce centimeter-sized aggregates. Growth is primarily due to sweepup of small particles by larger ones due to size-dependent settling velocities. A numerical model for computing simultaneous coagulation and settling is described. Relative velocities are determined by gas drag and the non-Keplerian rotation of the nebula. The settling is very nonhomologous. Most of the solid matter reaches the central plane as centimeter-sized aggregates in a few times 103 revolutions, but some remains suspended in the form of fine dust. Drag-induced relative velocities result in collisions. The growth of bodies in the central plane is initially rapid. After sizes reach ～103 cm, relative velocities decrease and the growth rate declines. Gas drag rapidly damps the out-of-plane motions of these intermediate-sized bodies. They settle into a thin layer which is subject to gravitational instability. Kilometer-sized planetesimals are formed by this composite process. 相似文献
12.
Collisions between planetesimals at speeds of several kilometres per second were common during the early evolution of our Solar System. However, the collateral effects of these collisions are not well understood. In this paper, we quantify the efficiency of heating during high-velocity collisions between planetesimals using hydrocode modelling. We conducted a series of simulations to test the effect on shock heating of the initial porosity and temperature of the planetesimals, the relative velocity of the collision and the relative size of the two colliding bodies. Our results show that while heating is minor in collisions between non-porous planetesimals at impact velocities below 10 km s−1, in agreement with previous work, much higher temperatures are reached in collisions between porous planetesimals. For example, collisions between nearly equal-sized, porous planetesimals can melt all, or nearly all, of the mass of the bodies at collision velocities below 7 km s−1. For collisions of small bodies into larger ones, such as those with an impactor-to-target mass ratio below 0.1, significant localised heating occurs in the target body. At impact velocities as low as 5 km s−1, the mass of melt will be nearly double the mass of the impactor, and the mass of material shock heated by 100 K will be nearly 10 times the mass of the impactor. We present a first-order estimate of the cumulative effects of impact heating on a porous planetesimal parent body by simulating the impact of a population of small bodies until a disruptive event occurs. Before disruption, impact heating is volumetrically minor and highly localised; in no case was more than about 3% of the parent body heated by more than 100 K. However, heating during the final disruptive collision can be significant; in about 10% of cases, almost all of the parent body is heated to 700 K (from an initial temperature of ∼300 K) and more than a tenth of the parent body mass is melted. Hence, energetic collisions between planetesimals could have had important effects on the thermal evolution of primitive materials in the early Solar System. 相似文献
13.
G. P. Horedt 《Earth, Moon, and Planets》1982,26(1):89-92
There are obtained upper limits for the relative velocity at infinity of accreting planetesimals for a nearly constant mass of the largest accreting planetesimal and also in the case of variable mass. We conclude, that while the larger planets cannot be brought to the stage of rotational instability by stochastic collisions, the asteroids could be brought. provided that the relative velocities in the asteroid belt were larger than about 2 km s–1. 相似文献
14.
Abstract— Some recent information on the Mn‐Cr and Al‐Mg systems is reviewed. This information is used to derive constraints on the timing of processes and events, which took place in the early solar system. Using reasonable assumptions, a timeline is constructed where the estimated age of the solar system is ～4571 Ma. This age is taken to mark the time when most calcium‐aluminum‐rich inclusions (CAIs) were starting to form, a process that may have lasted for several 105 years. Almost contemporaneously small planetesimals have accreted that served to store these CAIs for later dispersal among larger planetesimals. By the time large numbers of planetesimals of several tens of kilometers in size had formed, the interior of these objects started to melt through the decay of 26Al. Collisional disruption of these planetesimals allowed gases, dust, and melt to escape into the surrounding space. The fine droplets of melt reacted with gas and dust to form chondrules, which, after rapid cooling, were partially re‐accreted onto the residual rubble pile. This process of primary chondrule formation, in most cases involving several generations of planetesimals, most plausibly lasted only for ～2 Ma. Towards the end of this period and during the following 3 to 4 Ma planetary objects of several hundred kilometers in size were formed. They still stored enough energy to continue melting from the inside to finally differentiate into chemically stratified layers, with basaltic volcanism occurring within a few million years. 相似文献
15.
As planetary embryos grow, gravitational stirring of planetesimals by embryos strongly enhances random velocities of planetesimals and makes collisions between planetesimals destructive. The resulting fragments are ground down by successive collisions. Eventually the smallest fragments are removed by the inward drift due to gas drag. Therefore, the collisional disruption depletes the planetesimal disk and inhibits embryo growth. We provide analytical formulae for the final masses of planetary embryos, taking into account planetesimal depletion due to collisional disruption. Furthermore, we perform the statistical simulations for embryo growth (which excellently reproduce results of direct N-body simulations if disruption is neglected). These analytical formulae are consistent with the outcome of our statistical simulations. Our results indicate that the final embryo mass at several AU in the minimum-mass solar nebula can reach about ∼0.1 Earth mass within 107 years. This brings another difficulty in formation of gas giant planets, which requires cores with ∼10 Earth masses for gas accretion. However, if the nebular disk is 10 times more massive than the minimum-mass solar nebula and the initial planetesimal size is larger than 100 km, as suggested by some models of planetesimal formation, the final embryo mass reaches about 10 Earth masses at 3-4 AU. The enhancement of embryos’ collisional cross sections by their atmosphere could further increase their final mass to form gas giant planets at 5-10 AU in the Solar System. 相似文献
16.
G.P. Horedt 《Icarus》1985,64(3):448-470
We derive first-order differential equations for the late stages of planetary accretion (planetesimal mass >1013 g). The effect of gravitational encounters, energy exchange, collisions, and gas drag has been included. Two simple models are discussed, namely, (i) when all planetesimals have the same mass and (ii) when there is one large planetesimal and numerous small planetesmals. Gravitational two-body encounters are modeled according to Chandrasekhar's classical theory from stellar dynamics. It is shown that the velocity increase due to mutual encounters can be modeled according to the simple theory of random flights. We find analytical equations for the average velocity decrease due to collisions. Gas drag, if present, is modeled in averaged form up to the first order in the eccentricities and inclinations of the planetesimals. Characteristic time scales for the formation of the terrestrial planets are found for the most favorable models to be of order 108 year. The calculated mass of rock and ice of the giant planets is too low as compared to the observed one. This difficulty of our model could be overcome by assuming a several times larger surface density, an enlarged accretion cross section, and gas accretion during the final stages of accretion of the solid cores of the giant planets. Analytical and numerical results are presebted, the evolutionary tracks showing satisfactory agreement with observations for some models. 相似文献
17.
Richard Greenberg 《Earth, Moon, and Planets》1980,22(1):63-66
Safronov's (1972) demonstration that relative velocities of planetesimals would be comparable to the dominant size bodies' escape velocities, combined with a plausible size distribution that has most mass in the largest bodies, yielded his evolution model with limited growth of the largest planetesimal with respect to its next largest neighbors. A numerical simulation of planetesimal accretion (Greenberget al., 1978) suggests that at least over one stage of collisional accretion, velocities were much lower than the escape velocity of the largest bodies, because the bulk of the mass still resided in km-scale bodies. The low velocities at this early stage may conceivably have permitted early runaway growth, which, in turn, would have kept the velocities low and permitted continued runaway growth of the largest bodies.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy. 相似文献
18.
LON L. HOOD 《Meteoritics & planetary science》1998,33(1):97-107
Abstract— We test the hypothesis that chondrules (and Type B and C calcium-aluminum-rich inclusions, CAIs) originated during passage of precursors through bow shocks upstream of planetesimals moving supersonically relative to nebula gas. A two-dimensional piecewise parabolic method (PPM) hydrocode, supplemented by a one-dimensional adiabatic shock model, is employed to simulate the postshock gas density, temperature, and velocity fields for given planetesimal sizes, velocities, and ambient nebular densities and temperatures. Thermal histories of incident silicate particles are calculated in the free molecular flow approximation by integration of the one-dimensional equations of gas-grain energy and momentum transfer. For gas number densities >1014 cm?3, Mach numbers in the range of 4 to 5 are sufficient to melt isolated spherical particles with radii in the range 0.05 to 0.5 mm during passage of shocked gas thicknesses of 25–35 km. Minimum gas-planetesimal relative velocities are in the range 5.5–7 km/s, implying orbital eccentricities >0.2 and/or inclinations >15°. Melting of centimeter-sized CAI precursors requires either higher Mach numbers (6–7) or ambient gas densities >1015 cm?3. For a constant radial distribution of planetesimal orbital eccentricities and inclinations, the model predicts more efficient melting of precursor particles at decreasing radial distances from the Sun where planetesimal velocities are largest. In order to process a significant fraction of solids in the nebula, planetesimals near ～2.5 AU during the chondrule formation epoch must have had a range of eccentricities and inclinations comparable to those presently observed in the residual asteroid belt. The most likely energy source for maintaining the necessary gas-planetesimal relative velocities is external gravitational perturbations associated with the forming outer planets, primarily Jupiter. 相似文献
19.
Ignacio R. Ferrín 《Icarus》1975,26(1):45-52
“Condensations” of light have been observed when Saturn's rings are seen almost edge on, and the Sun and the Earth are on opposite sides of the ring plane. These condensations are associated with ring C and Cassini's division. If the relative brightness between the two condensations and the optical thickness of ring C are known, we can calculate the optical thickness of Cassini's division, τCASS. Using Barnard's and Sekiguchi's measurements, we have obtained 0.01 ? τCASS ? 0.05. A brightness profile of the condensations which agrees well with visual observations is also presented.We are able to set an upper limit of about 0.01 for the optical thickness of any hypothetical outer ring. This rules out a ring observed by C. Cragg in 1954, but does not eliminate the D′ ring observed by Feibelman in 1967.It is known that the outer edge of ring B is almost at the position of the 1/2 resonance with Mimas. Franklin, Colombo, and Cook explained this fact in 1971, postulating a total mass of ring B of 10?6MSATURN. We have derived a formula for the mass of the rings, which is a linear function of the mean particle size. We find that 10?6MSATURN implies large particles (～70m). If the particles are small (～10cm), as currently believed, the total mass of ring B is not enough to shift the outer edge. We conclude that the above explanation and current size estimates are inconsistent. 相似文献
20.
S. J. Weidenschilling 《Meteoritics & planetary science》2019,54(5):1115-1132
Thermal models of asteroids generally assume that they accreted either instantaneously or over an extended interval with a prescribed growth rate. It is conventionally assumed that the onset of accretion of chondrite parent bodies was delayed until a substantial fraction of the initial 26Al had decayed. However, this interval is not consistent with the early melting, and differentiation of parent bodies of iron meteorites. Formation time scales are tested by dynamical simulations of accretion from small primary planetesimals. Gravitational accretion yields rapid runaway growth of large planetary embryos until most smaller bodies are depleted. In a given simulation, all asteroid‐sized bodies have comparable growth times, regardless of size. For plausible parameters, growth times are shorter than the lifetime of 26Al, consistent with thermal models that assume instantaneous accretion. Rapid growth after planetesimal formation is consistent with differentiation of parent bodies of iron meteorites, but not with the assumed delay in formation of chondritic bodies. After the initial growth stage, there is an interval of slower evolution until the belt is stirred and the embryos are dynamically removed. During this interval, a fraction of asteroid‐sized bodies experience large accretional impacts, allowing bodies of the same final size to have very different histories of radius versus time. Accretion from small primary planetesimals leaves some fraction of material in bodies small enough to preserve CAIs while avoiding heating by 26Al. Unheated material can be a significant fraction of the mass that remains after large embryos are removed from the Main Belt. 相似文献