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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.

— The main asteroid belt has lost >99.9% of its solid mass since the time at which the planets were forming, according to models for the protoplanetary nebula. Here we show that the primordial asteroid belt could have been cleared efficiently if much of the original mass accreted to form planetsized bodies, which were capable of perturbing one another into unstable orbits. We provide results from 25 N-body integrations of up to 200 planets in the asteroid belt, with individual masses in the range 0.017–0.33 Earth masses. In the simulations, these bodies undergo repeated close encounters which scatter one another into unstable resonances with the giant planets, leading to collision with the Sun or ejection from the solar system. In response, the giant planets' orbits migrate radially and become more circular. This reduces the size of the main-belt resonances and the clearing rate, although clearing continues. If ∼3 Earth masses of material was removed from the belt this way, Jupiter and Saturn would initially have had orbital eccentricities almost twice their current values. Such orbits would have made Jupiter and Saturn 10–100x more effective at clearing material from the belt than they are on their current orbits. The time required to remove 90% of the initial mass from the belt depends sensitively on the giant planets' orbits, and weakly on the masses of the asteroidal planets. 18 of the 25 simulations end with no planets left in the belt, and the clearing takes up to several hundred million years. Typically, the last one or two asteroidal planets are removed by interactions with planets in the terrestrial region

We have constructed an improved statistical method for the calculation of planetary accumulation using the currently standard model of terrestrial planet formation and using the latest results of planetary dynamical theory. The method is applicable for the range of masses in which velocity changes are dominated by gravitational forces, mutual collisions, and gas drag. Calculations are reported both with and without nebular gas. This method has been compared with N-body simulations, and the results of the two calculations are in agreement. As in earlier calculations, the growth of bodies in this mass range and at 1 AU occurs on a ∼105 year time scale and is characterized by the evolution of an initially continuous mass distribution into a bimodal distribution, the high mass end of which consists of runaway bodies in the size range of ∼1026 g. In this general way, these results are in agreement with those reported earlier (e.g., Wetherill and Stewart 1993, Icarus106, 190–209), but significant differences are also found as a result of the greater precision of the collision rate and the velocity evolution rate of planetesimals used in the present work.

Previous calculations of the accumulation of small (~ MO km) planetesimals at ~1 AU to form Mars-sized bodies assumed that the initial assemblage of planetesimals were all present at the outset. This is an obviously reasonable assumption in systems in which the time scale for growth time of ~1026 g planetary bodies is long compared to estimates of the evolutionary time scale of a protosolar disk, as was the case in the pioneering work of Safronov (1969). It is now found that as a result of the preplanetary assemblage being unstable with respect to the runaway growth of the largest bodies, this is unlikely to be the case. The more realistic alternative of adding the initial planetesimals on a ~105 year time scale is considered here, as well as the consequences of the initial planetesimals being considerably smaller than those assumed previously. It is found that although the time scale for runaway growth is now actually controlled by the availability of planetesimals, for planetesimal production time scales of ~105 yrs, the final consequences are very similar. These calculations do show, however, that as a consequence of continuous infall during the runaway growth process, the late initial planetesimals are likely to be catastrophically disrupted by mutual collisions. For this reason, a more detailed treatment of the growth of planetesimals into planetary embryos will require a better understanding of the difficult problem of formation of the initial planetesimals themselves.

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 (Venc) between bodies of similar mass. Plantesimals of identical mass have Venc approximately 1 and approximately 10 m s-1 (near 1 and 2.6 AU, respectively) while bodies differing by approximately 10 in mass have Venc approximately 10 and approximately 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 approximately 10(6)-year timescale, initially by nonrunaway growth and transitioning to runaway growth after approximately 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.

We simulate the late stages of terrestrial-planet formation using N-body integrations, in three dimensions, of disks of up to 56 initially isolated, nearly coplanar planetary embryos, plus Jupiter and Saturn. Gravitational perturbations between embryos increase their eccentricities,e, until their orbits become crossing, allowing collisions to occur. Further interactions produce large-amplitude oscillations ineand the inclination,i, with periods of ∼105years. These oscillations are caused by secular resonances between embryos and prevent objects from becoming re-isolated during the simulations. The largest objects tend to maintain smallereandithan low-mass bodies, suggesting some equipartition of random orbital energy, but accretion proceeds by orderly growth. The simulations typically produce two large planets interior to 2 AU, whose time-averagedeandiare significantly larger than Earth and Venus. The accretion rate falls off rapidly with heliocentric distance, and embryos in the “Mars zone” (1.2 2 AU) is efficiently cleared as objects scatter one another into resonances, where they are lost via encounters with Jupiter or collisions with the Sun, leaving, at most, one surviving object. Accretional evolution is complete after 3 × 108years in all simulations that include Jupiter and Saturn. The number and spacing of the final planets, in our simulations, is determined by the embryos' eccentricities, and the amplitude of secular oscillations ine, prior to the last few collision events.

A system of two small planets orbiting the Sun on low-eccentricity, low-inclination orbits is stable with respect to close encounters if the initial semi-major axis difference, Δ, measured in mutual Hill radii,RH, exceeds[formula], due to conservation of energy and angular momentum. We investigate the stability of systems of more than two planets using numerical integrations. We find that systems with Δ 10 are also unstable. The slopebdepends weakly on the number of planets, but is independent of planetary mass,m, if we measure Δ in units that are proportional tom1/4rather than the usualRH∝m1/3. Instability in multi-planet systems arises because energy and angular momentum are no longer conserved within each two-planet subsystem due to perturbations by the additional planet(s). These results suggest that planetary embryos will not become isolated prior to the final stage of terrestrial-planet formation simply due to a failure to achieve close encounters. Other factors leading to isolation cannot be ruled out at this stage.

A quantitative numerical program, developed to model the formation of the terrestrial planets and asteroids of our solar System (Wetherill 1992), has been extended to include a more general range of stellar and preplanetary nebular parameters, as may be expected elsewhere in the Galaxy and Universe. The results of about 500 new simulations of planetary formation are reported. It is found that for circumstellar disk parameters that are not too different from those of the Solar System, the number and radial distribution of final terrestrial planets are insensitive to stellar mass and these planets concentrate in the vicinity of 1 AU. In contrast, the position of the biologically habitable heliocentric distances are strongly dependent on stellar mass (Kastinget al.1993), and the frequency of habitable planets is therefore also dependent on stellar mass. Stars of 1.0 solar mass (M⊙) almost always have at least one planet of mass >1/3 Earth mass (M⊕) in their habitable zones. Larger planets of the smaller stars tend to be too cold, those of the larger stars too hot. Nevertheless, some ∼5 to 15% of the simulated planetary systems associated with stars as small as 0.5M⊙and as large as 1.5M⊙contain a habitable planet. The position and number of simulated terrestrial planets are also insensitive to the initial surface density of solid bodies in the circumstellar disk, but the size of the planets is approximately proportional to the surface density. These results represent planetary systems associated with radial variation of surface densities, disk parameters, and giant planet populations not very different from those of our Solar System. The outer boundary of their “peak” in semimajor axis distribution at 1 AU is determined by the increasing proximity of more distant bodies to strong resonances by Jupiter and Saturn. As a consequence, this boundary will move in or out in accordance with the position, or absence, of such bodies in other systems. In the complete absence of Jupiter, the median planetary mass in the terrestrial planet region is almost 2M⊕, for the same initial surface density used in the models characteristic of our Solar System. The inner boundary is determined by the minimum distance at which planet-forming solids condense in the disk. For some, not necessarily likely, variations in these parameters, abundant populations of habitable planets can be obtained for all the values of stellar mass considered.

A general overview of the events surrounding the fall of the Peekskill meteorite is presented.

THE dusty disk around the star β Pictoris is believed to contain a large number of comet-like bodies1,2. Transient absorption events associated with β Pictoris have been observed at many wavelengths3–6 and attributed to cometary objects on eccentric orbits passing between the star and the Earth7. One unexplained aspect of these events is the large asymmetry between red-shifted and blue-shifted features: ∼90% of the events are red-shifted6. We show here that such an asymmetry is a natural consequence of the influence on cometary orbits of secular resonances associated with some planetary systems. Results from numerical integrations of test particles in a model of our Solar System show that the v6secular resonance excites objects initially on near-circular orbits to high eccentricities while aligning their perihelia. Depending on the location of a distant observer, this alignment can produce an asymmetry similar to that observed for β Pictoris. Our results imply the presence of at least two planets (a prerequisite for the existence of secular resonances) around β Pictoris.

Collision cascades play a prominent role in processing the present asteroid belt, as well as formative planetary systems. As a first step toward understanding how this mechanism operates, an analytical solution has been obtained for the steady-state size distribution of a self-similar collisional fragmentation cascade. It is found that this corresponds to a power law for the differential mass distribution dn = Cm -α dm , where the exponent α is very nearly 11/6, equivalent to a differential radius distribution dn = C * r -3.5 dr . This is in agreement with the earlier conclusion of J. S. Dohnanyi (1969, J. Geophys. Res. 74, 2531-2554). The work of Dohnanyi has been extended considerably to include a full treatment of the simultaneous occurrence of cratering and catastrophic fragmentation. A more physically realistic model of catastrophic fragmentation is used in which the size of the largest fragment decreases with projectile mass. The average steady-state value of the exponent α (1.8333) is found to be extremely insensitive to the assumed physical parameters of the fragmentation process, such as the strength of the target, the threshold for catastrophic fragmentation, the relative contribution of cratering and catastrophic fragmentation, the size and number of the largest fragments, and the size distribution of the fragments produced by individual fragmentation events. The robust nature of the result is a consequence of the steady-state solution being primarily the consequence of geometrical rather than mechanical considerations.

An earlier investigation of the formation of approximately 10(26) g planetary embryos from much smaller planetesimals (G.W. Wetherill and G.R. Stewart 1989, Icarus 77, 350-357) has been extended to include the effects of collisional fragmentation, the low relative velocity regime in which the effects due to solar gravity are important, and independent perturbations of eccentricity and inclination. In agreement with this earlier work, it if found that at 1 AU runaway growth occurs on a approximately 10(-5)-year time scale as a consequence of equipartition of energy between large and small planetesimals. It is now seen that the runaway is initiated after approximately 10(4) years, when the relative velocities of the larger bodies temporarily fall into the low-velocity regime, lowering their inclinations and increasing their gravitational capture rates. After approximately 2 X 10(4) years, relative velocities between most bodies emerge from the low-velocity regime, and these higher velocities tend to inhibit further runaway growth. This rapid runaway growth is self-regulated, however, by these same higher velocities, causing fragmentation of the smaller bodies. The velocities of the collision fragments are reduced by gas drag, facilitating their capture by the growing runaway embryos. Variations in which different fragmentation models are used, or long-range forces between nonrunaway bodies are absent, give similar results. When fragmentation is not included, the time scale for growth increases to approximately 3 X 10(5) years as a result of loss of the self-regulating process described above.

The growth and orbital evolution of a swarm of ∼1026-g “planetary embryos,” originally distributed throughout both the terrestrial planet and the asteroidal regions has been simulated using a Monte Carlo technique previously used by the author to study the formation of the terrestrial planets alone. The effects of the giant planets, primarily Jupiter, are simply assumed to be those operative at present: chaotic acceleration in resonance regions and gravitational ejection of objects by encounters with Jupiter at aphelia ≳4.75 AU. It is found that the asteroidal embryos are very effective in scattering one another into resonance regions. The resulting orbital evolution clears the asteroid belt of embryos in about half of the simulations. Embryos accumulate in the terrestrial planet region to form a stochastically determined variety of planetary configurations that are similar in total mass, specific energy, specific angular momentum, planetary size, and orbital elements to our Solar System. The small quantity of material remaining in the asteroid region has a velocity distribution very much like that of the observed asteroids. It is concluded that this model, although certainly imperfect, represents a viable alternative to models in which the initial asteroidal population is limited to bodies the size of the present asteroids.

Three cases for which the analytic solutions to the planetary embryo coagulation equation are known, namely those of constant coagulation rate, of rate proportional to the sum of the masses of the two colliding bodies, and of rate proportional to the product of their masses, are presently used to test the mathematical validity of the Wetherill and Stewart (1989) physical model for the evolution of planetary embryos' mass distribution. In all cases, excellent agreement is found between numerical physical modeling results and those of the analytic solutions. The treatment of the runaway case can proceed via extension of the efforts of Trubnikov (1971).

The origin of the earth is discussed in the context of the formation of the sun and the planets, and a standard model for such a formation assuming gravitational instability in a dense interstellar molecular cloud is outlined, along with the most significant variant of the model in which the loss of the nebular gas occurred after the formation of the earth. The formation of the sun and solar nebulae is addressed, and the coagulation of grains and the formation of small planetesimals are covered, along with the gravitational accumulation of planetesimals into planetary embryos and final stages of accumulation - embryos of planets. It is pointed out that the final stage of accumulation consists of the collision of these embryos; because of their large size, particularly after their further growth, these collisions represent giant impacts. It is concluded that the earth was initially an extremely hot and melted planet, surrounded by a fragile atmosphere and subject to violent impacts by bodies of the size of Ceres and even the moon.

ON 9 October 1992, a bright fireball appeared over West Virginia, travelled some 700 km in a northeasterly direction, and culminated in at least one impact: a 12.4-kg ordinary chondrite was recovered in Peekskill, New York1. Fortuitously, the event was captured on several video recordings, which provide a detailed record of both the fragmentation of the object and related atmospheric effects. These are the first motion pictures of a fireball from which a meteorite has been recovered. We report here the preliminary analysis of 14 video recordings of the event, from which we determine the ground path and the original orbit of the object.

About 30% of detected extrasolar planets exist in multiple-star systems. The standard model of planet formation cannot easily accommodate such systems and has difficulty explaining the odd orbital characteristics of most extrasolar giant planets. We demonstrate that the formation of terrestrial-size planets may be insulated from these problems, enabling much of the framework of the standard model to be salvaged for use in complex systems. A type of runaway growth is identified that allows planetary embryos to form by a combination of nebular gas drag and perturbations from massive companions—be they giant planets, brown dwarfs, or other stars.

The existence of Uranus and Neptune presents severe difficulties for the core accretion model for the formation of ice giant planets. We suggest an alternative mechanism, namely disk instability leading to the formation of gas giant protoplanets, coagulation and settling of dust grains to form ice/rock cores at their centers, and photoevaporation of their gaseous envelopes by a nearby OB star, as a possible means of forming ice giant planets., Comment: TeX file, 20 pages, no figures, 1 table, accepted by Icarus, Preprints available at http://www.ciw.edu/boss/ftp/planets/icaice.ps

Large Near-Earth-Asteroids have played a role in modifying the character of the surface geology of the Earth over long time scales through impacts. Recent modeling of the disruption of large meteoroids during atmospheric flight has emphasized the dramatic effects that smaller objects may also have on the Earth's surface. However, comparison of these models with observations has not been possible until now. Peekskill is only the fourth meteorite to have been recovered for which detailed and precise data exist on the meteoroid atmospheric trajectory and orbit. Consequently, there are few constraints on the position of meteorites in the solar system before impact on Earth. In this paper, the preliminary analysis based on 4 from all 15 video recordings of the fireball of October 9, 1992 which resulted in the fall of a 12.4 kg ordinary chondrite (H6 monomict breccia) in Peekskill, New York, will be given. Preliminary computations revealed that the Peekskill fireball was an Earth-grazing event, the third such case with precise data available. The body with an initial mass of the order of 10(4) kg was in a pre-collision orbit with a = 1.5 AU, an aphelion of slightly over 2 AU and an inclination of 5 degrees. The no-atmosphere geocentric trajectory would have lead to a perigee of 22 km above the Earth's surface, but the body never reached this point due to tremendous fragmentation and other forms of ablation. The dark flight of the recovered meteorite started from a height of 30 km, when the velocity dropped below 3 km/s, and the body continued 50 km more without ablation, until it hit a parked car in Peekskill, New York with a velocity of about 80 m/s. Our observations are the first video records of a bright fireball and the first motion pictures of a fireball with an associated meteorite fall.

Models of planetary formation can be tested by comparison of their ability to predict features of our Solar System in a consistent way, and then extrapolated to other hypothetical planetary systems by different choice of parameters. When this is done, it is found that the resulting systems are insensitive to direct effects of the mass of the star, but do strongly depend on the properties of the disk, principally its surface density. Major uncertainty results from lack of an adequate theoretical model that predicts the existence, size, and distribution of analogs of our Solar System, particularly the gas giants Jupiter and Saturn. Nevertheless, reasons can be found for expecting that planetary systems, including those containing biologically habitable planets similar to Earth, may be abundant in the Galaxy and Universe.

Earlier work on the simultaneous accumulation of the asteroid belt and the terrestrial planets is extended to investigate the relative contribution to the final planets made by material from different heliocentric distances. As before, stochastic variations intrinsic to the accumulation processes lead to a variety of final planetary configurations, but include systems having a number of features similar to our solar system. Fifty-nine new simulations are presented, from which thirteen are selected as more similar to our solar system than the others. It is found that the concept of “local feeding zones” for each final terrestrial planet has no validity for this model. Instead, the final terrestrial planets receive major contributions from bodies ranging from 0.5 to at least 2.5 AU and often to greater distances. Nevertheless, there is a correlation between the final heliocentric distance of a planet and its average provenance. Together with the effect of stochastic fluctuations, this permits variation in the composition of the terrestrial planets, such as the difference in the decompressed density of Earth and Mars. Biologically important light elements, derived from the asteroidal region, are likely to have been significant constituents of the Earth during its formation.

The formation of the gas giant planets Jupiter and Saturn probably required the growth of massive approximately 15 Earth-mass cores on a time scale shorter than the approximately 10(7) time scale for removal of nebular gas. Relatively minor variations in nebular parameters could preclude the growth of full-size gas giants even in systems in which the terrestrial planet region is similar to our own. Systems containing "failed Jupiters," resembling Uranus and Neptune in their failure to capture much nebular gas, would be expected to contain more densely populated cometary source regions. They will also eject a smaller number of comets into interstellar space. If systems of this kind were the norm, observation of hyperbolic comets would be unexpected. Monte Carlo calculations of the orbital evolution of region of such systems (the Kuiper belt) indicate that throughout Earth history the cometary impact flux in their terrestrial planet regions would be approximately 1000 times greater than in our Solar System. It may be speculated that this could frustrate the evolution of organisms that observe and seek to understand their planetary system. For this reason our observation of these planets in our Solar System may tell us nothing about the probability of similar gas giants occurring in other planetary systems. This situation can be corrected by observation of an unbiased sample of planetary systems.

Present theories of terrestrial planet formation predict the rapid ;;runaway formation'' of planetary embryos. The sizes of the embryos increase with heliocentric distance. These embryos then merge to form planets. In earlier Monte Carlo simulations of the merger of these embryos it was assumed that embryos did not form in the asteroid belt, but this assumption may not be valid. Simulations in which runaways were allowed to form in the asteroid belt show that, although the initial distributions of mass, energy, and angular momentum are different from those observed today, during the growth of the planets these distributions spontaneously evolve toward those observed, simply as a result of known solar system processes. Even when a large planet analogous to ;;Jupiter'' does not form, an Earth-sized planet is almost always found near Earth's heliocentric distance. These results suggest that occurrence of Earth-like planets may be a common feature of planetary systems.

George W. Wetherill was awarded the Harry H. Hess Medal at the AGU 1991 Fall Meeting in San Francisco for outstanding achievements in research in the constitution and evolution of Earth and its sister planets

For models of planetary accumulation in the presence of solar nebular gas, the initial surface temperature of the earth is controlled by the grain opacity of the atmosphere. The surface temperature in turn controls the quantity of neon dissolved and trapped within the interior of the earth. To compare accumulation theory with observation, calculations have been made of the grain opacity expected to be associated with accumulation in a gaseous nebula. There are two parameters that are in principle determined by the theory, but actually are at present uncertain: the mean eccentricity(e) of the planetesimal swarm, and the fraction (xi) of the accretional energy that is expended in the release of grains into the atmosphere by ablation of the incoming planetesimal. It is found that if e is low (0.001), rather low values of xi (0.00001) are required to match the observed neon data. In contrast higher values of xi (0.1) are required for the most probable case with e = 0.01. For the high-eccentricity case (e = 0.1), xi must be greater than 0.01. The results show that avoidance of excess trapped neon of solar composition places restrictive, but not necessarily impossible, conditions on the parameters of the accumulation theory.

Gravitational perturbations in semimajor axis, eccentricity, and inclination resulting from close planetesimal encounters (near 1 AU) out to 10 Tisserand sphere of influence radii were calculated by two- and three-dimensional numerical integration. These are compared with the results of treating the encounter as a two-body problem, as is customary in Monte Carlo calculations of orbital evolution and in numerical and analytical studies of planetary accumulation. It is found that for values of ( V V e ) ⪅ 0.35 (V = relative velocity , V e = escape velocity of largest body ) , the two-body body approximation fails to describe the outcome of individual encounters. In this low-velocity region, the two-body “gravitational focusing” cross section is no longer valid; “anomalous gravitational focusing” often leads to bodies on distant unperturbed trajectories becoming close encounters and vice versa. In spite of these differences, average perturbations given by the two-body approximation are valid within a factor of 2 when V V e > 0.07 . In this same velocity range the “Arnold extrapolation,” whereby a few very close encounters are used to estimate the effect of many more distant encounters, is found to be a useful approximation.

The orbital evolutions of 1-45 km-diameter Apollo and Amor bodies generated by asteroid belt collisions interior to 2.6 AU are presently traced by Monte Carlo calculations. About 3 percent of the asteroidal fragments of this type and size that are ejected with velocities of 100 m/sec are perturbed into earth-crossing orbits by the 3:1 Jovian commensurability resonance at 2.5 AU, as well as a secular resonance in the innermost asteroid belt. While the initial earth-crossing orbits of these bodies are concentrated near 1 AU, their steady-state orbital distribution is widely dispersed. Additional objects that may be characterized as inactive comets are inferred from strongly suggestive data.

An examination is conducted concerning the circumstances under which the difference between earth and Venus (and Mars) fits naturally into theories in which the terrestrial planets formed by the gradual sweeping up of planetesimals in an essentially gas-free protoplanetary swarm. The primary purpose of the reported investigation is to use observational data to define restrictions on planetary formation theories that would be imposed if most of Venus' inert gases come from the solar wind. The observational data support the suggestion that the abundances of Ar, Kr, and Xe on Venus have been augmented by a component of solar composition. Solar wind implantation at an early stage of accumulation provides a natural way of producing the observed extreme heliocentric distribution of this component, provided that accumulation occurred after dissipation of solar gas from the solar nebula

During the last two decades the earth sciences community has become persuaded that the earth is a dynamic body; an engine driven by its internal heat. The major surface manifestation of this dynamism has been fragmentation of the earth's outer shell and subsequent relative horizontal movement of the pieces on a large scale. The driving force is convection within the earth, but much remains to be learned about the nature of the convection and the composition of the earth's interior. The other terrestrial planets show evidence of once having been hot, but their surfaces suggest long-term stability and lack evidence of continuing convection.

The velocity evolution of a general planetesimal population is treated by means of a self-consistent set of equations whose form is tailored to those early planetary accumulation stages in which the planetesimal swarm's modeling calls for gas dynamic methods. Dynamical friction is noted to be essential to the transfer of kinetic energy from larger to smaller planetesimals, thereby furnishing an energy source comparable to those furnished by viscous stirring.

The total number of Earth-crossing Apollo objects larger than 500 m in radius is estimated to be 600, based on failure of chance rediscovery, lunar crater frequency and completeness-of-search results of Shoemaker, Helin and Gillett. The number of Amor objects (perihelion between 1.0 and 1.3 A.U.) is estimated to be about 500. These estimates are about an order of magnitude higher than those given by previous workers, and these objects appear sufficiently numerous to dominate post-mare lunar and terrestrial cratering ( d ≥ 10 km). The terrestrial meteorite and meteorite yield of 100-10 6 g bodies derived from fragmentation of Apollo objects is re-evaluated using this estimate, together with more recent data on asteroid albedos and on hypervelocity impact. Terrestrial rate of impacts of these fragments at sufficiently low velocities to penetrate the atmosphere is estimated to be ~2 × 10 8 g/yr. This is in the middle of the range of the actual extraterrestrial impact rate based on photographic fireball surveys (Prairie Network), lunar seismometry, and recovery of meteorites. It is likely that most ordinary chondrites are fragments of Apollo objects, provided that these fragments are sufficiently strong to survive atmospheric entry. Possible asteroidal and cometary sources of Apollo objects are reviewed. Several mechanisms for the removal of asteroids into Earth-crossing orbit are qualitatively acceptable, but appear inadequate by at least an order of magnitude to supply the required number. Most Apollo objects are probably the cores of comets which have lost their volatile material by repeated solar evaporation, as proposed by Opik. The distribution of the component of the Apollo objects' angular momentum perpendicular to the plane of the solar system is tabulated. It is found that considerable non-random clustering of these values exists, for which no adequate explanation is known.

The orbital evolution of material ejected from Mars into heliocentric orbits is investigated, with particular emphasis on the origin of the shergottite, nakhlite, and chassignite achondrites. Two models are considered. In the first, meteorite-size bodies are ejected directly from Mars. In the second, the ejecta are ∼ 15 m diameter bodies, that are subsequently fragmented by collisions in space. In both cases a large fraction (∼ 35%) of the objects that will ever reach Earth do so within 10 m.y. For the “small body” model, it is found that about 0.03% of the Mars crater ejecta must be accelerated to the Mars escape velocity; the “large body” model requires an efficiency of 0.4%. Assuming that the acceleration of large bodies to be less probable, the results indicate that meteorites originating as small bodies should dominate the terrestrial flux of Mars ejecta. This result is in general agreement with data from SNC meteorites, but the reported short exposure age of EETA 79001 is hard to understand in a pure small body model. The yield of meteorites from Mercury is found to be at least a factor of 100 lower than from Mars.

The present gasdynamic study of the planetesimal-accumulation stage in which 10-km bodies in the neighborhood of 1 AU grow to 10 to the 25th-10 to the 27th g mass, or 'planetary embryo' size, attempts to identify the circumstances under which runaway growth forms a small number of massive embryos in the terrestrial-planet region on a 0.1-1.0 million year time-scale. No runaways are found, however, unless more plausible physical processes are invoked; in that case, runaways in the terrestrial planet region are probable on a 0.1 million-year time-scale, and the final stage of planetary accumulation may involve the growth of these embryos into the present planets on a 10-100 million-year time-scale.

Despite the negative tone of Chapman's article, it is pointed out that there is substantial agreement between his opinions and those given in my previous publications on this subject. These areas of agreement are identified and distinguished from those which require further investigation or discussion. It is also pointed out that the apparent discrepancy between the small crater population on the Mercury intercrater terrain and the lunar plains may argue against a simultaneous late heavy bombardment. Suggested ways to resolve this discrepancy should be thoroughly evaluated. The primary need at this time is to identify further specific observational, experimental, or theoretical tests in order to advance beyond the stage of agreeing that the available evidence permits a simultaneous late heavy bombardment, to the more difficult task of determining whether or not it probably occurred.

Plausible meteorite mass distributions imply that in the Prairie Network data there must be many fainter fireballs produced by meteorites with physical properties that, except for mass, are very similar to the recovered ordinary chondrite ( H 5) Lost City. Four criteria are proposed for identifying these other meteorites among the fireballs. These are: deceleration to final velocity ≤8 km/sec; a photometric mass/dynamic mass ratio within a factor of 2 of that of Lost City, agreement of the observed and theoretical single body end heights (calculated using dynamic mass), and a lightcurve no more irregular than those of the three recovered fireballs. These criteria can be related to the PE criterion of Ceplecha and McCrosky, but include a wider range of observational data, and also differ from the PE criterion in avoiding inclusion of data not helpful to the particular problem of identifying ordinary chondrite fireballs. By use of our criteria, 27 Prairie Network fireballs are identified as being meteorites comparable to or greater in strength and density to Lost City, most of these should be ordinary chondrites. The orbital element distributions of these objects span a wide range, include those of recovered fireballs, and show that the 4.0-AU aphelion of the Pribram meteorite is not unusually large. Perihelia are concentrated near 1.0 AU, in agreement with previous inferences from time-of-fall and radiant distributions, demonstrating the usefulness of these data based on visual observations.

The orbital evolution of asteroidal fragments with diameters ranging from 10 cm to 20 km, injected into the 3:1 Kirkwood gap at 2.50 A.U., has been investigated using Monte Carlo techniques. It is assumed that this material can become Earth-crossing on a time scale of 106 years, as a result of a chaotic zone discovered by Wisdom, associated with the 3:1 resonance. This phenomenon, as well as close encounter planetary perturbations, the v6 secular resonance, and the ablative effects of the Earth's atmosphere are included in the determination of the orbital characteristics of meteorites impacting the Earth derived by fragmentation of this asteroidal material. It is found that the predicted meteorite orbits closely match those found for observed ordinary chondrites, and the total flux is in approximate agreement with the observed fall rate of ordinary chondrites. About 10% of the predicted impacting bodies are meteorite-size bodies originating directly from the asteroid belt. The remainder are obtained by subsequent fragmentation of larger (∼1 m to 20 km diameter) Earth-crossing asteroidal fragments. The largest of these fragments are observable as Apollo-Amor objects. Thus the apparent paradox between the orbital characteristics of observed ordinary chondrites and those predicted from Apollo object sources is reconciled. Both appear to be complementary aspects of the same phenomena. No other asteroidal resonance is found to be satisfactory as a source of ordinary chondrites. These meteorites are therefore most likely to be derived from S asteroids in this limited region of the asteroidal belt, the largest of which are 11 Parthenope, 17 Thetis, and 29 Amphitrite.

An asteroidal collision model and Monte Carlo program used for studies of the terrestrial meteorite flux, the steady-state number of Apollo-Amor objects, and the orbital distribution of both meteorites and Apollo-Amor objects is used to calculate absolute and relative cratering rates on the terrestrial planets. It is found that the 'best' estimates of the predicted asteroidal cratering rate are three times lower than estimates of the observed terrestrial cratering rate. If this is due to errors in the asteroidal production rate of Apollo-Amor objects, the predicted present-day cratering rate per unit area on Mars is four times that on earth, whereas that on Mercury is twice that on earth.

The steady-state distribution of orbits of Apollo-Amor objects is calculated for a variety of possible sources. These include asteroids near the inner edge of the belt, cometary orbits similar to Encke, and hypothetical extinct cometary orbits with perihelia larger than that of Encke. In all but one case, the steady-state distributions are similar for all these sources, and predict Amor/Apollo ratios of 1.5 to 3. These ratios are lower than those predicted by work in which the effects of the ν 6 secular resonance were not considered. These results are in general agreement with observation, although the higher (∼3) Amor/Apollo ratios found for many of the sources may turn out to be unacceptably high. The absolute number of Apollo-Amors observed is found to require an injection rate of ∼15 objects/(10 6 years). This rate is easily achieved if the present existence of Encke is assumed to be a reasonably probable event, and if Encke becomes a ∼1-km-diameter Apollo object following exhaustion of its volatile material; best estimates of the injection rate from the asteroid belt [∼1.5/(10 6 years)] are too low. Hence a dominant cometary component is suggested. The predicted number of Apollo objects in small ( q a

Two growth mechanisms are identified for the development of the terrestrial planets: (1) gravitational instability leading to a collapse, and (2) gravitational accumulation caused by two-body collisions and coherence. The presence of a dynamically-significant gas phase would not affect either mechanism. Theoretical expressions are presented for the production of giant gaseous protoplanets by gravitational instability within a central dust layer. Gravitational accumulation is discussed with reference to the accumulation of planetesimals from a gas-free circumsolar swarm of bodies. Numerical simulations are given for the early stages of accumulation. The Safronov steady-state velocity is considered, noting that the competition between mutual collisional damping and gravitational acceleration by the members of a solar swarm yields a steady-state velocity distribution where the mean velocity is comparable to the escape velocity of the largest body. A time scale for accumulation is postulated on the basis of the radial distribution of a swarm of non-accreting bodies of equal size. The simultaneous gas-free accumulation of several terrestrial planets is noted. Attention is also given to growth mechanisms in gas-rich interplanetary media.