Low Velocity Collisions and the Growth of Planetesimals

The physics of low velocity collisions (5 m/s to 40 m/s) between basalt bodies ranging in size from 1 m to 10 km is studied in an effort to investigate the early phases of planetesimal accretions. To assess the importance of the internal structure of planetesimals on the outcome of the collisions, we model them either as solid spheres or as rubble piles with a filling factor of 0.5. The collisions are simulated using a three dimensional Smooth Particle Hydrodynamics (SPH) code that incorporates the combined effects of material strength and a brittle fragmentation model. This approach allows the determination not only of the mass of the largest fragments surviving the collisions but also their dynamical characteristics. We find that low velocity collisions are for equal incoming kinetic energy per gram of target material considerably more efficient in destroying and dispersing bodies than their high velocity counterparts. Furthermore, planetesimals modeled as rubble piles are found to be characterized by a disruption threshold about 5 times smaller than solid bodies. Both results are a consequence of a more efficient momentum transfer between projectile and fragments in collisions involving bodies of comparable sizes. Size and shape dependent gas drag is shown to provide relative collision velocities between similar meter-sized objects well in excess of the critical disruption threshold of either rubble piles or solid bodies. Unless accretion can proceed avoiding collisions between bodies of similar masses, the relative weakness of bodies in this size range creates a serious bottleneck for planetesimal growth. This revised version was published online in June 2006 with corrections to the Cover Date.     

Climate Variability on Venus and Titan

Venus and Titan are both slowly-rotating, approximately Earth-sized bodies with cloudy, dynamic atmospheres. Each has a complex climate system, even less well understood than the terrestrial equivalent, and the processes that appear to maintain the climate near the surface on both bodies have interesting similarities and differences with each other and with the Earth. By considering these factors and their possible evolution with the aid of elementary climate models, some interesting, albeit tentative, conclusions can be reached concerning the stability of climate on Earth-like planets, and the likely nature of past and future climate change.     

Water Reservoirs in Small Planetary Bodies: Meteorites,Asteroids, and Comets

Asteroids and comets are the remnants of the swarm of planetesimals from which the planets ultimately formed, and they retain records of processes that operated prior to and during planet formation. They are also likely the sources of most of the water and other volatiles accreted by Earth. In this review, we discuss the nature and probable origins of asteroids and comets based on data from remote observations, in situ measurements by spacecraft, and laboratory analyses of meteorites derived from asteroids. The asteroidal parent bodies of meteorites formed \(\leq 4\) Ma after Solar System formation while there was still a gas disk present. It seems increasingly likely that the parent bodies of meteorites spectroscopically linked with the E-, S-, M- and V-type asteroids formed sunward of Jupiter’s orbit, while those associated with C- and, possibly, D-type asteroids formed further out, beyond Jupiter but probably not beyond Saturn’s orbit. Comets formed further from the Sun than any of the meteorite parent bodies, and retain much higher abundances of interstellar material. CI and CM group meteorites are probably related to the most common C-type asteroids, and based on isotopic evidence they, rather than comets, are the most likely sources of the H and N accreted by the terrestrial planets. However, comets may have been major sources of the noble gases accreted by Earth and Venus. Possible constraints that these observations can place on models of giant planet formation and migration are explored.     

用三维欧拉方程计算机身与机翼绕流

本文用Jameson的三维欧拉方程有限体积法、四步Runge-Kutta时间推进格式,计算机身和大后掠细长机翼的三维可压缩绕流。对钝头机身,用C-O型网格;尖头机身与大后掠细长机翼用H-O型网格。本文介绍钝头旋成体、带座舱前机身和三角翼绕流的计算结果,显示流场等值M线分布,计算压强系数分布与实验比较,以及三角翼大迎角分离涡等。由于用了隐式残值光顺等加速收敛措施,有效地减少推进步数,节省机时。     

Unsteady separated flows over three-dimensional slender bodies

Many review articles have been written on the topic of the aerodynamics of slender bodies at incidence, some of which are referenced in this paper. Here, we review the unsteady behavior of these flows. Our aim is to review the material that contributes to our understanding of unsteady phenomena over slender bodies at incidence. Natural unsteadiness is explored first. Unexpectedly, we found a large number of contributions in this area. We found the material disjointed, making it difficult to draw general conclusions. Forced unsteadiness is conceptually easier to follow, but the number of contributions on this topic is much smaller. We consider both experimental and numerical contributions but we do not discuss the corresponding methodologies.     

The Contributions of Comets to Planets, Atmospheres, and Life: Insights from Cassini-Huygens, Galileo, Giotto, and Inner Planet Missions

Comets belong to a group of small bodies generally known as icy planetesimals. Today the most primitive icy planetesimals are the Kuiper Belt objects (KBOs) occupying a roughly planar domain beyond Neptune. KBOs may be scattered inward, allowing them to collide with planets. Others may move outward, some all the way into the Oort cloud. This is a spherical distribution of comet nuclei at a mean distance of ～50,000 AU. These nuclei are occasionally perturbed into orbits that intersect the paths of the planets, again allowing collisions. The composition of the atmosphere of Jupiter—and thus possibly all outer planets—shows the effects of massive early contributions from extremely primitive icy bodies that must have been close relatives of the KBOs. Titan may itself have a composition similar to that of Oort cloud comets. The origin and early evolution of its atmosphere invites comparison with that of the early Earth. Impacts of comets must have brought water and other volatile compounds to the Earth and the other inner planets, contributing to the reservoir of key ingredients for the origin of life. The magnitude of these contributions remains unknown but should be accessible to measurements by instruments on spacecraft.     

Analytical study of sonic boom from supersonic projectiles

Whitham's first-order theory for steady flow at moderate supersonic Mach numbers around slender axisymmetric bodies is reviewed and applied to determine sonic boom overpressure signatures from bodies of various shapes, particularly those of projectiles in steady and rectilinear flight. Based on his theory, certain closed-form solutions are derived, including extended first-order decay laws for signature evolution with increasing distance from the flight path. Also, for the case of arbitrary axisymmetric bodies of simple and smooth shape, whose axial profile can be defined piecewise by segments of polynomial curves, a new analytical solution is presented for Whitham's ‘smooth-body’ F-function integral. An alternate formulation for the F-function that was derived by Lighthill for non-smooth bodies is shown to be better for actual smooth and non-smooth projectile shapes. A computer code was developed to implement the analysis with various F-functions and compute sonic boom signatures for specified body shapes. These numerical studies were conducted to investigate and illustrate important features of these signatures and their evolution with increasing miss distance. The effects of body shape such as surface protuberances and afterbody flow are two examples.     

人－椅系统的动压计算问题

通过大量的分析、计算,提出了作用在人－椅系统上的动压修正系数F的半经验公式。给出选取修正因子ε、f（ε）的方法,仅需４个不同马赫数的阻力系数实验值。原则上,若实验结果精度较高,对阻力系数实验值的选取并无限制。但实验数据精度不高,则上述计算的阻力系数的均方根误差就会大些。此方法不仅适用于计算像人－椅系统这样的大钝体,而且也适用于计算其它大钝体在任意马赫数范围的阻力系数,其均方根误差小于01 05。     

Formation of Planetesimals and Accretion of the Terrestrial Planets

Planetesimals formed in the solar nebula by collisional coagulation. Dust aggregates settled toward the central plane, the larger ones growing by sweeping up smaller ones. A thin, dense layer of particles formed; shear-generated turbulence and differential motions induced by gas drag inhibited gravitational instability. Growth proceeded by collisions, producing planetesimals on a timescale of a few thousand years in the terrestrial zone. For bodies smaller than about a kilometer, motions were dominated by gas drag, and impact velocities decreased with size. At larger sizes gravitational interactions became significant, and velocities increased due to mutual perturbations. Larger bodies then grew more rapidly, this ``runaway' led to formation of tens to hundreds of lunar- to Mars-sized planetary embryos in the zone of terrestrial planets. The final accretion of these bodies into a few planets involved large impacts, and occurred on a timescale of 10⁷ to 10⁸ years. This scenario gives a reasonably consistent picture of the origin of the terrestrial planets, but does not account for the anomalously low eccentricities of the Earth and Venus. This revised version was published online in June 2006 with corrections to the Cover Date.     

Water and Volatile Inventories of Mercury,Venus, the Moon,and Mars

We review the geochemical observations of water, \(\mbox{D}/\mbox{H}\) and volatile element abundances of the inner Solar System bodies, Mercury, Venus, the Moon, and Mars. We focus primarily on the inventories of water in these bodies, but also consider other volatiles when they can inform us about water. For Mercury, we have no data for internal water, but the reducing nature of the surface of Mercury would suggest that some hydrogen may be retained in its core. We evaluate the current knowledge and understanding of venusian water and volatiles and conclude that the venusian mantle was likely endowed with as much water as Earth of which it retains a small but non-negligible fraction. Estimates of the abundance of the Moon’s internal water vary from Earth-like to one to two orders of magnitude more depleted. Cl, K, and Zn isotope anomalies for lunar samples argue that the giant impact left a unique geochemical fingerprint on the Moon, but not the Earth. For Mars, an early magma ocean likely generated a thick crust; this combined with a lack of crustal recycling mechanisms would have led to early isolation of the Martian mantle from later delivery of water and volatiles from surface reservoirs or late accretion. The abundance estimates of Martian mantle water are similar to those of the terrestrial mantle, suggesting some similarities in the water and volatile inventories for the terrestrial planets and the Moon.     

Viscous flows and instabilities near rotating bodies

This study is a survey of experiments on the flow near rotating bodies. The bodies discussed are bodies of revolution, such as spheres, disks, cylinders and cones. The flow and the instabilities around, between and within these rotating bodies and combinations of them are investigated. Special emphasis is placed on the first onset and the further development of instabilities. Depending on the geometry and the boundary condition spiral vortices, Görtler-type vortices and counter-rotating Taylor vortices are obtained in the unstable flow regime. Their behaviour and appearance for different initial and boundary conditions are analysed in detail and the development to transition to turbulence is described. The non-uniqueness of the flow in the supercritical Reynolds number regime results in different vortex configurations depending on the flow's history. The instabilities may occur in steady and unsteady form or in a combination of both types. The experimental results are compared with available theoretical results. These are mostly obtained numerically because of difficulties with closed form solutions of the governing equations. Some of the vortices in the unstable flow regime for different geometries show similar flow patterns. It is, therefore, a main purpose of this contribution to draw attention to their common properties as well as their differences.     

Asteroid surface materials: Mineralogical characterizations from reflectance spectra

The interpretation of diagnostic parameters in the spectral reflectance data for asteroids provides a means of characterizing the mineralogy and petrology of asteroid surface materials. An interpretive technique based on a quantitative understanding of the functional relationship between the optical properties of a mineral assemblage and its mineralogy, petrology and chemistry can provide a considerably more sophisticated characterization of a surface material than any matching or classification technique for those objects bright enough to allow spectral reflectance measurements. Albedos derived from radiometry and polarization data for individual asteroids can be used with spectral data to establish the spectral albedo, to define the optical density of the surface material and, in general, to constrain mineralogical interpretations.Mineral assemblages analogous to most meteorite types, with the exception of ordinary chondritic assemblages, have been found as surface materials of Main Belt asteroids. C1- and C2-like assemblages (unleached, oxidized meteoritic clay minerals plus opaques such as carbon) dominate the population (80%) throughout the Belt, especially in the outer Belt. A smaller population of asteroids exhibit surface materials similar to C3 (CO, CV) meteoritic assemblages (olivine plus opaque, probably carbon) and are also distributed throughout the Belt. The relative size (diameter) distributions for these two populations of objects are consistent with an origin by sequential accretion from a cooling nebula (C2 as surface layers, C3 as interior layers or cores). Based on information from meteoritic analogues and on qualitative models for the behavior of these materials during a heating episode, it seems unlikely that these C2- and C3-like asteroidal bodies have experienced any significant post-accretionary heating event either near surface or in the deep interior.The majority of remaining studied asteroids (20) of 65 asteroids exhibit spectral reflectance curves dominated by the presence of metallic nickel-iron in their surface materials. These objects are most probably the several end products of an intense thermal event leading to the melting and differentiating of their protobodies. These thermalized bodies are concentrated toward the inner part of the Asteroid Belt but exist throughout the Belt.The size of the proto-asteroid has apparently exercised control over the post-accretionary thermal history of these bodies. The available evidence indicates that all asteroids larger than about 450 km in (present) diameter have undergone a significant heating episode since their formation. The post-accretionary thermal history of the asteroidal parent bodies was apparently affected by both distance from the Sun and body size.The C2-like materials which dominate the main asteroid belt population appear to be relatively rare on earth-approaching asteroids. This suggests that most of these Apollo-Amor objects are not randomly derived from the main belt, but (a) may derive from a single event in recent time (10⁷ yr), (b) may derive from a favorably situated source body, (c) may derive from a particular, compositionally anomalous region of the belt, or (d) may derive from an alternate source (e.g. comets).     

Induced Magnetic Fields in Solar System Bodies

Electromagnetic induction is a powerful technique to study the electrical conductivity of the interior of the Earth and other solar system bodies. Information about the electrical conductivity structure can provide strong constraints on the associated internal composition of planetary bodies. Here we give a review of the basic principles of the electromagnetic induction technique and discuss its application to various bodies of our solar system. We also show that the plasma environment, in which the bodies are embedded, generates in addition to the induced magnetic fields competing plasma magnetic fields. These fields need to be treated appropriately to reliably interpret magnetic field measurements in the vicinity of solar system bodies. Induction measurements are particularly important in the search for liquid water outside of Earth. Magnetic field measurements by the Galileo spacecraft provide strong evidence for a subsurface ocean on Europa and Callisto. The induction technique will provide additional important constraints on the possible subsurface water, when used on future Europa and Ganymede orbiters. It can also be applied to probe Enceladus and Titan with Cassini and future spacecraft.     

Ptolemy – an Instrument to Measure Stable Isotopic Ratios of Key Volatiles on a Cometary Nucleus

A fundamental goal of cometary studies is to determine the exact relationship between these bodies and the Solar System – the question(s) can be summarised as follows: did comets originate during the same events that spawned the Sun and planets, are they more primitive bodies that record a pre-solar history, or are they interstellar materials collected in relatively more recent times? Now, whatever the origin of comets, it is entirely possible that they could, in part, contain interstellar or pre-solar components – indeed, it seems rather likely in light of the fact that primitive meteorites contain such entities. These particular components are likely to be refractory (dust, macromolecular organic complexes, etc.). Of more relevance to the issues above are the volatile constituents, which make up the bulk of a comet's mass. Since these materials, by their very nature, volatilise during perihelion passage of a comet they can, in some instances, be detected and measured spectroscopically. Perhaps the most useful species for isotopic investigations are C₂, HCN and CN. Unfortunately, spectroscopic measurements can only currently be made with accuracies of ±10 to ±20%. As such it is very often not practical to conclude anything further than the fact that isotopic measurements are compatible with ‘`solar’' values, which tends to imply an origin from the margins of the solar accretion disk. But there is another problem with the spectroscopic measurements – since these are made on gaseous species in the coma (and relatively minor species at that) it is impossible to be certain that these represent the true nuclear values. In other words, if the processes of sublimation, active jetting, and photochemistry in the coma impart isotopic fractionation, the spectroscopic measurements could give a false impression of the true isotope ratios. What is required is an experiment capable of measuring isotopic ratios at the very surface of a comet. Herein we describe the Ptolemy instrument, which is included on the Philae lander as part of the Rosetta mission to 67P/Churyumov-Gerasimenko. The major objective of Ptolemy is a detailed appraisal of the nature and isotopic compositions of all materials present at the surface of a comet.     

From Dust to Terrestrial Planets – Introduction

Terrestrial planets are accreted in a disk orbiting a central star. The basic challenge of their formation consists of assembling micron-sized or smaller dust grains to bodies with over 10⁴ km in diameter. This formation process, ultimately based on collisions, occurs in three very different physical regimes depending upon the size of the bodies present: 1) Early on, micron- to mm-sized dust grains, chondrules and chondrites are strongly coupled to the gas. 2) As they grow larger, gravity increases the collisional cross section allowing runaway growth to occur. 3) After this runaway phase stops from exhaustion of matter in the immediate surroundings of the protoplanets, further growth occurs on timescales typical of mutual gravitational perturbations. The emphasis of this book is on the timescales corresponding to these formation phases as well as the characteristic chemical and isotopic composition of the bodies involved. This revised version was published online in June 2006 with corrections to the Cover Date.     

落体法测定转动惯量

利用地球重力场可以测定转动惯量，我们称这种方法为落体法。文中介绍了两种落体测量方法，说明了它们的作用原理及其它有关问题。这些方法的测量不确定度为５％。利用这些方法可以测量质量未知物体的转动惯量。     

Formation of the Cores of the Outer Planets

The formation of the giant planets seems to be best explained by accretion of planetesimals to form massive cores, which in the case of Jupiter and Saturn were able to capture nebular gas. However, the timescale for accretion of such cores has been a problem. Accretion in the outer solar system differs qualitatively from planetary growth in the terrestrial region, as the larger embryo masses and lower orbital velocities make bodies more subject to gravitational scattering. The planetesimal swarm in the outer nebula may be seeded by earlier-formed large bodies scattered from the region near the nebular “snow line”. Such a seed body can experience rapid runaway growth undisturbed by competitors; the style of growth is not oligarchy, but monarchy.     

力学不均匀性对焊接接头疲劳裂纹扩展影响的研究

本文将焊接接头简化为夹层材料裂纹体模型，通过实验及弹塑性有限元方法研究了均匀材料和具有力学不均匀性的夹层材料裂纹体中心裂纹试件中疲劳裂纹的扩展规律。发现疲劳裂纹的扩展不但取决于裂纹尖端处材料的性质，而且还受裂纹尖端附近材料力学不均匀性的严重影响；不均匀体裂纹尖端的塑性区、应力应变场与均匀材料裂纹体显著不同；力学不均匀性对疲劳扩展寿命影响的本质在于力学不均匀性对疲劳裂纹闭合的影响     

Origin,age, and composition of meteorites

This paper attempts to bring together and evaluate all significant evidence on the origin of meteorites.The iron meteorites seem to have formed at low pressures. Laboratory evidence shows that the absence of a Widmanstätten pattern in meteorites with > 16% Ni cannot be attributed to high pressures, but to supercooling or an unusually fast cooling rate for these meteorites, which prevented the development of a pattern. The presence of tridymite in the Steinbach siderophyre provides further, direct proof that the Widmanstätten pattern can form at pressures less than 3 kb. Neither diamond, nor cliftonite, nor cohenite are reliable pressure indicators in meteorites. Diamonds were formed by shock while cliftonite may have been derived from a cubic carbide such as Fe₄C. Cohenite is apparently stabilized by kinetic rather than thermodynamic factors. Several lines of evidence suggest that the irons come from more than one parent body, perhaps as many as four.The frequency of pallasites is perfectly consistent with an origin in the transition zone between core and mantle of the parent body. Hybrid meteorites such as Brenham are not necessarily derived from the metal-silicate interface, but probably resulted from dendrite growth in the solidifying melt.Ordinary chondrites definitely are equilibrium assemblages rather than chance conglomerates. According to the best available evidence, Prior's rules seem to be valid. The metal particles in chondrites differentiated into kamacite and taenite in their present location, rather than in a remote earlier environment. Trace element abundances in ordinary and carbonaceous chondrites suggest that these meteorites accreted from two types of matter: an undepleted fraction that separated from its complement of gases at low temperatures, and a depleted fraction that lost its gases at high temperatures. These two fractions of primitive meteoritic matter are tentatively identified with the matrix and chondrules-plus-metal, respectively. New restrictive limits are placed on the iron-silicate fractionation in chondrites. No direct evolutionary path exists that connects the currently accepted solar abundances of Fe and Ni and the observed Fe/Si and Ni/Si ratios in chondrites. Apparently the solar abundance of iron is in error. The iron-silicate fractionation seems to have occurred while chondritic matter was in a more strongly reduced state than its present one.The U-He and K-Ar ages of hypersthene chondrites are systematically shorter than those of bronzite chondrites. Short ages are correlated with shock effects, and it seems that the hypersthene chondrites suffered reheating and partial-to-complete outgassing 0.4 AE ago. The cosmic-ray exposure ages of all classes of meteorites cluster distinctly, indicating that the meteorites were produced in a few discrete major collisions rather than by a quasi-continuum of smaller ones. The dates of the principal breakups are: irons, 0.6 and 0.9 AE; aubrites, 45 m.y.; bronzite chondrites, 4 m.y.; hypersthene chondrites, 0.025, 3, 7–13, and 16–31 m.y. All four clusters of hypersthene chondrites show evidence of severe outgassing 0.4 AE ago, which implies that most or all hypersthene chondrites come from the same parent body.As already noted by Signer and Suess, two distinct types of primordial gas occur in meteorites. Differentiated meteorites always contain unfractionated gas, while relatively undifferentiated meteorites contain fractionated gas. The former component is invariably associated with shock effects, and seems to have been derived from the solar wind. The latter component is correlated with other volatiles and seems to be a truly primitive constituent of meteoritic matter. Isotopic anomalies in the fractionated gas suggest that meteoritic matter was irradiated with 10¹⁷ protons/cm² at a very early stage of its history.There is very little doubt that most, if not all, meteorites come from the asteroid belt rather than from the moon. The orbits and geocentric velocities of stony meteorites resemble those of the Apollo asteroids (most of which are former members of the asteroid belt that have strayed into terrestrial space), but disagree strongly with the calculated orbits and velocities for lunar ejecta. Öpik's conclusions about the difficulty of accelerating lunar debris to escape velocity represent a further argument against a lunar origin of stony meteorites.The most likely parent bodies of the meteorites are the 34 asteroids which cross the orbit of Mars. Collisional debris from these objects will remain in Mars-crossing orbits, and perturbations by Mars will inject some fraction of this material into terrestrial space. Most of the Mars asteroids, comprising 98% of the mass and 92% of the cross-section, belong to three Hirayama families (Phocaea, Desiderata, and Aethra), and an additional, previously unrecognized family. These families were apparently produced by disruption of parent asteroids ca. 104, 105, and 46 km in diameter. The size distribution and light curves of asteroids indicate that the larger asteroids are original accretions, rather than collision fragments. There is no reason to believe that the meteorites ever resided in bodies larger than Ceres (d = 770 km).Various theories on the origin of the meteorites are critically reviewed in the light of the preceding evidence. Wood's theory, which postulates a high-temperature and a low-temperature variety of primordial matter, is in best accord with the evidence. Apparently the asteroids accreted from varying proportions of these two types of material, and were then heated by extinct radioactivity produced in the early irradiation.     

Aerial Mapping Planetary Bodies

Photographic mapping missions over planetary bodies present a number of interesting hardware, operational, data retrieval, and data analysis techniques. Broadly speaking, such a mapping mission can be conducted with present level state-of-the-art equipment. The space-craft and photographic equipment must perform over long periods of time unattended in the hostile space environment. Operations must support the mission and retrieve the photographic data. Maximum data are limited by photographic capacity, operations capacity, and analysis capacity. Data analysis techniques are under development and computer maps have been developed for RANGER analysis; these techniques can be especially suited to analysis of the video (analog or digital) signal transmitted back to Earth.