Engineering topics
Publications and source records attributed to Weidenschilling, S. J..
Research on a variety of dynamical processes relevant to the formation of planets, satellites and ring systems is discussed. The main focus is on studies of accretionary formation of early protoplanets using a numerical model, structures and evolution of ring systems and individual bodies within planetary rings, and theories of lunar origin.
The reduction and publication of an extensive data set collected in experiments over several years at Ames and PSI is briefly examined. Hartmann has been assembling data sets from his experiments on catastrophic fragmentation of various materials, including basalt, other igneous rock, ice, and weak dirt clods. Weidenschilling and Davis have continued to gather and reduce data on oblique impacts. The data indicate a power law distribution of ejecta mass vs. velocity, with a slope that is independent of azimuth, and does not vary with impact angle from normal impacts to at least 75 deg from vertical. In order to improve models of coagulation of dust aggregates in the solar nebula, SJW developed an apparatus for drop tests of fragile projectiles. Davis and Weidenschilling continued to collect and analyze experimental data on collisional catastrophic disruption at the Ames Vertical Gun Range.
A 'photometric geodesy' program is selected on the basis of light-curve data from five years' observations of large, rapidly rotating asteroids, where the observing protocol was designed to obtain precise, absolute photometry at a wide variety of orbital longitudes and phase angles. A total of 257 complete or partial light-curves are obtained for 26 asteroids; the data set will allow the future determination of pole positions and shapes, as well as to constrain the geophysical traits of these bodies.
Current theories on the accretion of the planets from the solar nebula are reviewed. The settling of solid material to the central plane of the nebula and the formation of planetesimals is reviewed for both the case of a laminar nebula and a turbulent nebula. The advances that have been made in understanding the accumulation of the terrestrial and giant planets in the solar nebula are reviewed along with the remaining problems.
The paper reveals the possibility that the moon could have formed from the long-term evolution of a circumterrestrial disk emplaced during the earth's final stages of formation. A model is presented which emphasizes silicate enrichment (or iron depletion) of lunar material within the disk. This model depends on the late-stage planetesimal population being dominated by small bodies.
Understanding asteroid collisional evolution is important for characterizing the physical state of asteroids today and for learning about the processes that acted in this region of the solar system early in its history. The collisional outcome algorithm in the numerical simulation of asteroid evolution was revised to reflect pressure-strengthening. Asteroid collisions are now treated as a distribution of oblique impacts rather than as only head-on collisions. The initial and evolved size distribution of a plausible asteroid population is compared with the observed size distribution. Asteroid accretion times and reconstruction of the primordial solar nebula suggest that there was significantly more mass in this part of the solar system when the asteroids were accreting.
The lunar origin model considered in this report involves processing of protolunar material through a circumterrestrial swarm of particles. Once such a swarm has formed, it can gain mass by capturing infalling planetesimals and ejecta from giant impacts on the Earth, although the angular momentum supply from these sources remains a problem. The first stage of formation of a geocentric swarm by capture of planetesimals from initially heliocentric orbits is examined. The only plausible capture mechanism that is not dependent on very low approach velocities is the mutual collision of planetesimals passing within Earth's sphere of influence. The dissipation of energy in inelastic collisions or accretion events changes the value of the Jacobi parameter, allowing capture into bound geocentric orbits. This capture scenario was tested directly by many body numerical integration of planetesimal orbits in near Earth space.
Planetesimal orbital evolution in a resisting medium near an accreting protoplanet was studied to explore mechanisms for capture into Trojan and satellite orbits. Various mechanisms for capture into libration were proposed, e.g., increase in Jupiter/Sun mass ratio, change in Jovian orbital radius, and collisions of asteroids with interplanetary dust. Studies include effects of solar nebula gas drag on orbital evolution. In general, the gas deviates from Keplerian motion, causing secular decay of planetesimal orbits, as well as damping eccentricity. The motion of bodies near Jupiter under the effect of a resisting medium was numerically explored. The equations of motion were integrated using the formalism of the planar restricted three body problem, modified to include effects by gas drag and a growing Jupiter.
Planetesimal formation by gravitational instability of a dust layer requires a nonturbulent solar nebula. The assumption that the solar nebula is a turbulent, convective accretion disk is explored. Self consistent models of a convective disk depend on high opacity of the disk material, which must be provided by grains. Grain coagulation is implied by the requirement of forming planetesimals, as the turbulent velocities (approx. 1/3 sound speed) in the accretion disk would disrupt any dust layer. Collisional coagulation could form large planetesimals, simultaneously leaving a sufficient fraction of matter in small grains to maintain the nebula's opacity. Or, coagulation of grains into small (approx. cm) aggregates could lower the opacity enough for turbulence to decay. The evolution of a population of grains in a turbulent solar nebula is calculated numerically.
Experimental impact studies were undertaken. Ejecta velocity distributions and related results from regolith targets were studied. The velocity distributions, energy partitioning, and related properties from 14 impacts at speeds 5 to 2321 m/s in vacuo into regolith-like fine powders were derived. Data are analyzed on: velocity and mass distributions as a function of azimuth around the crater during oblique impacts catastrophic disruption of spherical targets of variable strength, and catastrophic disruption of irregular-shaped natural rock targets and artificial granular aggregate targets.
The influence of gas drag and gravitational perturbations by a planetary embryo on the orbit of a planetesimal in the solar nebula was examined. Non-Keplerian rotation of the gas causes secular decay of the orbit. If the planetesimal's orbit is exterior to the perturber's, resonant perturbations oppose this drag and can cause it to be trapped in a stable orbit at a commensurability of order j/(j + 1), where j is an integer. Numerical and analytical demonstrations show that resonant trapping occurs for wide ranges of perturbing mass, planetesimal size, and j. Induced eccentricities are large, causing overlap of orbits for bodies in different resonances with j greater than 2. Collisions between planetesimals in different resonances, or between resonant and nonresonant bodies, result in their disruption. Fragments smaller than a critical size can pass through resonances under the influence of drag and be accreted by the embryo. This effect speeds accretion and tends to prevent dynamical isolation of planetary embryos, making gas-rich scenarios for planetary formation more plausible.
Numerical simulations of the collisional evolution of hypothetical initial asteroid populations have been run which are subject to three constraints: they must evolve to the current asteroid size distribution, preserve Vesta's basaltic crust, and produce at least the observed number of major Hirayama families. A 'runaway growth' initial asteroid population distribution is found to best satisfy these constraints, and a model is developed for the calculation of fragment size distribution in the disruption of large, gravitationally bound bodies in which the material strength is enhanced by hydrostatic self-compression. This model predicts that large asteroids behave as intrinsically strong bodies despite histories of collisional fracture.
Numerical simulation of the early stages of planet growth show that a few bodies nearly 1000 km in diameter may have formed within approx. 100,000 yr after solid material grew into km scale planetesimals by gravitational instability. Even after such large bodies formed, the bulk of the mass of the future terrestrial planet zone resided in small bodies. Subsequent evolution is difficult to model because it requires simultaneous consideration of continuum (multitudinous small bodies) and discrete (a few large bodies) evolution. Some relevant issues include definition of accretional feeding zones, evaluation of the range of gravitational influence, viscous transport and diffusion, orbital commensurabilities, role of gas, etc. The first large bodies may have been (1) the embryos of the final planets, which grew by accreting tiny planetesimals, or (2) merely the first of many 1000+ km bodies, which grew independently and later collided to form the planets. Models of late stage accretion that assume all bodies to be initially nearly Moon sized provide insight into relevant collisional and dynamical processes. The chief point in this research is that the correct size distribution during the later stages of planet growth remains unknown.
Problems which have arisen in formulating a mutually consistent picture of Mercury's evolution are outlined. It appears that one or more of the following widely adopted assumptions are wrong about Mercury: (1) its original composition at least approximately resulted from equilibrium condensation; (2) its magnetic field arises from a still-active dynamo; (3) its thermal evolution should have yielded early core formation followed by cooling and a global contraction approaching 20 km in the planet's radius; (4) Mercury's surface is basaltic and the intercrater plains are of volcanic origin. It is suggested that Mercury's role in comparative planetology be reevaluated in the context of an alternative timescale based on the possibility that Mercury was subjected to a continuing source of cratering projectiles over recent aeons, which have not impacted the other terrestrial planets. Although such vulcanoids have not yet been discovered, the evolution of Mercury's orbit due to secular perturbations could well have led to a prolonged period of sweeping out any intra-Mercurian planetesimals that were originally present. Mercury's surface could be younger than previously believed, which explains why Mercury's core is still molten.
In the present computation of the evolution of grain size distribution in a turbulent disk for turbulent solar nebula models, using realistic collisional outcomes and strengths of grain aggregates, the half space above the central plane of the disk is divided into a series of levels. At each level, the size distribution is represented by the population of a series of discrete size bins, each spanning an order of magnitude in mass. Coagulation, erosion, or disruption, occur for various combinations of relative particle sizes and velocities, together with assumed material strength, based on experimental impact data. The calculation is one-dimensional, in that it is performed at a single radial location in the disk.
The growth of Neptune and Uranus and the origin of the Oort comet cloud are simulated numerically, applying the planetesimal-growth model developed by Greenberg et al. (1978) for the terrestrial planets. The results of 12 experiments are presented in graphs and tables and discussed in detail. In the model which best fits observations, the planets grow relatively quickly from icy planetesimals of diameter 10 km or less which form by gravitational clumping of grains as they settle nonhomologously to the midplane of the solar system; the comets then represent unaltered remnants of the original planetesimal populations in the zone.
Although Saturn's rings are within the Roche zone, the accretion of centimeter-sized particles into large aggregates many meters in diameter occurs readily, on a time scale of weeks. These aggregates are disrupted when tidal stresses exceed their very low strengths; thus most of the mass of the ring system is continually processed through a population of large 'dynamic ephemeral bodies', which are continually forming and disintegrating. These large aggregates are not at all like the idealized ice spheres often used in modeling Saturn's ring dynamics. Their coefficient of restitution is low, hence they form a monolayer in the ring plane. The optically observable characteristics of the rings are dominated by the swarm of centimeter-sized particles.
Each of the Galilean satellites, as well as most other satellites whose initial rotations have been substantialy altered by tidal dissipation, has been widely assumed to rotate synchronously with its orbital mean motion. Such rotation would require a small permanent asymmetry in the mass distribution in order to overcome the small mean tidal torque. Since Io and Europa may be substantially fluid, they may not have the strength to support the required permanent asymmetry. Thus, each may rotate at the unknown but slightly nonsynchronous rate that corresponds to zero mean tidal torque. This behavior may be observable by Galileo spacecraft imaging. It may help explain the longitudinal variation of volcanism on Io and the cracking of Europa's crust.