In this note we present complete, closed-form expressions for random relative velocities between colliding particles of arbitrary size in nebula turbulence. These results are exact for very small particles (those with stopping times much shorter than the large eddy overturn time) and are also surprisingly accurate in complete generality (that is, also apply for particles with stopping times comparable to, or much longer than, the large eddy overturn time). We note that some previous studies may have adopted previous simple expressions, which we find to be in error regarding the size dependence in the large particle regime.

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Voyager 2 photography has complemented that of Voyager I in revealing many additional characteristics of Saturn and its satellites and rings. Saturn's atmosphere contains persistent oval cloud features reminiscent of features on Jupiter. Smaller irregular features track out a pattern of zonal winds that is symmetric about Saturn's equator and appears to extend to great depth. Winds are predominantly eastward and reach 500 meters per second at the equator. Titan has several haze layers with significantly varying optical properties and a northern polar "collar" that is dark at short wavelengths. Several satellites have been photographed at substantially improved resolution. Enceladus' surface ranges from old, densely cratered terrain to relatively young, uncratered plains crossed by grooves and faults. Tethys has a crater 400 kilometers in diameter whose floor has domed to match Tethys' surface curvature and a deep trench that extends at least 270 degrees around Tethys' circumference. Hyperion is cratered and irregular in shape. Iapetus' bright, trailing hemisphere includes several dark-floored craters, and Phoebe has a very low albedo and rotates in the direction opposite to that of its orbital revolution with a period of 9 hours. Within Saturn's rings, the "birth" of a spoke has been observed, and surprising azimuthal and time variability is found in the ringlet structure of the outer B ring. These observations lead to speculations about Saturn's internal structure and about the collisional and thermal history of the rings and satellites.

We outline a scenario which traces a direct path from freely-floating nebula particles to the first 10-100km-sized bodies in the terrestrial planet region, producing planetesimals which have properties matching those of primitive meteorite parent bodies. We call this primary accretion. The scenario draws on elements of previous work, and introduces a new critical threshold for planetesimal formation. We presume the nebula to be weakly turbulent, which leads to dense concentrations of aerodynamically size-sorted particles having properties like those observed in chondrites. The fractional volume of the nebula occupied by these dense zones or clumps obeys a probability distribution as a function of their density, and the densest concentrations have particle mass density 100 times that of the gas. However, even these densest clumps are prevented by gas pressure from undergoing gravitational instability in the traditional sense (on a dynamical timescale). While in this state of arrested development, they are susceptible to disruption by the ram pressure of the differentially orbiting nebula gas. However, self-gravity can preserve sufficiently large and dense clumps from ram pressure disruption, allowing their entrained particles to sediment gently but inexorably towards their centers, producing 10-100 km "sandpile" planetesimals. Localized radial pressure fluctuations in the nebula, and interactions between differentially moving dense clumps, will also play a role that must be allowed for in future studies. The scenario is readily extended from meteorite parent bodies to primary accretion throughout the solar system.

Size-selective concentration of particles in a weakly turbulent protoplanetary nebula may be responsible for the initial collection of chondrules and other constituents into primitive body precursors. This paper presents the main elements of this process of turbulent concentration. In the terrestrial planet region, both the characteristic size and size distribution of chondrules are explained. "Fluffier" particles would be concentrated in nebula regions which were at a lower gas density and/or more intensely turbulent. The spatial distribution of concentrated particle density obeys multifractal scaling, suggesting a close tie to the turbulent cascade process. This scaling behavior allows predictions of the probability distributions for concentration in the protoplanetary nebula to be made. Large concentration factors (> 10 5) are readily obtained, implying that numerous zones of particle density significantly exceeding the gas density could exist. If most of the available solids were actually in chondrule sized particles, the ensuing particle mass density would become so large that the feedback effects on gas turbulence due to mass loading could no longer be neglected. This paper describes the process, presenting its basic elements and some implications, without including the effects of mass loading.