On oscillatory motion in the problem of three bodies

In the case of oscillatory motion in the problem of three bodies it is shown that ast the mutual distances between particles cannot separate faster thanCt ^2/3 whereC is some positive constant. As bounding functions of time exist for the other classifications of motion in the three body problem, it follows in general that the mutual distances between particles is 0(t) ast.     

Environmental Controls on Groundwater Chemistry in an Offshore Island Aquifer: Fiesta Key, Florida

A field study was undertaken on the Florida Bay side of Fiesta Key, Florida, to identify the chemical characteristics of a previously unexplored offshore groundwater system and to define the critical parameters affecting groundwater movement and interaction with sediment pore fluids and bedrock. Emphasis was placed on the upper 2 meters of bedrock, where groundwater recharge and discharge potentials are maximized, along a 100 meter transect extending from the island margin. Bedrock cores were used to describe Pleistocene depositional textures, and were sampled at discrete depths to determine the extent of water-rock interaction. Piezometers installed into each core hole were used to monitor surface and ground water tide levels, and for the systematic collection of water samples for a large suite of chemical determinations.Aqueous chemical data indicate that these groundwaters are marine in origin, anoxic, and moderately hypersaline (S = 36–40). Exchange of bedrock pore fluids with overlying Bay waters is restricted by a layer of Holocene sediment and a discontinuous soilstone crust formed at the modern bedrock surface. Groundwater chemistry near the sediment/bedrock interface is marked by elevated concentrations of total alkalinity and Ca2+, and by significant Mg2+ depletion. These waters likely acquired their unusual chemistry by mixing between deeper groundwaters and overlying, early diagenetically altered, sediment porewaters. High alkalinity and calcium concentrations presumably result from the combination of the effects of aerobic metabolism, carbonate dissolution, and sulfate reduction. Mg-depletion most likely resulted from the precipitation of Mg-calcite. These unusual chemistries disappear by 2 m depth in the groundwater system, where Ca2+ and Mg2+ concentrations are similar to those expected for seawater under slightly hypersaline conditions.The Pleistocene bedrock contains low Mg, Sr, F, and P concentrations relative to the overlying unconsolidated Holocene carbonate sediments. This is consistent with the diagenetic recrystallization processes that the bedrock has undergone. Hydraulic conditions favor the net recharge of Florida Bay seawater to the groundwater system, but there are insufficient tide data to identify cyclical water exchange rates or groundwater flow patterns.     

Chandra and his students at Yerkes Observatory

S. Chandrasekhar’s interactions with graduate students in his more than a quarter century at Yerkes Observatory are described. His graduate teaching, Ph.D. thesis students, colloquia and colloquium series, and seminar series were all important aspects of this side of his scientific research career. His managing editorship ofThe Astrophysical Journal, his one experience in observational astrophysics, a second paper he wrote describing some of the early observational work at Yerkes Observatory, and a third on “the case for astronomy” are all discussed. A famous myth about one of his courses is corrected, and the circumstances under which the “S. Candlestickmaker” parody was written are recounted. Chandra’s computers, recruited in the Williams Bay community, are mentioned. A complete or nearly complete table of all the thesis students who received their Ph.D. degrees under his supervision, at Yerkes and on the campus in Chicago up through his last one in Astronomy and Astrophysics in 1973, is presented, with references to their published thesis papers.     

Hydrothermal jarosite and hematite in a pyroxene-hosted melt inclusion in martian meteorite Miller Range (MIL) 03346: Implications for magmatic-hydrothermal fluids on Mars

Low-temperature aqueous processes have been implicated in the generation of jarosite and hematite on the martian surface, but little is known regarding the role that high-temperature magmatic fluids may have played in producing similar assemblages on Mars. We have identified jarosite and hematite in a clinopyroxene-hosted melt inclusion in martian meteorite MIL 03346 that shows evidence of having been hydrothermally precipitated. In addition to jarosite and hematite, the melt inclusion contains titanomagnetite, pyrrhotite, potassic-chlorohastingsite, an iron-rich silicate glass and possibly goethite. These phases were identified and characterized using scanning electron microscopy (SEM), con-focal Raman-spectroscopy and electron probe microanalysis (EPMA).Based on observed textural relationships and the compositions of the hosted phases, we report that the jarosite-bearing melt inclusion in MIL 03346 has recorded a fluid-rich history that began in the magmatic stage and continued to low-temperatures. This history begins at entrapment of a volatile-rich silicate melt that likely reached fluid-saturation after only minor crystallization within the melt inclusion. This fluid, rich in chlorine, reacted with surrounding silicate material to produce the potassic-chlorohastingsite. As cooling proceeded, the liquid phase eventually became more oxidized and reacted with the pyrrhotite. Sulfide oxidation resulted in SO₄²⁻ formation and concomitant acid production, setting the stage for jarosite formation once the fluid cooled beyond the upper thermal stability of jarosite (∼200 °C). As the fluid cooled below 200 °C, jarosite continued to precipitate with hematite and/or goethite until equilibrium was established or reactions became kinetically unfavorable.This work suggests an additional jarosite-hematite formation pathway on Mars; one that may be important wherever magmatic-hydrothermal fluids come into contact with primary sulfide grains at the martian surface or subsurface. Moreover, hydrothermal fluids rich in chlorine, sulfur, and iron are important for ore-forming processes on Earth, and their indirect identification on Mars may have important implications for ore-formation on Mars.     

The spectral composition of fluxes and variances over land and sea out to the mesoscale

We discuss the accuracy requirements for measuring mesoscale (roughly horizontal scales > 10 km or 5 to 10 times the planetary boundary-layer (PBL) depth) fluxes in the convective PBL, and the ability of current research aircraft to achieve this accuracy. We conclude that aircraft equipped with inertial nagivation systems capable of < 3 km hr⁻¹ navigational accuracy are able to resolve mesoscale fluctuations in velocity, and thus variances and fluxes on the mesoscale. We then discuss measurements of velocity and scalar spectra, and cospectra of vertical velocity with horizontal velocity components and scalars, obtained from long flight legs with the National Center for Atmospheric Research Electra aircraft over the boreal forest of Canada in summer during the BOreal Ecosystem-Atmosphere Study (BOREAS), over the tropical Pacific Ocean from the Tropical Ocean Global Atmosphere Coupled Ocean-Atmosphere Response Experiment (TOGA COARE), and over the East China Sea during wintertime cold-air outbreaks from the Air Mass Transformation Experiment (AMTEX). Each of these studies has somewhat different forcings and boundary conditions, so we can compare their consequences on the spectra and cospectra. On average, we found no significant scalar or momentum fluxes for horizontal scales > 10 km. We also develop a simple model based on observed thermal structure to explain the phase angle between vertical velocity and the along-wind horizontal velocity as a function of height, which shows good agreement with the observed phase angle in AMTEX. The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Cosmic spherules in the geologic record

Abstract— Cosmic spherules obtained from the Greenland ice cap, deep-sea sediments, and ancient oceanic deposits of Eocene and Jurassic age were chemically and texturally compared. The proportions of spherule types were found to change as a function of time, with the number of iron spherules increasing as the age of the sample increased. It is not yet possible, however, to determine if the variation in spherule types represents a real change in the meteoroid complex or is a result of differential weathering of the spherules in the Earth's environment. The age of these spherules ranges from less than 3000 years to about 190 million years. Although only a few spherules older than 500 000 years are chemically unaltered, textural information is available even from the oldest spherules and, by comparison with contemporary spherules, gives some insight into the original compositions of the particles.     

Discriminant trace-element analysis of strata in the Witwatersrand System

Powdered rock samples from strata of the Witwatersrand System's sedimentary succession have been analyzed by x-ray fluorescence and optical spectroscopy techniques for nineteen elements. Using discriminant analysis it is possible to identify strata based on their trace-element compositions.