The Expansion of the Hamiltonian of the Planetary Problem into the Poisson Series in All Keplerian Elements (Theory)

The study of the evolution of planetary systems, primarily of the Solar System, is one of the basic problems of celestial mechanics. The stability of motion of giant planets on cosmogonic time scales was established by numerical and analytical methods, but the question about the evolution of orbits of terrestrial planets and arbitrary solar-type planetary systems remained open. This work initiates a series of papers allowing one to advance in solving the problem of the evolution of the solar-type planetary systems on cosmogonic time scales by using powerful analytical tools. In the first paper of this series, we choose the optimum reference system and obtain the Poisson series expansion of the Hamiltonian of the problem in all Keplerian elements. We propose to use the integral representation of the corresponding coefficients or the Poisson processor means instead of conventionally addressing any possible special functions. This approach extremely simplifies the algorithm. The next paper of this series deals with the calculation of the expansion coefficients.     

Low energy ions in the shuttle environment: Evidence for strong ambient-contaminant interactions

The quadrupole mass spectrometer flown by the Air Force Geophysics Laboratory on STS-4 in 1982 detected large intensities of several ions, primarily O⁺, H₂O⁺ and H₃O⁺, with energies less than 1.5 e V with respect to the Shuttle Orbiter. Ion-molecule reactions and non-reactive scattering between the outgassing neutral flux from the Orbiter surfaces and the ambient ionic species are identified as the primary source of these low energy ions.     

Wave Beams in an Inhomogeneous Plasma in a Transverse Magnetic Field

The propagation of axisymmetric magnetohydrodynamic waves near the equatorial plane of the crust of a neutron star in a transverse magnetic field is considered. The magnetic field is perpendicular to the equatorial plane. The magnetic fields and electric currents excited by this wave beam at the stellar surface are determined.     

Solar neutrino in relation to solar activity

Here we have carried out a power-spectrum analysis of solar nuclear gamma-ray (NGR) flares observed by SMM and HINOTORI satellites. The solar NGR flares show a periodicity of 152 days, confirming the existence of a 152–158 days periodicity in the occurrence of solar activity phenomena and also indicating that the NGR flares are a separate class of solar flares. The power-spectrum analysis of the daily sunspot areas on the Sun for the period 1980–1982 shows a peak around 159 days while sunspot number data do not show any periodicity (Verma and Joshi, 1987). Therefore, only sunspot area data should be treated as an indicator of solar activity and not the daily sunspot number data.     

The stable isotope signature of kilometre-scale fracturedominated metamorphic fluid pathways, Mary Kathleen, Australia

Abstract Large calcite veins and pods in the Proterozoic Corella Formation of the Mount Isa Inlier provide evidence for kilometre-scale fluid transport during amphibolite facies metamorphism. These 10- to 100-m-scale podiform veins and their surrounding alteration zones have similar oxygen and carbon isotopic ratios throughout the 200 × 10-km Mary Kathleen Fold Belt, despite the isotopic heterogeneity of the surrounding wallrocks. The fluids that formed the pods and veins were not in isotopic equilibrium with the immediately adjacent rocks. The pods have δ¹³C_calcite values of –2 to –7% and δ¹⁸O_calcite values of 10.5 to 12.5%. Away from the pods, metadolerite wallrocks have δ¹⁸O_whole-rock values of 3.5 to 7%. and unaltered banded calc-silicate and marble wallrocks have δ¹³C_calcite of –1.6 to –0.6%, and δ¹⁸O_calcite of 18 to 21%. In the alteration zones adjacent to the pods, the δ¹⁸O values of both metadolerite and calc-silicate rocks approach those of the pods. Large calcite pods hosted entirely in calc-silicates show little difference in isotopic composition from pods hosted entirely in metadolerite. Thus, 100- to 500-m-scale isotopic exchange with the surrounding metadolerites and calc-silicates does not explain the observation that the δ¹⁸O values of the pods are intermediate between these two rock types. Pods hosted in felsic metavolcanics and metasiltstones are also isotopically indistinguishable from those hosted in the dominant metadolerites and calc-silicates. These data suggest the veins are the product of infiltration of isotopically homogeneous fluids that were not derived from within the Corella Formation at the presently exposed crustal level, although some of the spread in the data may be due to a relatively small contribution from devolatilization reactions in the calc-silicates, or thermal fluctuations attending deformation and metamorphism. The overall L-shaped trend of the data on plots of δ¹³C vs. δ¹⁸O is most consistent with mixing of large volumes of externally derived fluids with small volumes of locally derived fluid produced by devolatilization of calc-silicate rocks. Localization of the vein systems in dilatant sites around metadolerite/calc-silicate boundaries indicates a strong structural control on fluid flow, and the stable isotope data suggest fluid migration must have occurred at scales greater than at least 1 km. The ultimate source for the external fluid is uncertain, but is probably fluid released from crystallizing melts derived from the lower crust or upper mantle. Intrusion of magmas below the exposed crustal level would also explain the high geothermal gradient calculated for the regional metamorphism.     

The middle pleistocene deposits of Waverley Wood Pit,Warwickshire, England

A complex of channels underlying the Baginton-Lillington Gravel (Baginton Formation) at Waverley Wood Quarry, Warwickshire is described. Fossil pollen and plant macrofossils, Coleoptera, Ostracoda, Mollusca and Mammalia are described from the channel-fill deposits. Consideration of all the evidence allows the identification of four separate stages of channel fill which largely occurred under a cool temperate climate. At the top of Channel 2 evidence for a cold, continental climatic episode can be recognised, suggesting that the whole complex was deposited under a fluctuating climate at the end of a temperate stage. At two levels in the channels human artefacts were recovered confirming the presence of Palaeolithic people in Warwickshire during the deposition of the sediments. Amino-acid geochronology suggests an age within the ‘Cromerian Complex’ Stage for the channels. The small vertebrate and molluscan faunas indicate that the deposits are no older than the latter part of the ‘Cromerian Complex’ Stage of East Anglia. The regional stratigraphic significance of the Waverley Wood succession is outlined.     

Cathodoluminescence imaging and titanium thermometry in metamorphic quartz

Cathodoluminescence (CL) of quartz from metamorphic rocks representing a range of conditions from the garnet grade to the migmatite grade reveals a variety of textures, that is, a function of metamorphic grade and deformation history. Ti concentrations, determined by electron microprobe and ion microprobe, generally correlate with CL intensity (blue wavelengths), and application of the Ti‐in‐quartz thermometer (TitaniQ) reflects the temperature of quartz growth or recrystallization, and, in some settings, modification by diffusion. Quartz from garnet grade samples is not visibly zoned, records temperatures of 425–475 °C, and is interpreted to have recrystallized during fabric formation. Quartz grains from staurolite grade samples are zoned in CL with markedly darker cores and brighter rims, some of which are interpreted to have been produced by the dominant staurolite‐producing reaction, whereas others are interpreted as having formed by diffusion of Ti into quartz rims. Quartz from the matrix of kyanite and sillimanite grade samples are generally unzoned, although locally displays slightly brighter rims (higher Ti); quartz inclusions within garnet and staurolite have distinctly brighter rims, which are interpreted as having been produced by diffusive exchange with the host mineral. Quartz from migmatite grade samples displays highly variable CL intensity, which is dependent on the location of the grain. Matrix grains in melanosomes are largely unzoned or rarely zoned with darker cores. Leucosome quartz is strongly zoned with bright cores and dark rims and is interpreted as having formed during crystallization of the melt. Locally within the leucosome is observed oscillatory‐zoned quartz, which is interpreted as a subsolidus recrystallization to achieve strain relaxation. Quartz inclusions within garnet or plagioclase crystals often show bright domains separated by zones of dark CL. These enigmatic textures possibly reflect local melting fluxed by fluid inclusions. Temperatures calculated from the Ti–in–quartz thermometer are a function of the metamorphic grade of the sample, the textural setting of the quartz, the reaction history and the deformation history of the rock. The TitaniQ temperatures can be used to constrain the conditions at which various metamorphic processes have occurred.     

Late Quaternary vegetation changes around Lake Rutundu,Mount Kenya,East Africa: evidence from grass cuticles,pollen and stable carbon isotopes

Woody, subalpine shrubs and grasses currently surround Lake Rutundu, Mount Kenya. Multiple proxies, including carbon isotopes, pollen and grass cuticles, from a 755‐cm‐long core were used to reconstruct the vegetation over the past 38 300 calendar years. Stable carbon‐isotope ratios of total organic carbon and terrestrial biomarkers from the lake sediments imply that the proportion of terrestrial plants using the C₄ photosynthetic pathway was greater during the Late Pleistocene than in the Holocene. Pollen data show that grasses were a major constituent of the vegetation throughout the Late Pleistocene and Holocene. The proportion of grass pollen relative to the pollen from other plants was greatest at the last glacial maximum (LGM). Grass cuticles confirm evidence that C₄ grass taxa were present at the LGM and that the majority followed the cold‐tolerant NADP‐MEC₄ subpathway. Copyright © 2003 John Wiley & Sons, Ltd.     

Melting in the martian mantle: Shergottite formation and implications for present‐day mantle convection on Mars

Abstract— Radiometric age dating of the shergottite meteorites and cratering studies of lava flows in Tharsis and Elysium both demonstrate that volcanic activity has occurred on Mars in the geologically recent past. This implies that adiabatic decompression melting and upwelling convective flow in the mantle remains important on Mars at present. I present a series of numerical simulations of mantle convection and magma generation on Mars. These models test the effects of the total radioactive heating budget and of the partitioning of radioactivity between crust and mantle on the production of magma. In these models, melting is restricted to the heads of hot mantle plumes that rise from the core‐mantle boundary, consistent with the spatially localized distribution of recent volcanism on Mars. For magma production to occur on present‐day Mars, the minimum average radioactive heating rate in the martian mantle is 1.6 times 10^?12 W/kg, which corresponds to 39% of the Wanke and Dreibus (1994) radioactivity abundance. If the mantle heating rate is lower than this, the mean mantle temperature is low, and the mantle plumes experience large amounts of cooling as they rise from the base of the mantle to the surface and are, thus, unable to melt. Models with mantle radioactive heating rates of 1.8 to 2.1 times 10 ^?12 W/kg can satisfy both the present‐day volcanic resurfacing rate on Mars and the typical melt fraction observed in the shergottites. This corresponds to 43–50% of the Wanke and Dreibus radioactivity remaining in the mantle, which is geochemically reasonable for a 50 km thick crust formed by about 10% partial melting. Plausible changes to either the assumed solidus temperature or to the assumed core‐mantle boundary temperature would require a larger amount of mantle radioactivity to permit present‐day magmatism. These heating rates are slightly higher than inferred for the nakhlite source region and significantly higher than inferred from depleted shergottites such as QUE 94201. The geophysical estimate of mantle radioactivity inferred here is a global average value, while values inferred from the martian meteorites are for particular points in the martian mantle. Evidently, the martian mantle has several isotopically distinct compositions, possibly including a radioactively enriched source that has not yet been sampled by the martian meteorites. The minimum mantle heating rate corresponds to a minimum thermal Rayleigh number of 2 times 10⁶, implying that mantle convection remains moderately vigorous on present‐day Mars. The basic convective pattern on Mars appears to have been stable for most of martian history, which has prevented the mantle flow from destroying the isotopic heterogeneity.