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.     

Regolith Surface Reflectance: A New Attempt to Model

The reflectance coefficient of the regolith layer of celestial bodies has been studied in relation to the physical properties of regolith particles (size, refractive index, and packing density) on the basis of an accurate numerical radiative-transfer algorithm for a semi-infinite flat layer. Using the geometric-optics approximation, we have found that a shape mixture of randomly oriented spheroids can successfully model the single-scattering phase function of independent soil grains. In order to take into account the effect of packing density in a regolith layer, the concept of the so-called static structure factor was used. The main effect of increasing packing density is to suppress the forward-scattering peak of the phase function and to increase the albedo of the reflecting surface. We also investigated the influence of fine dust on the reflected light. An addition of small particles not only increases the surface albedo, but also changes the brightness profile and enhances the backscattering. Although the problem of unique solution, which is inherent in the retrieval of the properties of a medium from the measurements of the intensity of light scattered by this media, cannot be removed in the proposed model, the procedure used here, in contrast to widely used approximations, allows us to fit observational data with a set of real characteristics of the regolith. Semiempirical approaches are able to fit the measurements well with a small number of free parameters, but they do not explicitly contain crucial physical characteristics of the regolith such as grain sizes or the refractive index. We compared the numerical solution of the radiative-transfer equation with the Hapke approximation, which is most often used by investigators. The errors introduced by the Hapke model are small only for near-isotropic scattering by isolated particles. However, independent regolith grains are known to scatter light mainly in the forward direction.     

Challenging a Paradigm: Do We Need Active and Inactive Areas to Account for Near-Nuclear Jet Activity?

We briefly describe an advanced 3D gas dynamical model developed for the simulation of theenvironment of active cometary nuclei. The model canhandle realistic nucleus shapes and alternative physical models for the gas and dust production mechanism.The inner gas coma structure is computed by solving self-consistently(a) near to the surface the Boltzman Equation(b) outside of it, Euler or Navier-Stokes equations.The dust distribution is computed from multifluid ``zero-temperature' Euler equations,extrapolated with the help of a Keplerian fountain model.The evolution of the coma during the nucleus orbital and spin motion,is computed as a succession of quasi-steady solutions. Earlier versions of the model using simple,``paedagogic' nuclei have demonstrated that the surface orographyand the surface inhomogeneity contribute similarly to structuring the near-nucleusgas and dust coma,casting a shadow on the automatic attribution of such structures to ``active areas'.The model was recently applied to comet P/Halley, for whichthe nucleus shape is available. In the companion paper of this volume,we show that most near-nucleus dust structuresobserved during the 1986 Halley flybys are reproduced, assuming that the nucleus is strictly homogeneous. Here, we investigate the effect of shape perturbations and homogeneityperturbations. We show that the near nucleus gas coma structure is robust vis-a-vissuch effects. In particular, a random distribution of active and inactive areaswould not affect considerably this structure, suggesting that such areas,even if present, could not be easily identified on images of the coma.     

Ultra-Deep Optical Spectroscopy with PMAS. Using the Nod-and-Shuffle Technique

PMAS, the Potsdam Multi-Aperture Spectrophotometer, is a new integral field spectrograph in the optical, which is optimized for good transmission and high image quality from 350 nm to 1 μm. We present our plan to implement a CCD charge-shuffle mode to allow for beam switching with a very high degree of sky subtraction accuracy for faint object 3-D spectroscopy. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

A Critical review of theoretical models of negatively polarized light scattered by atmosphereless solar system bodies

About a dozen physical mechanisms and models aspire to explain the negative polarization of light scattered by atmosphereless celestial bodies. This is too large a number for the reliable interpretation of observational data. Through a comparative analysis of the models, our main goal is to answer the question: Does any one model have an advantage over the others? Our analysis is based on new laboratory polarimetric and photometric data as well as on theoretical results. We show that the widely used models due to Hopfield and Wolff cannot realistically explain the phase-angle dependence of the degree of polarization observed at small phase angles. The so-called interference or coherent backscattering mechanism is the most promising model. Models based on that mechanism use well-defined physical parameters to explain both negative polarization and the opposition effect. They are supported by laboratory experiments, particularly those showing enhancement of negative polarization with decreasing particle size down to the wavelength of light. According to the interference mechanism, pronounced negative branches of polarization, like those of C-class asteroids, may indicate a high degree of optical inhomogeneity of light-scattering surfaces at small scales. The mechanism also seems appropriate for treating the negative polarization and opposition effects of cometary dust comae, planetary rings, and the zodiacal light.     

A high‐resolution pollen and geochemical analysis of late Holocene human impact and vegetation history in southern Cumbria,England

The historic era, which in Cumbria begins with the Roman invasion of AD 71, is a frequently neglected period in palaeoecological research, but its study can bring benefits in improving knowledge of landscape history and in understanding the significance and limitations of palaeoecological records. Pollen and geochemical data are presented for late Holocene records from Deer Dyke and Hulleter Mosses in southern Cumbria. The records show initially low levels of anthropogenic impact, followed by a phase of forest clearance and mixed agriculture from the 7th to 11th centuries AD. The timing of these clearances suggests that they were initially Anglo‐Saxon in origin, rather than Norse. Further clearances in the 16th century AD are interpreted as a response to monastic dissolution and late Tudor population pressures; the landscapes reached their contemporary form following extensive clearances in the 17th century AD. Silicon and titanium concentrations at Deer Dyke Moss were used to reconstruct past levels of atmospheric dust loading, which is broadly related to soil erosion. Geochemical influx was found to peak during periods of landscape transition rather than from established land use. This relationship with pollen data is thought to reflect the predominantly low levels of anthropogenic impact in the region, which changes as substantial woodland clearances during the 16th century AD and continuous land use pressure since then have greatly increased the supply of airborne dust. Copyright © 2008 John Wiley & Sons, Ltd.     

The origin of the correlation between the spin parameter and the baryon fraction of galactic disks

The puzzling correlation between the spin parameter λ of galactic disks and the disk-to-halo mass fraction f _disk is investigated. It is shown that such a correlation arises naturally from large uncertainties in determining the virial masses of dark matter halos. This result indicates that halo properties derived from fits to observed rotation curves are still very uncertain. An analysis of λ versus f _disk as function of the adopted halo virial mass shows that for reasonable halo concentrations f _disk ≈ 0.01 - 0.07 which is significantly smaller than the universal baryon fraction. Most of the available gas either never settled into the galactic disks or was ejected subsequently. This revised version was published online in August 2006 with corrections to the Cover Date.     

Kinematic Analysis of Near and Far Stars in the Hipparcos Catalog

The proper motions of stars in the main sequence and of luminosity class III giants are analyzed kinematically. A new method has been used for reliably separating all the parameters of the Ogorodnikov-Milne model based on representing the proper motions of the stars in coordinate systems whose poles lie on each of the three principal axes of the galactic trihedron. Solutions for stars in different spectral classes are obtained. The main sequence is found to subdivide into two zones (near and far stars) with a fairly sharp boundary at B-V=0.5. It is shown that the Parenago effect may be related to the different distances from the sun of the main sequence stars.