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.     

The Effect of Atmospheric Drag on Satellite Orbits During the Bastille Day Event

Geomagnetic storms driven by solar eruptions are known to have significant effects on the total density of the upper atmosphere in the altitude range 250–1000 km. This in turn causes a measurable effect on the orbits of resident space objects in this altitude range. We analyzed a sample of these orbits, both from sensor data and from orbital element sets, during the period surrounding the 14 July 2000 solar activity. We present information concerning the effects of this event on the orbits of resident space objects and how well accepted atmospheric models were able to represent it. As part of this analysis, we describe a technique for extracting atmospheric density information from orbital element sets. On daily time scales, the effect of geomagnetic activity appears to be more important than that of prompt radiation. However, the limitations in time and amplitude quantization of the accepted solar indices are evident. A limited comparison is also made with previous solar storm events.     

Structure of Early-Type Galaxies

We outline the results of a two-dimensional (2D) fit to the light distribution of early-type galaxies belonging to a complete volume-limited sample and discuss briefly the significant correlations among the structural parameters. In particular we reconfirm that the lack of structural homology is probably a characteristic of hot stellar systems. This revised version was published online in July 2006 with corrections to the Cover Date.     

Seismotectonic significance of the 29 January 1989 Etne earthquake, SW Norway

The integrated analysis of geological, seismological and field observations with lineament data derived from satellite images allows the identification of a possible seismogenic fault zone for an earthquake which occurred near Etne in southwestern Norway, on 29 February 1989. The hypocentre of the earthquake was located at the mid-crust at a depth of 13.8±0.9 km which is typical of small intraplate earthquakes. The Etne earthquake occurred as a result of normal faulting with a dextral strike-slip component on a NW–SE trending fault. Available geological and lineament data indicate correlation of the inferred seismogenic fault with the NW–SE trending Etne fault zone. An aeromagnetic anomaly related to the Etne fault zone forms a regional feature intersecting both Precambrian basement and allochthonous Caledonian rocks. Based on these associations the occurrence of the Etne event is ascribed to the reactivation of a zone of weakness along the Etne fault zone. Slope-instabilities developed in the superficial deposits during the Etne event demonstrate the existence of potentially hazardous secondary-effects of such earthquakes even in low seismicity areas such as southwestern Norway.     

Predicted interplanetary distribution of Lyman-σ intensity and polarization

Our current understanding of the spatial and temporal distribution of interplan etary neutral hydrogen is currently limited to a comparison of Lyman-σ photometric data with predictions of the solar backscattered radiation using theoretical models. In this paper, how the uncertainties in current model calculations could be reduced through the future use of polarization measurements made from interplanetary spacecraft is investigated. In particular, inquiry into how a mapping of the degree of linear polarization made from a spacecraft at various locations in the Solar System can improve knowledge of the interstellar wind parameters, number density, temperature, and velocity, is made. A polarization measurement can, in principle, be made with very high precision. In this regard, being a relative quantity, a polarization measurement can be made independent of instrumental calibration and long-term sensitivity degredation. Furthermore, the sky distribution of both intensity and polarization has been calculated using a variety of models for the neutral hydrogen. It is found that the polarization distribution over the sky is quite different from that of the intensity distribution. It is also showed that the maximum degree of polarization of the Laymam-σ line increases with heliocentric distance of the spacecraft, varying from 0 up to ～ 18% at 20 AU.     

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.     

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.