Angular momentum and gyroscope in flat space-time theory of gravitation

The study of a previously proposed theory of gravitation in flat space-time (Petry, 1981a) is continued. A conservation law for the angular momentum is derived. Additional to the usual form, there must be added a term coming from the spin of the gravitational field. The equations of motion and of spin angular momentum for a spinning test particle in a gravitational field are given. An approximation of the equations of the spin angular momentum in the rest frame of the test particle is studied. For a gyroscope in an orbit of a rotating massive body (e.g., the Earth) the precession of the spin axis agrees with the result of Einstein's general theory of relativity.     

Further eötvös correction error reduction through the utilization of baseline radio navigation systems

The current accuracy of sea‐going and airborne gravity measurements is not bounded by the precision of the gravimeter but by the precision with which external parameters such as vehicle velocity (speed), azimuthal heading, and geographic position can be determined. Uncertainties in these parameters are summed up in the Eötvös correction in the reduction of the measured data. This work investigates the suitability of baseline navigation systems, in particular Loran‐C and Omega, to further reduce the uncertainty of the Eötvös correction. Emphasis is placed on the velocity measurement error. A new algorithm is developed which derives velocity based upon the change in hyperbolic (or circular) grid readings, as opposed to the standard change in geographic position technique. A comparative analysis shows the new algorithm to be as precise as the currently used conventional calculation. Further, this simplified technique is accompanied with a 20‐fold reduction in computational complexity. Application of the results presented in this paper to the Loran‐C and Omega systems shows a velocity determination capability of 0.1 knot over a six minute integration time, and 0.05 knot for a 15 minute integration time for Loran‐C. The minimum error attainable in Omega is 0.1 knot when determined over a 17 minute measurement time. Further precision can be gleaned by applying the calculated error as a correction to subsequent velocity calculations.     

The trigonometric parallax of the neutron star Geminga

We obtained a series of four observations of the isolated neutron star Geminga over an 18 month period using the Advanced Camera for Surveys (ACS) Wide Field Camera (WFC) on the Hubble Space Telescope in order to determine its trigonometric parallax. We find the parallax π=4.0±1.3 mas, corresponding to a distance to Geminga of 250 _?62 ⁺¹²⁰  pc, a result 60% larger than the previously published value. The proper motion is 178.2±1.8 mas/year. In this paper, we describe the analysis techniques in detail since the amplitude of the parallactic shift is smaller than the camera’s pixel size. We fit each star in the images with an appropriate effective PSF and applied a distortion correction to generate stellar positions accurate to 0.01 pixels (～0.5 mas). The 134 stars common to all images serve to establish a reference frame for alignment of the image series. Our observations were made around the times of maximum parallactic shift. We discuss the implications of this new distance measurement for the inferred radius of Geminga, and the neutron star equation of state.     

Radar observations and the shape of near-Earth asteroid 2008 EV5

We observed the near-Earth ASTEROID 2008 EV5 with the Arecibo and Goldstone planetary radars and the Very Long Baseline Array during December 2008. EV5 rotates retrograde and its overall shape is a 400 ± 50 m oblate spheroid. The most prominent surface feature is a ridge parallel to the asteroid’s equator that is broken by a concavity about 150 m in diameter. Otherwise the asteroid’s surface is notably smooth on decameter scales. EV5’s radar and optical albedos are consistent with either rocky or stony-iron composition. The equatorial ridge is similar to structure seen on the rubble-pile near-Earth asteroid (66391) 1999 KW4 and is consistent with YORP spin-up reconfiguring the asteroid in the past. We interpret the concavity as an impact crater. Shaking during the impact and later regolith redistribution may have erased smaller features, explaining the general lack of decameter-scale surface structure.     

Mineral inclusions in sublithospheric diamonds from Collier 4 kimberlite pipe, Juina, Brazil: subducted protoliths, carbonated melts and primary kimberlite magmatism

We report on a suite of diamonds from the Cretaceous Collier 4 kimberlite pipe, Juina, Brazil, that are predominantly nitrogen-free type II crystals showing complex internal growth structures. Syngenetic mineral inclusions comprise calcium- and titanium-rich phases with perovskite stoichiometry, Ca-rich majoritic-garnet, clinopyroxene, olivine, TAPP phase, minerals with stoichiometries of CAS and K-hollandite phases, SiO₂, FeO, native iron, low-Ni sulfides, and Ca–Mg-carbonate. We divide the diamonds into three groups on the basis of the carbon isotope compositions (δ¹³C) of diamond core zones. Group 1 diamonds have heavy, mantle-like δ¹³C (−5 to −10‰) with mineral inclusions indicating a transition zone origin from mafic protoliths. Group 2 diamonds have intermediate δ¹³C (−12 to −15‰), with inclusion compositions indicating crystallization from near-primary and differentiated carbonated melts derived from oceanic crust in the deep upper mantle or transition zone. A ²⁰⁶Pb/²³⁸U age of 101 ± 7 Ma on a CaTiSi-perovskite inclusion (Group 2) is close to the kimberlite emplacement time (93.1 ± 1.5 Ma). Group 3 diamonds have extremely light δ¹³C (−25‰), and host inclusions have compositions akin to high-pressure–temperature phases expected to be stable in pelagic sediments subducted to transition zone depths. Collectively, the Collier 4 diamonds and their inclusions indicate multi-stage, polybaric growth histories in dynamically changing chemical environments. The young inclusion age, the ubiquitous chemical and isotopic characteristics indicative of subducted materials, and the regional tectonic history, suggest a model in which generation of sublithospheric diamonds and their inclusions, and the proto-kimberlite magmas, are related genetically, temporally and geographically to the interaction of subducted lithosphere and a Cretaceous plume.     

Morphology and recent history of the Rhone River Delta in Lake Geneva (Switzerland)

The current topographic maps of the Rhone Delta—and of Lake Geneva in general—are mainly based on hydrographic data that were acquired during the time of F.-A. Forel at the end of the nineteenth century. In this paper we present results of a new bathymetric survey, based on single- and multi-beam echosounder data. The new data, presented as a digital terrain model, show a well-structured lake bottom morphology, reflecting depositional and erosional processes that shape the lake floor. As a major geomorphologic element, the sub-aquatic Rhone Delta extends from the coastal platform to the depositional fans of the central plain of the lake at 310 m depth. 9 canyons cut the platform edge of the delta. These are sinuous (“meandering”) channels formed by erosional and depositional processes, as indicated by the steep erosional canyon walls and the depositional levees on the canyon shoulders. Ripples or dune-like morphologies wrinkle the canyon bottoms and some slope areas. Subaquatic mass movements are apparently missing on the delta and are of minor importance on the lateral lake slopes. Morphologies of the underlying bedrock and small local river deltas are located along the lateral slopes of Lake Geneva. Based on historical maps, the recent history of the Rhone River connection to the sub-aquatic delta and the canyons is reconstructed. The transition from three to two river branches dates to 1830–1840, when the river branch to the Le Bouveret lake bay was cut. The transition from two to one river branch corresponds to the achievement of the correction and dam construction work on the modern Rhone River channel between 1870 and 1880.     

Correlative and comparative characterization of main ion concentrations in laterite groundwater in semi-arid northern Burkina Faso

About 24 samples from hand-dug wells and boreholes were used to characterize concentrations of the main inorganic ions in a laterite environment under semi-arid climatic conditions in Tikaré, northern Burkina Faso. It was found that the most represented groundwater anion in groundwater was HCO₃ ⁻ with average levels of 49.1 mg/L in the dry season and 33.5 mg/L in the rainy season. The most represented cation was Ca²⁺ with mean concentrations of 13.7 and 9.5 mg/L, respectively. The main processes, which influence the concentrations of these ions, are evaporation (dry season), local enrichment of recharge water in some elements, ion exchange and fixation by clay minerals (in case of K⁺). The best correlations were found between Ca²⁺ and Mg²⁺ (r = 0.95), Cl⁻ and Na⁺ (r = 0.95), HCO₃ ⁻ and Mg²⁺ (r = 0.89), HCO₃ ⁻ and Ca²⁺ (r = 0.89), and between HCO₃ ⁻ and Na⁺ (r = 0.80). In general, the quality of the groundwater from the different wells sampled for this study was good enough to serve as drinking water. However, there were situations where the quality of water was polluted because of anthropogenic contaminants (mainly NO₃ ⁻, K⁺, Cl⁻) from septic tanks and manure pits located in the vicinity of some sampled wells. In addition, application of fertilizers also represents a potential anthropogenic contamination source with regard to SO₄ ²⁻, Ca²⁺, K⁺, Na⁺, and Mg²⁺. Considering the high concentrations of SO₄ ²⁻, Mg²⁺, Na⁺ and Ca²⁺ found in one borehole, the deeper, fractured aquifers were also likely to be enriched in these elements. In contrast, the shallow aquifers are likely to be contaminated with Cl⁻, NO₃ ⁻ and K⁺. Cl⁻ and K⁺ seem to be locally present in recharge water as shown by their relative higher mean concentrations in the rainy season samples.