Literal solution for Hill's lunar problem

A computer program for the manipulation of power series in several variables is used to find the first order solution to Hill's lunar problem. The ratiom of the mean motion of the Sun to that of the Moon is kept as a formal parameter. The series inm are known to converge very poorly. It is shown how efficient algorithms among them the Lie transformation allow us to compute the series inm as far as they are needed. When the series are evaluated at Brown's numerical value form the results achieve or exceed his accuracy.     

Low δ18O eclogites from the Kokchetav massif, northern Kazakhstan

Oxygen isotopic compositions of silicates in eclogites and whiteschists from the Kokchetav massif were analyzed by whole‐grain CO₂‐laser fluorination methods. Systematic analyses yield extremely low δ¹⁸O for eclogites, as low as ?3.9‰ for garnet; these values are comparable with those reported for the Dabie‐Sulu UHP eclogites. Oxygen isotopic compositions are heterogeneous in samples of eclogite, even on an outcrop scale. Schists have rather uniform oxygen isotope values compared to eclogites, and low δ¹⁸O is not observed. Isotope thermometry indicates that both eclogites and schists achieved high‐temperature isotopic equilibration at 500–800 °C. This implies that retrograde metamorphic recrystallization barely modified the peak‐metamorphic oxygen isotopic signatures. A possible geological environment to account for the low‐δ¹⁸O basaltic protolith is a continental rift, most likely subjected to the conditions of a cold climate. After the basalt interacted with low δ¹⁸O meteoric water, it was tectonically inserted into the surrounding sedimentary units prior to, or during subduction and UHP metamorphism.     

Fabric at granodiorite-schist contact,Bear Island,Maryland

Summary The essential difference between the granodiorite and its wall rock fabric consists in the two well-defined deformation plans. The wall rock is a B-tectonite, the granodiorite an S-tectonite. Transport in the former was rotational and monoclinic, in the latter possibly by laminar flow parallel with the contact.The granite fabric could hardly be an in place fabric or replacement without differential movement. It would have retained the wall rock fabric, even if not the mineral composition. Transport in the granodiorite was presumably along the wall parallel S₄ and the contact. The present study is barely a beginning, but it is hoped that it can be continued in the near future and extended over a wider area.With 9 figures.     

The distribution of aluminum-26 in the early Solar System—A reappraisal

Abstract— A compilation of over 1500 Mg-isotopic analyses of Al-rich material from primitive solar system matter (meteorites) shows clearly that ²⁶Al existed live in the early Solar System. Excesses of ²⁶Mg observed in refractory inclusions are not the result of mixing of “fossil” interstellar ²⁶Mg with normal solar system Mg. Some material was present that contained little or no ²⁶Al, but it was a minor component of solar system matter in the region where CV3 and CO3 carbonaceous chondrites accreted and probably was a minor component in the accretion regions of CM chondrites as well. Data for other chondrite groups are too scanty to make similar statements. The implied long individual nebular histories of CAIs and the apparent gap of one or more million years between the start of CAI formation and the start of chondrule formation require the action of some nebular mechanism that prevented the CAIs from drifting into the Sun. Deciding whether ²⁶Al was or was not the agent of heating that caused melting in the achondrite parent bodies hinges less on its widespread abundance in the nebula than it does on the timing of planetesimal accretion relative to the formation of the CAIs.     

Exact Brans-Dicke-Bianchi types-II,VIII, and IX stiff matter solutions

Exact solutions of the Brans-Dicke field equations of Bianchi types-II, VIII, and IX are derived. The solutions represent locally rotationally symmetric universes with stiff matter content.     

Provenance of Palaeozoic sandstones from the Carnic Alps (Austria): petrographic and geochemical indicators

An integrated approach of petrographic analysis, whole rock geochemistry and microprobe analysis has been applied to obtain information on the geodynamic development and the provenance for Ordovician to Permian siliciclastic successions exposed within the Carnic Alps (Austria). Sandstone detrital mode and geochemical results refine previous geodynamic interpretations. Late Ordovician samples indicate a stable craton and recycled orogenic and, possible, extensional setting. The Early Carboniferous is interpreted to represent a compressional environment, followed by a Late Carboniferous molasse-type foreland basin, and a Permian extensional geodynamic setting. Contrasting geochemical patterns of post-Variscan and Permian sequences suggest a rift setting. Electron microprobe data of detrital white mica also indicate changes in the provenance. Compositional data reflect a shift from low- to medium-grade metamorphic (Ordovician) to high-grade metamorphic (Carboniferous) to low- to medium-grade metamorphic and plutonic source rocks (Permian). Additionally, our data show that various chemical discrimination diagrams do not include all possible ranges of sandstones, and that high contents of detrital mica and ultra-stable heavy minerals may cause misclassification. Consequently, we propose the use of multi-method approach for provenance studies, including the control of geochemical data by modal analysis and heavy mineral investigations.     

SNR Surface Density Distribution in Nearby Galaxies

Since supernova remnants (SNRs) are believed to be the primary sources of Galactic cosmic rays (CRs), their distribution in galaxies is an important basis for modelling and understanding the distribution of the CRs and their γ-ray spectrum. We analysed the radial surface density of X-ray and radio selected SNRs in the Large Magellanic Cloud (LMC) and M 33. Both in X-rays and in radio, the surface densities of the SNRs are in excellent agreement in both galaxies, showing an exponential decay in radius. The results were compared to the SNR distribution in the spiral galaxies M 31 and NGC 6946 as well. The radial scale length of the distribution is $\frac{1} {4} $ ? $\frac{1} {3} $ of the radius of the galaxies, fully consistent with values derived for the Milky Way, the LMC, and M 33. Therefore, not only the radio SNRs, but also the X-ray detected SNR sample can be interpreted to be representative for the CR sources within a galaxy.     

The Central Scandinavian Dolerite Group—Protracted hotspot activity or back-arc magmatism?: Constraints from U–Pb baddeleyite geochronology and Hf isotopic data

The Central Scandinavian Dolerite Group (CSDG) occurs in five separate complexes in central Sweden and SW Finland. U–Pb baddeleyite ages of dolerite dikes and sills fall into three age intervals: 1264–1271 (the Dalarna complex), 1256–1259 (the Västerbotten-Ulvö-Satakunta complexes) and 1247 Ma (the Jämtland complex). Timing and spatial distribution of CSDG are unlike expressions of the voluminous and short-lived magmatism which characterises plume-associated large igneous provinces (LIPs). Protracted mafic magmatism in association with mantle plume tail (hotspot) activity beneath the Fennoscandian lithosphere or discrete events of extension behind an active margin (subduction) are considered more plausible tectonic settings. Both settings are consistent with timing, relative magma volumes between complexes and vertical ascent of individual magma pulses through the crust, as inferred from seismic sections [Korja, A., Heikkinen, P., Aaro, S., 2001. Crustal structure of the northern Baltic Sea palaeorift. Teconophysics 331, 341–358]. In the hotspot model, the lack of a linear track of intrusions can be explained by an almost stationary position of Fennoscandia relative to the hotspot, in agreement with palaeomagnetic data [Elming, S.-Å., Mattsson, H., 2001. Post Jotnian basic intrusion in the Fennoscandian Shield, and the break up of Baltica from Laurentia: a palaeomagnetic and AMS study. Precambrian Res. 108, 215–236]). Together with geological evidence, dolerite sill complexes and dike swarms in Labrador (Canada), S Greenland and central Scandinavia in the range 1234–1284 Ma are best explained by long-lived subduction along a continuous Laurentia-Baltica margin preceding Rodinia formation. There is no support for the hypothesis that CSDG was fed by magma derived from a distal mantle plume located between Baltica and Greenland and, hence, for rifting between the cratons at 1.26 Ga.The epsilon-Hf in various members of the CSDG varies between 4.7 and 10.3, which are overall higher than both older and younger Mesoproterozoic mafic intrusions in central Fennoscandia. Magma generated from a hotspot mantle source that was mixed to highly variable degrees with an enriched subcontinental lithospheric mantle could account for the wide range in Hf isotope composition. In the course of Hf isotope development work during this project we have analysed four fragments of the Geostandard 91500 reference zircon and after evaluating the existing ICPMS and TIMS data we calculate a mean ¹⁷⁶Hf/¹⁷⁷Hf value of 0.282303 ± 0.000003 (2σ).