Newtonian cosmology with a varying gravitational constant

Newtonian cosmology is developed with the assumption that the gravitational constantG diminishes with time. The functional form adopted forG(t), a modification of a suggestion of Dirac, isG=A(k+t) ^–1, wheret is the age of the Universe and a small constantk is inserted to avoid a singularity in the two-body problem. IfR is the scale factor, normalized to unity at an epoch time , the differential equation is then . Here ₀ is the mean density at the epoch time. With the above form forG(t), the solution is reducible to quadratures.The scale factorR either increases indefinitely or has one and only one maximum. LetH ₀ be the present value of Hubble's constant /R and _0c the minimum density for a maximum ofR, i.e., for closure of the Universe. The conditions for a maximum lead to a boundary curve of _0c versusH ₀ and the numbers indicate strongly that thisG-variable Newtonian model corresponds to an open universe. An upward estimate of the age of the Universe from 10¹⁰ yr to five times such a value would still lead to the same conclusion.The present Newtonian cosmology appears to refute the statement, sometimes made, that the Dirac model forG necessarily leads to the conclusion that the age of the Universe is one-third the Hubble time. Appendix B treats this point, explaining that this incorrect conclusion arises from using all the assumptions in Dirac (1938). The present paper uses only Dirac's final result, viz,G(k+t)^–1, superposing it on the differential equation .     

Diffusion-deposition patterns in Martian streaks

The spreading angle of a number of light and dark Martian streaks is determined from selected Mariner 9 images. The resulting frequency distributions of spreading half-angles have maxima at ～5° for light, and ～7° for dark streaks; however the dark streaks have a secondary maximum spreading angle at ～14°. The smaller values, which include most streaks, are interpreted as crater-wake spreading phenomena. The larger value, found in only a few dark streaks or “tails,” may result from atmospheric diffusion and subsequent deposition of material from isolated sources such as vents or blowouts. An atmospheric diffusion-deposition analysis is presented, assuming this streak origin, from which it is possible to deduce the eddy diffusivity, K, in Mars' boudary layer. Calculated K values are found to agree with various theoretical estimates. They lie in the range 10⁷ and 10⁹ cm² sec^?1 and exhibit the proper scale dependence. Thus it appears that, in addition to streak-derived wind direction patterns and speed information, it is possible in a few cases to derive information on Mars' boundary-layer turbulence from streak-spreading measurements.     

Velocity-space maps and transforms of tracking observations for orbital trajectory state analysis

The orbital state of a satellite in a central force field can be uniquely described by its velocity hodograph, a circle, rather than the Keplerian conic. Also, its coordinate-frame rotation about the attracting center is definable, without singularity, by the four-parameter set of Euler parameters. A unified state model of orbital trajectory and attitude dynamics has previously been developed by use of state variables of the orbital velocity hodograph and Euler parameters. The dynamical constraint equations of this orbital state model are especially effective in advanced techniques of state estimation, used for orbit determination and prediction. External observations of orbital vehicles, such as provided by optical and radar sensors of tracking systems, are transformable into corresponding velocity state maps, as presented in this paper. These transformations and the consequent state maps are essential for development of the orbit observation matrix used with the unified state matrix, in recursive estimators such as the Kalman filters. Line-of-sight rays and range spheres (or hemispheres) of observations map conformally into orthogonal spherical surfaces in velocity space, as the result of the point-contact transformations. In bispherical coordinates, the field of observation maps for a ground-based tracking system site is shown to be a reduced (or degenerate) form of the general field of observation maps for a satellite-based tracking site. These orbital state maps and transforms are directly useful in development of observation matrices for candidate observation sets, such as range only, angle only, or range plus range-rate tracking schemes. Also, surface coverage patterns can be generated for proposed new tracking systems, in mission analysis and system synthesis studies.     

Mudrocks from the Siberian Hypostratotype of the Riphean and Vendian: Chemistry,Sm–Nd Isotope Systematics of Sources,and Formation Stages

Lithology and Mineral Resources - The chemical composition and Nd isotope systematics were obtained for mudrocks (mudstones) from sections of the Siberian hypostratotype of the Riphean and Vendian...     

A canonical theory for short GPS baselines. Part II: the ambiguity precision and correlation

The present contribution is the second of four parts. It considers the precision and correlation of the least-squares estimators of the carrier phase ambiguities. It is shown how the precision and correlation of the double-differenced ambiguities as well as of the widelane ambiguities are effected by the observation weights, by the number of satellites tracked, by the number of observation epochs used, and by the change over time of the relative receiver-satellite geometry. Also the ability of the widelane transformation to decorrelate and to improve the precision is investigated. Received: 16 July 1996 / Accepted: 14 November 1996     

Late Cretaceous rift-related upwelling and melting of the Trindade starting mantle plume head beneath western Brazil

High mantle potential temperatures and local extension, associated with the Late-Cretaceous impact of the Trindade mantle plume, produced substantial widespread and voluminous magmatism around the northern half of the Paraná sedimentary basin. Our previous studies have shown that, above the central and eastern portions of the postulated impact zone where lithosphere extension is minimal, heat conducted by the plume caused large-scale melting of the more fusible parts of the subcontinental lithospheric mantle beneath the margin of the São Francisco craton and the surrounding Brasilía mobile belt. Here we combine geochemical data and field evidence from the Poxoreu Igneous Province, western Brazil to show how more intense lithospheric extension above the western margin of the postulated impact zone permitted greater upwelling and melting of the Trindade plume than further east. Laser ⁴⁰Ar/³⁹Ar age determinations indicate that rift-related basaltic magmas of the Poxoreu Igneous Province were emplaced at ? 84 Ma. Our detailed geochemical study of the mafic magmas shows that the parental melts underwent polybaric crystal fractionation within the crust prior to final emplacement. Furthermore, some magmas (quartz-normative) appear to have assimilated upper crust whereas others (nepheline- and hypersthene-normative) appear to have been unaffected by open-system crustal magma chamber processes. Incompatible trace element ratios (e.g. chondrite-normalised La/Nb?=?1) and isotopic ratios (⁸⁷Sr/⁸⁶Sr?=?0.704 and ¹⁴³Nd/¹⁴⁴Nd?=?0.51274) of the Hy-normative basalts resemble those of oceanic islands (OIB). We therefore propose that these “OIB-like” magmas were predominantly derived from convecting-mantle-source melts (i.e. Trindade mantle plume). Inverse modelling of rare-earth element (REE) abundances suggests that the initial melts were predominantly generated within the depth range of ?80–100 km, in mantle with a potential temperature of ?1500 °C.