An impact model of Newton’s law of gravitation

The far-reaching gravitational force—in the approximation of Newton’s law of gravitation—is described by a heuristic model with hypothetical massless particles propagating at the speed of light in vacuum and transferring momentum and energy between physical entities through interactions on a local basis. The model has some similarities with the impact theory presented by Nicolas Fatio de Duillier to the Royal Society in 1690. Objections raised against this idea are dispelled by invoking the Special Theory of Relativity, considering non-local interactions, and replacing the shielding concept by a secular mass increase of massive bodies. Some consequences and applications of the model are discussed.     

The structure and development of greater Lagos

In the period between 1965 and 1976, when German geographers carried out their fieldwork for the Afrika-Kartenwerk under the sponsorship of the German Research Society, remarkable progress in urban development especially in Lagos could be observed. The cooperation with the Federal Survey Department of Nigeria gave the opportunity for collecting several series of aerial photographs which bring into focus some stages of the overwhelming urban expansion.The materials presented here have been selected to demonstrate some regional structures of the Nigerian capital. — In the geography of today the scientific evaluation of aerial photographs together with findings from local observation and historical as well as statistical data is still undervalued. Through this technique, the more classical and conservative method of geographical analysis, relying on subjective judgement, may regain some of its importance, which it once had in the age of exploration of new territories.Where data is scarce and written records of urban expansion are not available or difficult to extract, aerial photographs can give an impression of certain stages of urban growth. A functional analysis under geographical aspects has to be regarded by changes within spatial units in order to the factors of influence. Those factors are numerous, their influence will cause changes in a series of pushes arising from economic developments of the vast hinterland as well as from social conditions of certain groups of the population. In a metropolitan center, as Lagos, the highest ranking central place of Africa's most populous nation, heterogenous events and a confusing number of planning decisions must be taken into consideration. One consequence of nationwide regional interactions with the metropolis is migratory population dynamics. In pursuing lines of interaction, which originate from economic power, population density, and natural resources, one can hardly isolate a single element of influence because all factors are closely interrelated. For Lagos, there is only limited data available on the social and economic standard of the population, valid basic demographic figures of some value are not available.One still has to accept very rough estimates on population figures, number of industrial workers, the standards of housing and the social and economic hierarchy of the population. The present retrospective analysis of aerial photographs gives an interpretation of the regional structure of the town and indicate possible future development.     

Sur la repartition de densite a l'interieur de l'ellipsoide equipotentiel

Résumé Une solution générale du problème de la répartition de densité à l'intérieur de l'ellipso?de équipotential est appliquée à quelques modèles spéciaux.

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A general solution of the problem of density distribution for the equipotential ellipsoid is applied to obtain some special models.

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Zusammenfassung Eine allgemeine L?sung des Problems der Massenverteilung für das Niveauellipsoid wird auf einige spezielle Modelle angewendet.

     

Multi-stage Ag–Bi–Co–Ni–U and Cu–Bi vein mineralization at Wittichen,Schwarzwald, SW Germany: geological setting,ore mineralogy,and fluid evolution

The Wittichen Co–Ag–Bi–U mining area (Schwarzwald ore district, SW Germany) hosts several unconformity-related vein-type mineralizations within Variscan leucogranite and Permian to Triassic redbeds. The multistage mineralization formed at the intersection of two fault systems in the last 250 Ma. A Permo-Triassic ore stage I with minor U–Bi–quartz–fluorite mineralization is followed by a Jurassic to Cretaceous ore stage II with the main Ag and Co mineralization consisting of several generations of gangue minerals that host the sub-stages of U–Bi, Bi–Ag, Ni–As–Bi and Co–As–Bi. Important ore minerals are native elements, Co and Ni arsenides, and pitchblende; sulphides are absent. The Miocene ore stage III comprises barite with the Cu–Bi sulfosalts emplectite, wittichenite and aikinite, and the sulphides anilite and djurleite besides native Bi, chalcopyrite, sphalerite, galena and tennantite. The mineral-forming fluid system changed from low salinity (<5 wt.% NaCl) at high temperature (around 300°C) in Permian to highly saline (around 25 wt.% NaCl + CaCl₂) at lower temperatures (50–150°C) in Triassic to Cretaceous times. Thermodynamic calculations and comparison with similar mineralizations worldwide show that the Mesozoic ore-forming fluid was alkaline with redox conditions above the hematite–magnetite buffer. We suggest that the precipitation mechanism for native elements, pitchblende and arsenides is a decrease in pH during fluid mixing processes. REE patterns in fluorite and the occurrence of Bi in all stages suggest a granitic source of some ore-forming elements, whereas, e.g. Ag, Co and Ni probably have been leached from the redbeds. The greater importance of Cu and isotope data indicates that the Miocene ore stage III is more influenced by fluids from the overlying redbeds and limestones than the earlier mineralization stages.     

THE INMAN,McPHERSON COUNTY,KANSAS METEORITE

Inman (find, 1966) is a single, relatively unweathered stone of 7.25 kg that contains fresh metal and only few weathering products away from fractures. It has a pronounced chondritic texture, with 38 vol % of the meteorite being made up of chondrules of virtually all textural types. The recalculated bulk analysis, particularly the ratios of Fe_total/SiO₂ (0.46), Fe°/Fe_total (0.35), and Fe°/Ni° (6.67) and the contents of Fe_total (19.45%) and metallic nickel-iron (7.94%), indicate that Inman is an L-group chondrite. The pronounced chondritic texture; the compositional variabilities of olivine, pyroxene, chromite, and ilmenite; the presence of a fine-grained, nearly opaque matrix, glass and twinned monoclinic low-Ca pyroxene indicate that the chondrite belongs to petrologic type 3.     

The adapted solar wind system as cause for a momentum transfer to the sun and its consequences for the orbital motions of keplerian objects

In the following paper we argue that each wind-driving star in relative motion with respect to the ambient interstellar medium experiences a force exerted on its central wind-generating body. The exact magnitude of this force depends on the actual geometry of the counterflow configuration of stellar and interstellar winds for a particular kinematic situation which is especially sensitive to whether the interstellar flow is subsonic or supersonic. It will, however, be demonstrated here that this force is of an accelerating nature, i.e., it operates like a rocket-motor, as long as the peculiar motion of the wind-driving star with respect to the ambient interstellar medium remains subsonic.Here we use a specific analytical model to describe theoretically the specific counterflow configuration for the case of the solar system in a subsonic peculiar motion with respect to the local interstellar medium assuming irrotational and incompressible flows. We can work out a quantitative number for the accelerating force governing the Sun's motion at present. The net reaction force exerted on the solar body is then mediated by the asymmetric boundary conditions to which the distant solar wind field has to adapt.Next we study the indirect action of such a force on orbiting Keplerian objects like planets, planetesimals and comets. Since this force only influences the central solar body, but not the planets themselves, the problem is different from the treatment of a constant perturbation force perturbing the Keplerian orbits. We present a perturbation analysis treating the action of a corresponding position-dependent perturbation force resulting in secular changes of the orbital elements of Keplerian objects. It is found that changes are accumulating more rapidly in time the closer to the sun the orbiting bodies are. Main axis and perihelion distances are systematically increasing. Especially pronounced are changes in the perihelion position angle of the objects. For solar wind mass losses larger than the Sun's present value by a factor of 1000 (T-Tauri phase of the Sun,) the migration periods calculated for the planet Mercury are of the same order of magnitude as that for corresponding general relativistic migration.     

40Ar/39Ar geochronology of mafic rocks from the granite—rhyolite terrane of southeastern Missouri

The predominant 1480 Ma granites and rhyolites of the St. Francois Mountains, southeastern Missouri, are intruded by mafic rocks. A ⁴⁰Ar—³⁹Ar study of some of these, the Skrainka Mafic Group, indicates an age of ～ 1240 Ma, significantly younger than the host rocks, significantly older than Grenville/Keweenawan age, and close to the age of similar rocks in Labrador.