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Spiral galaxies are discrete spheroidal objects with highly organized, circular internal motions about a special axis. Available models do not describe these key features or explain why the central regions rotate like a solid body. Practically all previous models describe galaxies as a collection of orbiting test particles, utilize numerous fitting parameters, and require either copious amounts of surrounding dark matter that have not been detected, or modifications to Newton's law, to fit the observed dependence of equatorial velocity on radius. Our paper probes the reasonable alternative that galaxies are discrete, spinning objects. Our analytical forward models, constructed by applying the virial theorem and Newton's law to Maclaurin's spinning spheroids with varying internal density, explain why galactic rotation is organized into this three-dimensional shape. Without invoking dark matter, our spin model explains why the outermost rotational velocities are nearly constant, yet depend on galaxy size, and, with no free parameters, provides masses of 14 important galaxies consistent with their luminosities. We show that proposed modifications to Newton's law compensate for the dynamical differences between a flattened, spinning, Newtonian spheroid, and a collection of orbits. Key words: virial theorem, galactic rotation, dark matter, non-Newtonian forces, spin. Les galaxies spirales sont des objets discrets avec des mouvements circulaires internes hautement organises autour d'un axe special. Les modeles disponibles ne decrivent pas ces caracteristiques centrales ni n'expliquent pourquoi la region centrale tourne comme un corps rigide. Pratiquement tous les modeles anterieurs decrivent les galaxies comme une collection de particules tests en orbite, utilisent de nombreux parametres d'ajustement et requierent des quantites genereuses de matiere noire qui n'ont pas ete detectees, ou encore des modifications a la loi de Newton, afin de s'ajuster aux resultats observes de la dependance de la vitesse equatoriale sur le rayon. Nous sondons ici une alternative raisonnable ou les galaxies sont des objets discrets en rotation. Notre modele analytique, construit en appliquant le theoreme du viriel et la loi de Newton a des spheroides en rotation de Mclaurin avec une densite interne variable, explique pourquoi la rotation galactique est organisee sous cette forme trois-dimensionnelle. Sans besoin de matiere noire, notre modele explique pourquoi les vitesses de rotation externes sont pratiquement constantes, tout en dependant de la grandeur de la galaxie et, sans parametre libre, fournit les masses de 14 galaxies importantes coherentes avec leur luminosite. Nous montrons que les modifications apportees a la loi de Newton compensent pour la difference dynamique entre le spin d'un spheroide newtonien aplati et une collection d'orbites. [Traduit par la Redaction] Mots-cles: theoreme du viriel, rotation galactique, matiere noire, forces non newtoniennes, spin., 1. Introduction Despite decades of intensive searches, non-baryonic particles have not been directly detected [1, 2]. Observational evidence for dark matter is thus limited to forward (fitting) models of galactic [...]

By exploring diverse simple cases, we show that the virial theorem (VT) of Clausius rests on limits of integration in temporal averages being specified by spatial symmetry, rather than on long durations as heretofore claimed. We show the VT results from linear momentum cancelling in all directions over the restricted space that defines any given bound state, via a balance that involves canonical conjugate pairs of position and momentum; this constraint differs from conservation of energy or momentum. The importance of space is underscored by considering behavior of the ideal gas, which is time- independent. Because each distinct force induces a specific type of motion, which in turn has a characteristic length scale, separate VTs are required for each process, which we confirm by example. Combining unrelated potentials in the VT or in its underlying mathematical identity is invalid because this procedure, used in astrophysics, permits energy exchanges that violate selection rules, symmetry constraints, or thermodynamic law. Our analysis unearths an erroneous numerical factor concerning rotation, helps explain the origin of axial spin in our Solar System, and casts doubt on the historical link of gravitation with temperature. Key words: virial theorem, Lagrange-Jacobi identity, ideal gas, canonical conjugates. En examinant plusieurs cas simples, nous montrons que le theoreme du viriel (VT) de Clausius repose sur des limites finies d'integration de moyennes dans le temps basees sur des symetries spatiales, plutot que sur de longues durees comme generalement presente. Nous montrons que le moment lineaire s'annule dans toutes les directions sur un espace borne qui definit tout etat lie, en utilisant un equilibre qui implique la paire canonique conjuguee d'impulsion-position; cette contrainte est differente de celles basees sur la conservation de l'energie ou de l'impulsion. L'importance de l'aspect spatial est soulignee en considerant le comportement du gaz parfait, qui est independant du temps. Parce que chaque force distincte induit un mouvement different, qui a sa propre echelle de longueur caracteristique, differents VT sont requis pour chaque processus, ce que nous confirmons par un exemple. La combinaison de potentiels non relies dans le meme VT ou dans sa formulation mathematique est invalide, parce que cette procedure, utilisee en astrophysique, permet des echanges d'energie qui violent les regles de selection, les contraintes de symetrie ou les lois de la thermodynamique. Notre analyse fait ressortir des facteurs numeriques errones concernant la rotation, aide a expliquer l'origine du spin axial dans notre systeme solaire et jette un doute sur le lien historiquement fait entre la gravite et la temperature. [Traduit par la Redaction] Mots-cles: theoreme du viriel, formulation Lagrange-Jacobi, gaz parfait, canonique conjuguee. PACS Nos.: 11.27.+d, 05.70.-a., 1. Introduction The virial theorem (VT) of Clausius [1] describes diverse phenomena in bound, conservative systems whose scales range from quantum to astronomical [2-4]. Because Clausius was concerned with temperature [...]

Extremely slow recession of the Moon from the Earth has been recently proposed and attributed to conversion of Earth's axial spin to lunar orbital momentum. This hypothesis is inconsistent with long-standing recognition that the Moon's orbit involves three-body interactions. This and other short-comings, such as Earth's spin loss being internal, are summarized here. Considering point-masses is justified by theory and observational data on other moons. We deduce that torque in the Earth-Moon-Sun system increases eccentricity of the lunar orbit but decreases its inclination over time. Consequently, the average lunar orbital radius is decreasing. We also show that lunar drift is too small to be constrained through lunar laser ranging measurements, mainly because atmospheric refraction corrections are comparatively large and variations in lunar cycles are under-sampled. Our findings support co-accretion and explain how orbits evolve in many-body point-mass systems. [ABSTRACT FROM AUTHOR]

Data from the 1803-1806 Lewis and Clark expedition and nineteenth century stage records are used to quantitatively benchmark natural, premanagement hydrology of the lower Missouri River and assess the magnitude and timing of hydrologic change over nearly two centuries. Data show doubling in daily stage variability from the nineteenth century to 2005. Annual maximum stages have, at some sites, become more extreme, and their seasonality is less regular. Observed changes adversely affect riverine habitat and flood levels; their timing, beginning as early as 1900, suggests that channelization is the major driver. Keywords: basin management, Missouri River, hydrology, channelization, Lewis and Clark.

Landslides whose slide surface is gentle near the toe and relatively steep in the middle and rear part are common in the Three Gorges Reservoir area, China. The mass that overlies the steep part of the slide surface is termed the driving section and that which overlies the gentle part of the slide surface is termed the locking section. A driving-locking model is presented to elucidate the deformation mechanism of reservoir landslides of this type, as exemplified by Shuping landslide. More than 13 years of field observations that include rainfall, reservoir level and deformation show that the deformation velocity of Shuping landslide depends strongly on the reservoir level but only slightly on rainfall. Seepage modelling shows that the landslide was destabilized shortly after the reservoir was first impounded to 135 m, which initiated a period of steady deformation from 2003 to 2006 that was driven by buoyancy forces on the locking section. Cyclical water-level fluctuations in subsequent years also affected slope stability, with annual jumps in displacement coinciding with drawdown periods that produce outward seepage forces. In contrast, the inward seepage force that results from rising reservoir levels stabilizes the slope, as indicated by decreased deformation velocity. Corrective transfer of earth mass from the driving section to the locking section successfully reduced the deformation of Shuping landslide, and is a feasible treatment for huge reservoir landslides in similar geological settings. [ABSTRACT FROM AUTHOR]

Galactic mass consistent with luminous mass is obtained by fitting rotation curves (RC = tangential velocities vs. equatorial radius r) using Newtonian force models, or can be unambiguously calculated from RC data using a model based on spin. In contrast, mass exceeding luminous mass is obtained from multi-parameter fits using potentials associated with test particles orbiting in a disk around a central mass. To understand this disparity, we explore the premises of these mainstream disk potential models utilizing the theorem of Gauss, thermodynamic concepts of Gibbs, the findings of Newton and Maclaurin, and well-established techniques and results from analytical mathematics. Mainstream models assume that galactic density in the axial (z) and r directions varies independently: we show that this is untrue for self-gravitating objects. Mathematics and thermodynamic principles each show that modifying Poisson’s equation by summing densities is in error. Neither do mainstream models differentiate between interior and exterior potentials, which is required by potential theory and has been recognized in seminal astronomical literature. The theorem of Gauss shows that: (1) density in Poisson’s equation must be averaged over the interior volume; (2) logarithmic gravitational potentials implicitly assume that mass forms a long, line source along the z axis, unlike any astronomical object; and (3) gravitational stability for three-dimensional shapes is limited to oblate spheroids or extremely tall cylinders, whereas other shapes are prone to collapse. Our findings suggest a mechanism for the formation of the flattened Solar System and of spiral galaxies from gas clouds. The theorem of Gauss offers many advantages over Poisson’s equation in analyzing astronomical problems because mass, not density, is the key parameter. [ABSTRACT FROM AUTHOR]

Fertilizer use has increased 10-fold since World War II. Current application rates are staggering and greatly exceed the amounts absorbed by plants. For example, the average amount of nitrogen applied [...]

Flood stages for constant discharge have increased 2-4 m over the past century at numerous locations in the Mississippi River basin. However, no increases are observed on rivers such as the Meramec and the upper Missouri, which have been spared extensive river engineering projects. Flood-stage increases on the middle Mississippi River and lower Missouri River are mostly attributable to channelization.

Proposed explanations of galactic rotation curves (RC = tangential velocity vs. equatorial radius, determined from Doppler measurements) involve dramatically different assumptions. A dominant, original camp invoked huge amounts of unknown, non-baryonic dark matter (NBDM) in surrounding haloes to reconcile RC simulated using their Newtonian orbital models (NOMs) for billions of stars in spiral galaxies with the familiar Keplerian orbital patterns of the few, tiny planets in our Solar System. A competing minority proposed that hypothetical, non-relativistic, non-Newtonian forces govern the internal motions of galaxies. More than 40 years of controversy has followed. Other smaller groups, unsatisfied by explanations rooted in unknown matter or undocumented forces, have variously employed force summations, spin models, or relativistic adaptations to explain galactic rotation curves. Some small groups have pursued inverse models and found no need for NBDM. The successes, failures, and underlying assumptions of the above models are reviewed in this paper, focusing on their mathematical underpinnings. We also show that extractions of RC from Doppler measurements need revising to account for the effect of galaxy shape on flux-velocity profiles and for the possible presence of a secondary spin axis. The latter is indicated by complex Doppler shift patterns. Our findings, combined with independent evidence such as hadron collider experiments failing to produce non-baryonic matter, suggest that a paradigm shift is unfolding. [ABSTRACT FROM AUTHOR]

Spiral galaxies are spinning, internally densified objects. The Virial Theorem explains galactic rotation curves via its linkage of the rotation rate to the gravitational self-potential (Ug) and the moment of inertia of oblate spheroids. We devise a new analytical solution that allows galactic mass and volumetric density (kg m−3) profiles to be extracted from velocity and its derivative as functions of equatorial radius. This inverse model of rotation curves is direct, unambiguous, and parameter-free. To probe galactic evolution, we combine energy minimization, angular momentum conservation, and the Virial Theorem. The characteristic flat shape of spiral galaxies results from an initial vertical collapse of a spinning, colossal molecular cloud, which reduces Ug while conserving angular momentum. Subsequent inward densification further lowers Ug, producing bulges, but conserving angular momentum requires mass loss, achieved by the outward movement of the distal parts of the spiral arms. Many of the evolutionary patterns of spiral galaxies are exhibited by the changing shapes of hurricanes during formation and dissipation. In contrast, elliptical galaxies evolve from a cloud with roughly random orbits into progressively rounder, internally denser objects, with angular momentum conserved by the development of vertically oriented jets. Galactic evolution is governed by the initial inventory of mass and angular momentum, resulting in separate paths for elliptical and spiral galaxies, as is codified in Hubble's tuning fork diagram. [ABSTRACT FROM AUTHOR]