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The historic, classical thermodynamic model of star interiors neglects luminosity (L), and consequently predicts ultrahigh central solar temperatures (T - 15 x 106 K). Modern models yield similar T profiles mostly because local thermal equilibrium and multiple free parameters are used. Instead, long-term stability of stars signifies disequilibrium where energy generated equals energy emitted. We assume that heat is generated in a shell defining the core and use Fourier's model, which describes diffusion of heat, including via radiation. to predict the T profile. Under steadystate, power L transmitted through each shell is constant above the zone of energy generation. Hence, L is independent of spherical radius (s), so the Stefan-Boltzmann law dictates T(s), and material properties are irrelevant. Temperature is constant in the core and proportional to Dtr-1/2 above. A point source core sets the upper limit on T(s). giving Taverage = (6/5) 1 451 r| ace• Core size or convecting regions little affect our results. We also construct a parameter-free model for interior pressure (P) and density (p) by inserting our T(s) formula into an ideal gas law (P/poLT) while using the equation for hydrostatic gravitational compression. We find P oc s-·1, p (X s-.5~, and paverage =6x p,uN-ace· Another result, Ln< mass·3·3, agrees with accepted empirical rules for main sequence stars, and validates our model. The total solar mass already "burned" suggests that fusion occurs near L„4400 where P - 0.5 x 1012 Pa, in agreement with H-bomb pressure estimates. Implications are discussed. [ABSTRACT FROM AUTHOR]

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 [...]