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Available inventories of baryonic mass in the universe are based largely on galactic data and empirical calculations made >20 years ago. Values falling below cosmological estimates underlie proposals that certain rarified gassy regions could have extremely high T, which motivated absorption measurements and hydrodynamic models. Yet, the shortfall remains. We inventory the total baryonic mass, focusing on gravitational interactions and updated measurements. A recent analytical inverse method for analyzing galactic rotation curves quantified how baryon mass and associated volumetric density (ρ) depend on distance (r) from galactic centers. The model is based on the dynamical consequences of the observed oblate shape of galaxies and the Virial Theorem. The parameter-free solution provides ρ(r) ∝ 1/r2 which describes star-rich galactic interiors, gas-rich outer discoids, circumgalactic media, and gradation into intergalactic media. Independent observational determinations of baryonic ρ validate that our 1/r2 result describes baryons alone. This solution shows that total baryonic mass associated with any galaxy is 2.4 to 40 times detectable luminosity, depending on galaxy size and spacing. Luminosity data within 50 Mpc show that Andromeda equivalents separated by ~1 Mpc represent the local universe. Combining the above yields (6 ± 2) × 10−25 kg m−3 for the present-day universe. Three other approaches support this high density: (1) evaluating trends and luminosity data near 1000 Mpc; (2) using a recent estimate for the number of galaxies in the universe; (3) calculating an energy balance. We discuss uncertainties in the critical density. Implications of large baryonic ρ are briefly 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. [ABSTRACT FROM AUTHOR]

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. [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]