Eddingtons Zahlen,Einsteins Kriterium und Rydbergs rationelles Dimensionssystem

The discussions about the meaning of the “hierarchy of interactions” and in connection with this about the role of Eddington's “cosmological number” imply the question of the “big numbers” in physics. According to Einstein's and Bridgman's criteria such “big numbers” are hints at unsolved problems in the foundations of physics. Eddington gives a theory of the big number like cosmological quantities. – A new point of view on this question may be to remember Rydberg's suggestion on independigly physical dimensions of lengths L, surfaces S, and volumina V, and to remember Dällenbach's suggestion to introduce a new universal constant α which describes the operational connections between the quardrate of lengths L² and the surface S in microphysics. Coulomb's and Nwton's laws have the same structure. But, the electrical forces are depending on L^-2 and the gravitational forces are depending on S^-1 ∼ (1/α) L^-2 because “gravitation is geometry”. In Planck's elementary units h, c and f Dällenbach's “surface-constant of the vacuum” α is a pure number α ≈ hc/fm², th. i. Eddington's cosmological number ω ∼ 10⁴⁰. However, Rydberg's physical dimensions in geometry and Dällenbach's constant suggest new formulations of the question of “geometrization of physics” and “physicallization of geometry” and the connections between cosmology and microphysics.     

Das Korrespondenzprinzip in der Kosmologie I. Der isotrope Kosmos als NEWTONscher Grenzfall der relativistischen Gravitationstheorien

According to the principle of correspondence (in HEISENBERG 's formulation) each general relativistic theory of gravitation must give a NEWTON ian representation for an isotropic cosmos with the ROBERTSON -WALKER metric. Indeed, the FRIEDMANN equations can be interpreted as the expression for the HAMILTON ian H of a closed NEWTON ian system of the cosmic fundamental particles, written in the rest-system of the center of gravity. In this HAMILTON ian H only the relative-coordinates and the relative-velocities of the particles are present and one can write H without absolute quantities but only with MILNE 's relative-quantities. The time-independence of the HAMILTON ian H = 0 is the FRIEDMANN equation. – This NEWTON ian deduction of the FRIEDMANN equation is more general than the relativistic deduction and than MILNE 's deduction for a NEWTON ian fluid, too. In the general NEWTON ian form H the parameter f M of the active mass can be an arbitrary function of the cosmic time t. The choice f = f(t), M = M(t) defines the divers modifications of relativistic cosmology. – In general relativity fM = const and M = const are resulting from EINSTEIN 's equations and from EINSTEIN 's principle of equivalence.     

Impact origin of the Vesta family

Abstract— The compelling petrographic link (Consolmagno and Drake, 1977; Gaffey, 1983) between basaltic achondrite meteorites and the ～530 km diameter asteroid 4 Vesta has been tempered by a perceived difficulty in launching rocks from this asteroid's surface at speeds sufficient to bring them to Earth (Wasson and Wetherill, 1979) without obliterating Vesta's signature crust. I address this impasse in response to recent imaging (Zellner et al, 1996; Dumas and Hainaut, 1996) of a ～450 km impact basin across Vesta's southern hemisphere (Thomas et al., 1997) and model the basin-forming collision using a detailed two-dimensional hydrocode with brittle fracture including self-gravitational compression (cf., Asphaug and Melosh, 1993). A ～42 km diameter asteroid striking Vesta's basaltic crust (atop a denser mantle and iron core) at 5.4 km/s launches multikilometer fragments up to ～600 m/s without inverting distal stratigraphy, according to the code. This modeling, together with collisional, dynamical, rheological and exposure-age timescales (Marzari et al., 1996; Welten et al., 1996), and observations of V-type asteroids (Binzel and Xu, 1993) suggests a recent (<～1 Ga) impact origin for the Vesta family and a possible Vesta origin for Earth-approaching V-type asteroids (Cruik-shank et al., 1991).     

New Light Curve Analyses for the Eclipsing Binaries u Her and UV Leo

Using WOOD's (1972) model we have analyzed two sets of photoelectric observations as yet unsolved, i.e., ROVITHIS ' and ROVITHIS -LIVANIOU's (1980) B and V light curves of the semi-detached system u Her and BROGLIA's (1961) three-colour observation of the detached system UV Leo. The observations of u Her have yielded solutions in which the secondary's radius exceeds its ROCHE lobe. On the other hand, our new elements of UV Leo confirm the most recent investigations, thus giving for the primary eclipse an unexpected occulatation solution which hardly permits a simple picture of UV Leo.     

NEWTONsche Relativ-Mechanik

The NEWTONian mechanics involves the dynamical absoluteness of motions which means the presence of absolute accelerations in NEWTON's equations of motion. Against NEWTON's point of view HUYGENS (and LEIBNIZ and the young KANT and later MACH and POINCARÉ) have postulated that the dynamics of a closed system of n particles P_a is depending on relative kinematical quantities, only. These relative quantities have to be the differences of the absolute kinematical quantities of each particle P_a according to HUYGENS, KANT and POINCARÉ. — We prove that a closed system of N NEWTONian particles with the same atomic masses m (according to the hypothesis of HERTZ) can be described by a HUYGENsian relative dynamics in the rest system of the center of masses. In this reference system the HAMILTONian, the LAGRANGian, the virial, the angular momentum etc. of the N particle system are depending on the difference quantities, only. — However, the absolute dynamical meaning of motion in the NEWTONian mechanics leads to a paradoxon for this relativistic representation. This paradoxon is resulting by an ideal combination of two independing particle systems to one system in the mind. No such paradoxon is existing by a very modification of NEWTON's dynamics with respect to MACH's principle of the relativity of inertia.     

Das Korrespondenzprinzip in der Kosmologie. II. Klassische und relativistische Darstellungen der Weltmodelle

According to the equivalence between the FRIEDMANN equation of relativistic cosmology and the condition for the time-independence H = o of the HAMILTON ian H of an isotropic particle-system in the NEWTON ian mechanics (which equivalence is proved in the part I of our paper) we construct the corresponding classical HAMILTON ians to the relativistic world-models. Each cosmological model which is resulting from a physically meaningful gravitation theory must give a FRIEDMANN equation as the cosmological formulation of the time-independence condition of the energy H for the corresponding NEWTON ian N-particle system. In general relativity, EINSTEIN's field equations are including EINSTEIN's strong principle of equivalence and are giving the constance f = o and M = o of the gravitation-number f and of the mass M of the universe additional to FRIEDMANN's equation. – In special relativity, we have fM = o and this MILNE -universe is possessing a NEWTON ian and a general relativistic interpretation, too. – However, if the postulate together with the “cosmological principle” other principles about the world structure, too (p. e. MACH'S or DIRAC'S principle or the “perfect cosmological principle” by the steady-state cosmology), then EINSTEIN'S weak principle of equivalence can be fulfilled, only. In these world models the gravity-mass fM becomes a function of the cosmic time t [d/dt(fM) ± o] and this variability of fM is compatible with the constance H = o of the energy H of the NEWTON ian particle-system. For flat three-dimensional cosmological spaces (with H = Ḣ = o) a creation of rest-mass (M > o) is possible. This creation is the pecularity of the steady-state cosmos (with M > o, f = o) and of JORDAN'S cosmos (with M > o, f < o). The MACH -EINSTEIN -doctrine about the perfect determination of the inertia and of the space-time-metric by the cosmic gravitation is founded on the substitution of the NEWTON ian HAMILTON ian by a GAUSS -RIEMANN ian gravitation potential U^*(r_AB' v_AB) (TREDER 1972). Therefore, the FRIEDMANN equation for a universe with MACH'S principle is resulting from the analytical expression of the time-independence of this RIEMANNian potential U* = 0. In the case of such MACH-EINSTEIN's-Universes EINSTEIN'S condition 3fM = c8r between the mass A4 and the radius Y of the universe is valid additional to FRIEDMANN'S equation. For these universes, the EINSTEIN condition determinates the instantaneous value of the gravitation-number f. - The explicite form of the conditions H = o or h' = o gives the equation of motion for the cosmic fundamental particles with attraction and repulsion forces, generally.     

Study of a neutral hydrogen feature previously observed by Cugnon

An anomalous velocity cloud nearl=349°,b=+3°, was investigated by Cugnon (1968). The authors made a new set of observations in order to obtain a more complete picture of the feature, including the region originally out of Cugnon's limit of observation. A comparison with optical and radio observations was made and several possibilities of interpretation as to the nature of the object were analyzed.     

Light‐time effect in the eclipsing binary system AM Leonis

We report four new times of minimum light and the improved ephemeris for the well known contact binary AM Leo. The O‐C diagram, constructed with all reliable timings found in the literature was analyzed and the the light‐time effect in the system was confirmed. We found a periodicity of 44.82 years in the O‐C residuals with an amplitude of 0.0058 day. The periodic curve representing the O‐C values is asymmetric indicating a large eccentricity of 0.73 of the third body orbit. The mass of the third body is found to be 0.175 M_⊙ for the orbital inclination of the eclipsing pair's orbit. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

MINERALOGY,PETROLOGY AND CHEMISTRY OF THE ISNA (C3) METEORITE

A total chemical analysis of the Isna, Egypt, meteorite is similar to analyses for chondrites of type C3, Ornans sub-type; however, comparison with one group of chemical data indicates that Isna is intermediate between the C3(O)'s and C3(V)'s in terms of total Fe. On the basis of atom ratios of Fe, Ca, Al, and Ti to Si, Isna can also be placed into a chemical group which includes types C1 and C2, as well as C3(O). Thin sections show a variety of small, closely-packed chondrules, fragments, and aggregate-like masses in a poorly translucent matrix. Olivine + clinoenstatite inclusions rich in metal and troilite, and olivine-rich inclusions are abundant and show evidence of shock. Ca-Al-Ti-rich inclusions, of probable high-temperature origin, contain olivine, spinel, Ca-rich nepheline, gehlenite, diopside, augite, enstatite, and anorthite. Kamacite and taenite from various occurrences in the meteorite have rather uniform Ni and Co contents, and Ni/Co for kamacite is close to that for several C3(O)'s.     

Experimental laboratory simulation of Titan’s atmosphere: aerosols and gas phase

The discovery that Titan, the largest satellite of Saturn, has an atmosphere and that methane is a significant constituent of it, was the starting point for a systematic study of Titan’s atmospheric organic chemistry. Since then, the results from numerous ground-based observations and two flybys of Titan, by Voyager I and II, have led to experimental laboratory simulation studies and photochemical and physical modeling. All these works have provided a more detailed picture of Titan. We report here a continuation of such a study performing an experimental laboratory simulation of Titan’s atmospheric chemistry, and considering the two physical phases involved: gases and aerosols. Concerning the gaseous phase, we report the first detection of C₄N₂ and we propose possible atmospheric abundances for 70 organic compounds on Titan’s upper atmosphere. Concerning the solid phase, we have characterized aerosol analogues synthesized in conditions close to those of Titan’s environment, using elemental analysis, pyrolysis, solubility studies and infrared spectroscopy.     

On the evaluation of an integral connected with the thermonuclear reaction rate in closed form

The standard expression of the reaction rate for low-energy, nonresonant nuclear reactions in nondegenerate plasma contains a parameter-dependent integral which in all previous calculations with physical or astrophysical background is considered as not capable of being evaluated in a closed form. So one usually resorts to approximation methods concerning large values of the parameter. At first we point out that CONSUL (1964) has given a series representation of the integral which was identified with a MEIJER 's G-function by MATHAI (1971). Next, in view of a physically more exact determination of the reaction rate formula, especially in connection with calculations concerning stellar energy generation, we consider a more general integral containing the mentioned one as special case and give an approximation-free representation by means of MEIJER 's G-function. The G-function so obtained may be conceived as complex-valued continuation of CONSUL 's series representation of a certain class of integrals contained in the considered one. From the series we extract a small parameter approximation of the special integral.     

Photometric Elements of the Eclipsing Binary AZ Vir

Using WOOD 's (1972) model we have analyzed MEINUNGER 's (1977) B and V photoelectric light curves – as yet unsolved–of the W UMa-type eclipsing binary AZ Vir, for which no photometric elements have as yet been determined. Our results describe AZ Vir as a contact pair in which the star eclipsed at the deeper minimum is smaller than its companion. AZ Vir appears to conform to the general properties of the W-type subclass of W UMa systems.     

Magnetic properties of the LL5 ordinary chondrite Chelyabinsk (fall of February 15, 2013)

Here we characterize the magnetic properties of the Chelyabinsk chondrite (LL5, S4, W0) and constrain the composition, concentration, grain size distribution, and mineral fabric of the meteorite's magnetic mineral assemblage. Data were collected from 10 to 1073 K and include measurements of low‐field magnetic susceptibility (χ₀), the anisotropy of χ₀, hysteresis loops, first‐order reversal curves, Mössbauer spectroscopy, and X‐ray microtomography. The REM and REM′ paleointensity protocols suggest that the only magnetizations recorded by the chondrite are components of the Earth's magnetic field acquired during entry into our planet's atmosphere. The Chelyabinsk chondrite consists of light and dark lithologies. Fragments of the light lithology show logχ₀ = 4.57 ± 0.09 (s.d.) (n = 135), while the dark lithology shows 4.65 ± 0.09 (n = 39) (where χ₀ is in 10^?9 m³ kg^?1). Thus, Chelyabinsk is three times more magnetic than the average LL5 fall, but is similar to a subgroup of metal‐rich LL5 chondrites (Paragould, Aldsworth, Bawku, Richmond) and L/LL5 chondrites (Glanerbrug, Knyahinya). The meteorite's room‐temperature magnetization is dominated by multidomain FeNi alloys taenite and kamacite (no tetrataenite is present). However, below approximately 75 K remanence is dominated by chromite. The metal contents of the light and dark lithologies are 3.7 and 4.1 wt%, respectively, and are based on values of saturation magnetization.     

The young open cluster Trumpler 3

We present a photometric and spectroscopic study of the poorly investigated open cluster Trumpler 3. Basic parameters such as the age of 70 ± 10 Myr, the color excess E (B – V) = 0.30 ± 0.02 mag, the distance of 0.69 ± 0.03 kpc and the limiting radius of 12′ were redetermined and compared with previous preliminary studies. The distance of 0.65 ± 0.09 kpc was determined independently by spectral parallaxes. Simultaneously, our analysis allowed us to estimate a total number of members to be N_tot = 570 ± 90 and a total mass of the cluster to be M_tot = 270 ± 40 M_⊙. We also determined a state of cluster's dynamical evolution. We conclude that Trumpler 3 is a young low‐massive stellar ensemble with a typical mass function slope, located near to the outer edge of the Galaxy's Orion Spur. As a result of a wide‐field search for short period variable stars, 24 variables were discovered in the cluster's area. Only one of them – a variable of the γ ‐Dor type – was found to be a likely cluster member (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Eigenschaften singularitätenfreier,statischer, zentralsymmetrischer Lösungen gewisser Gravitationsfeldgleichungen 4. Ordnung

FIEDLER and SCHIMMING (1983) proved that the fourth order gravitational field equations with a linear combination of Bach's and Einstein's tensors on the left-hand side, which were proposed by TREDER , admit static centrally symmetric solutions which are analytical and non-flat in some neighbourhood of the centre of symmetry. The existence of these solutions, known at first only in a small neighbourhood of r = o (r radius), can now be extended to intervals o ≦ r ≦ α with arbitrarily large α , using the abstract theorem on inverse functions. Further it is proved that the Schwarzschild metrics are in a certain sense the only solutions of the above equations that are analytic, asymptotically flat, static and centrally symmetric around r = +∞.     

Imprint of Galactic dynamics on Earth's climate

A connection between climate and the Solar system's motion perpendicular to the Galactic plane during the last 200 Myr years is studied. An imprint of galactic dynamics is found in a long‐term record of the Earth's climate that is consistent with variations in the Solar system oscillation around the Galactic midplane. From small modulations in the oscillation frequency of Earth's climate the following features of the Galaxy along the Solar circle can be determined: 1) the mass distribution, 2) the timing of two spiral arm crossings (31 Myr and 142 Myr) 3) Spiral arm/interarm density ratio (ρ _arm/ρ _interarm ≈ 1.5–1.8), and finally, using current knowledge of spiral arm positions, a pattern speed of Ω_P = 13.6 ± 1.4 km s^–1 kpc^–1 is determined. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Die Asymmetrie der kosmischen Zeit und RIEMANNS Gravitationstheorie1)

RIEMANN himself has considered his formulation of the differential geometry of curved spaces as a first step to a unified geometrical theory of “one ether of gravity, electricity and magnetism”. RIEMANN has pointed out that a fundamental point in such a theory of gravitation has to be the asymmetry of its sources: only positive masses exist. – According to RIEMANN this asymmetry of sources to be coupled with an asymmetry of gravitation field equation against the time-reversion t → - t. Therefore, the gravitation field equation is of the type of a continuity-equation of a velocity field v_i˜g^ikθ _k Φ. RIEMANN 's ether is incompressible in empty space-domains: θ _k (g^1/2v^k) = o. But, in domains with a massdensity σ > o it is θg^1/2/θt = −2 kcσ = − 2 kcg^1/2σ₀ (with a universal constant kc). The matter-density defines depressions of the ether. In a general-relativistic approach RIEMANN 's ansatz means that in empty space-time domains the world-geometry is the purely metrical “RIEMANN ian” geometry. However, in domains with a non-vanishing matter-tensor T_μ^v ≠ o the geometry becomes “non-RIEMANN ian” affine connecting and is of the type of WEYL 's geometry or of the “EINSTEIN -CARTAN theories of gravitation”. Especially, RIEMANN 's field equation for the empty space θ _k ((g^1/2g^ikθ _k Φ) = o. is the EINSTEIN equation (-|g_μv|)^1/2 R₀⁰ = o with g₀₀ = - Φ²c^-4.     

Rings and moons the rings of saturn and jupiter controlled by spacecraft informations and their origin

The two great divisions of the Saturn rings, one of them discovered by the spacecraft observations of 1979, can be explained as narrow zones of meteorites. The new informations by soacecraft encounters raise the probability of a real value of the series 2ⁿ(3–4–5), pointed out by the author in 1928 as approached by the sequence of Saturn's rings and moons. The Titius-Bode-series of planets and a similar series of Jupiter's moons also profit from this support. The author's attempt to explain these correspondences dynamically (first published in Havemann 1978) starts with the assumption of a thin central disk in the preplanetary nebulas. The chance of the Titius-Bode series concerning the sequence of planets is much raised by the result of spacecraft informations that Saturn contains an iron core comparable with that of the Earth. This supports the author's conjecture that iron cores of planets have first formed without envelopes.     

Binary star statistics: the mass ratio distribution for very wide systems

The distribution of mass ratios for a sample of common proper motion (CPM) binaries is determined and compared with that of 798 visual binaries (VB's) studied earlier, in hopes of answering the question: Can the member stars of these systems have been drawn at random from the normal initial mass function for single stars? The observed distributions peak strongly toward q = 1·0 for both kinds of systems, but less strongly for the CPM's than for the VB's. Due allowance having been made for assorted observational selection effects, it seems quite probable that the CPM's represent the observed part of a population drawn at random from the normal IMF, while the VB's are much more difficult to interpret that way and could, perhaps, result from a formation mechanism that somewhat favors systems with roughly equal components.