Polteilchen in der TREDERSchen Tetradentheorie

In the framework of TREDERS ' tetrad theory of gravitation the interaction of pole-particles is considered in post-NEWTON ian approximation. The perihelion shift for the two-body problem is calculated for different matter-field-couplings. In general it depends not only from the sum of the masses but also from the reduced mass. The additional term is connected with the absorption of gravitation.     

Secular Post-NEWTONian Effects for the Restricted Three-Body Problem in TREDER'S Dynamics with Induced Inertia

In the framework of TREDER'S dynamics, in which according to the MACH -EINSTEIN -doctrin the inertial masses are induced by the gravitational interaction with the particles of the cosmos, we calculate the secular post-NEWTON ian effects for the restricted three-body problem. The dominant secular post-NEWTON ian variation of nodes and apsides is shown to be the same as in EINSTEIN'S theory of gravitation. The formulation of the gravodynamics in the HERTZ ian configuration space allows – as in General Relativity – the explanation of the effect as an “geodetic precession” of the lines of nodes and apsides.     

Die post-NEWTONschen Effekte in der Gravodynamik und die EINSTEIN-Effekte in der Allgemeinen Relativitätstheorie

We discuss the post-NEWTON ian effects in our HERTZ ian gravodynamics and compare its values with the EINSTEIN effects in GRT. Generally, our gravodynamics gives quite the same values of the post-NEWTON ian effects in celestial mechanics and in the gravo-optics like in GRT. However, these values are defined by measurement operations which have quite different meanings in gravodynamics and in GRT. P.e., the RIEMANN ian curvature of the three-dimensional space which is resulting in gravodynamics according to the MACH -EINSTEIN doctrine becomes bigger by a factor 3/2 than the curvature resulting by the EINSTEIN equations. — GRT and gravodynamics are congruent in reference to the astronomical fundamental system. This consequence defines the fundamental system according to MACH 's principle.     

On Expanding MACH-EINSTEIN Universes

The “telescopic” gravodynamics of the MACH -EINSTEIN -Doctrine gives expanding “MACH ian clouds” as world models. The universe becomes a closed system (according to the classical statistical mechanics) if and only if the total energy H of this cloud, i.e. its HAMILTON ian, vanishes. This cloud is the MACH ian equivalent to the EINSTEIN-de SITTER universe of general relativity (or of “NEWTON ian cosmology”). However, the MACH ian cloud with H = o describes a linearly expanding universe.     

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.     

Trägheitsfreie Dynamik und HAMILTONsche Bewegungsgleichung

We formulate the canonical equations of motion for particles with an (post-HEWTON ian) interaction potential and the HAMILTON ian form of our MACH ian dynamics without 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.     

Linear perturbations in a universe with a cosmological constant

There is now evidence that the cosmological constant Λ has a non-zero positive value. Alternative scenarios to a pure cosmological constant model are provided by quintessence, an effective negative pressure fluid permeating the Universe. Recent results indicate that the energy density ρ and the pressure p of this fluid are constrained by − ρ ≤ p ≲−0.6 ρ . As p =− ρ is equivalent to the pure cosmological constant model, it is appropriate to analyse this particular, but important, case further.
We study the linear theory of perturbations in a Friedmann–Robertson–Walker universe with a cosmological constant. We obtain the equations for the evolution of the perturbations in the fully relativistic case, for which we analyse the single-fluid and two-fluid cases. We obtain solutions to these equations in appropriate limits. We also study the Newtonian approximation. We find that for a positive cosmological constant universe (i) the perturbations will grow more slowly in the relativistic regime for a two-fluid composed of dark matter and radiation, and (ii) in the Newtonian regime the perturbations stop growing.     

Die Absorption der Schwerkraft und das SEELIGER-YUKAWA-Potential,Akademiker W. A. AMBARZUMJAN zum 65. Geburtstag zugeeignet

In our tetrad-formulation of the gravitation theory a potential-like interaction between the gravitationpotential and the matter-tensor is postulated. In the case of a dust-like matter from this interaction results a screening of the quasi-NEWTON ian potential by the matter-density given by a SEELIGER -YUKAWA -potential with the absorptionconstant approximately. — In the cosmological case from this screening of gravitation a finite effective gravitationradius R of the universe is resulting which radius R is given by the condition for an EINSTEIN -universe 4.     

Empirical Status in Cosmology and the Problem of the Nature of Redshifts

When comparing the results of the cosmological tests obtained by various authors using various methods, it is found that there has not been any trend of convergence in the values obtained for the deceleration parameter q₀, in spite of the accumulated and more accurate data. The empirical data – those on the global and the local cosmological tests and those pointing to the non-existence of cosmic evolutionary effects – can be interpreted in a plausible way in the framework of a static EUCLID ean model. This well reconciles the non-DOPPLER ian nature of redshifts implied by the studies of the redshift phenomenon itself.     

Ion escape at Mars: Comparison of a 3-D hybrid simulation with Mars Express IMA/ASPERA-3 measurements

We have analysed ion escape at Mars by comparing ASPERA-3/Mars Express ion measurements and a 3-D quasi-neutral hybrid model. As Mars Express does not have a magnetometer onboard, the analysed IMA data are from an orbit when the IMF clock angle was possible to determine from the magnetic field measurements of Mars Global Surveyor. We found that fast escaping planetary ions were observed at the place which, according to the 3-D model, is anticipated to contain accelerated heavy ions originating from the martian ionosphere. The direction of the interplanetary magnetic field was found to affect noticeably which regions can be magnetically connected to Mars Express and to the overall 3-D Mars-solar wind interaction.     

Martian fluidized crater distribution: tectonic implications

Little scaled studies on the entire planet Mars, and large scale studies of a local area (3600 km in diameter) seem to indicate geographic relations between martian fiuidized craters and ridges: all the intensely ridged areas exhibit a lot of fluidized craters. Because the presence of fluidized craters indicates low viscosity states of the martial surface, this relation would indicate that the compressive stresses only induced ridges when they occurred at times and places of low viscosity states of the martian surface.     

The amplitude of the opposition effect due to weak localization of photons in discrete disordered media

Weak localization of photons in discrete disordered media is considered as a possible physical mechanism of the opposition effect of some atmosphereless bodies. The amplitude of the opposition effect is calculated by using the rigorousvector multiple-scattering theory and thescalar approximation. It is shown that the scalar approximation can significantly overestimate the amplitude of the opposition effect. Thus, this approximation should not be used in interpreting the observational data, and some previous results obtained with this approximation may require substantial revision.     

A comparison of the anelastic and subseismic approximations for low-frequency gravity modes in stars

A comparative study of the properties of the anelastic and subseismic approximations is presented. The anelastic approximation is commonly used in astrophysics in compressible convection studies, whereas the subseismic approximation comes from geophysics where it is used to describe long-period seismic oscillations propagating in the Earth's outer fluid core. Both approximations aim to filter out the acoustic waves while retaining the density variations of the equilibrium configuration. However, they disagree on the form of the equation of mass conservation. We show here that the anelastic approximation is in fact the only consistent approximation as far as stellar low-frequency oscillations are concerned. We also show that this approximation implies Cowling's approximation which neglects perturbations of the gravity field. Examples are given to demonstrate the efficiency of the anelastic approximation.     

Fine structure of motions in a quiescent prominence

The Ca⁺ K line of the quiescent prominence of 15 October 1969 observed at the Abastumani Astrophysical Observatory of the Academy of Sciences of Georgia, U.S.S.R. is studied in detail. The behaviour of various fragments of the prominence with the line-of-sight Doppler velocities is investigated for different places of the prominence along the spectrum height. Due to superposition of the fragments and the radial velocities a complex non-gaussian profile of the spectral line is formed. Decomposition of the non-gaussian profile into suitable gaussian ones is made with a computer yielding objectivity and high accuracy. The rms error for the intensities in the decomposition is about 5%.It is found that the components into which the Ca⁺ K line decomposes at each level, are traced while proceeding from one photometric section to another throughout the spectral height.A hypothesis on the preferably filamentary structure of the prominence is put forward.     

The range of validity of the Eddington approximation

The Eddington approximation is often assumed to be useful only for optically thick media having a single-scattering albedo near unity. We present detailed evidence in this paper that, for homogeneous layers illuminated by a beam of radiation, the Eddington approximation predicts albedo and absorptivity reasonably well for all values of optical depth and single-scattering albedo, for several scattering phase functions (Rayleigh, Henyey-Greenstein, and Mie) having asymmetry factors less than or equal to $\text{1}\text{2}$. The worst errors are in the neighborhood of optical depth unity and single-scattering albedo 0.5. The Eddington approximation is further found to maintain good accuracy over almost the full range of incident beam directions and surface albedos. It is least accurate for the Mie phase function example, where one can obtain a dramatic improvement in accuracy by going over to the δ-Eddington approximation; this shows that the forward peak of the Mie phase function, and not its detailed shape, is the primary cause of diminished accuracy in the Eddington approximation.     

The boundary-layer flow of a radiating gas by the integral equation method

The flow in the boundary layer of a very hot two-component plasma is analysed when the radiative heat flux is given by the exact integral equation expression. The basic nonlinear integro-differential equation is solved by perturbing it about the differential approximation for radiation. In this way some light is shed on the order of accuracy of the differential approximation of radiation. In fact an error of about 4% may be incurred by invoking the differential approximation.     

Angular distribution of radiation in an isotropically scattering slab

The equation of radiative transfer in an isotropically scattering slab subject to general boundary conditions is solved. The Padé approximation technique is used to calculate the reflected and transmitted angular distributions. Numerical results for angular distributions through and at the boundaries of a finite slab are calculated by the Padé approximation technique. The results for a Padé approximation of [0/1] are compared with results obtained by the Galerkin method.     

2-post-Newtonian approximation of a nonstationary spherically symmetric star in flat space-time theory of gravitation

Starting from a previously stated theory of gravitation in flat space-time the 2-post-Newtonian approximation of a nonstationary spherically symmetric star is derived. The theory forces retarded effects for one part of the solutions of the 2-post-Newtonian approximation. The equations of motion and the conserved total energy of a nonstationary star are given up to 2-post-Newtonian order. The solution in the exterior of the body is studied to this accuracy. Birkhoff's theorem is violated. For the special case of a static spherically symmetric star we get deviations of the exterior solution in the 2-post-Newtonian approximation relative to Einstein's theory.