Die Ablenkung des Lichtes an der Sonne und die Änderung Seiner Geschwindigkeit und Wellenlänge

Zusammenfassung Die Ergebnisse der Radar-Echo-Messungen von I. I. Shapiro, welche auf eine Verringerung der Lichtgeschwindigkeit beim Vorübergang des Lichtes an der Sonne hinweisen, werden zusammen mit der Ablenkung des Lichtes und der Verschiebung seiner Spektrallinien wellentheoretisch erklärt. Es genügt hierzu die Annahme eines materiellen lichtwellentragenden Mediums mit einer Dichte unterhalb des empirischen Vakuums; das Medium muss dann radial zur Sonne eine geringe Inhomogenität besitzen, die in entsprechenden kleinen Zusatzgliedern in den Maxwellschen Gleichungen ihren Ausdruck findet.Auf protophysikalischer Grundlage aufbauend wird die Phasengleichung (22) der an der Sonne vorbeigehenden Lichtwellen unter einfachsten Annahmen abgeleitet und integriert; als Resultat ergeben sich die drei genannten Effekte in Übereinstimmung mit der Erfahrung (Gleichung (39), (44), (47)).

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Shapiro (1968) published the first results of radar-echo-observations on Venus and Mercury in the neighbourhood of upper conjunctions with the Sun; the observations indicate a decrease of the velocity of light passing the Sun. The theory of Soldner is disproved; and the general relativity is in accord with the observed facts. But not this theory alone. In this publication the deflection of light, decrease of the velocity of light, and displacement of spectral-lines are explained with the aid of a wavetheory. Hereby the assumption of a material medium carrying light-waves is sufficient, the density of which is below that of the empirical vacuum; hence, the medium must have a small inhomogeneityh radial to the Sun, and the Maxwell equations contain small additional terms (Equation (3)). They lead to the field equations (4) and (5). The protophysical fundamentals of the wave-theory (6), (8), (9), (10a) lead to the Equations (12) of wave-phase. If we assume that the behaviour of the light passing the Sun is independent (in first approximation) from the wave-form (F), the Equation (22) of wave-phase, is deduced for simple-periodic waves of light. Figure 1 outlines the slope and deflection of the ray of light by the Sun. Section 5 contains the solution of (22); and Section 6 the results. The constant of inhomogeneity =1/210^–5 (of the radius of the Sun) produces a deflection (39) of light passing the Sun. The length of waves of the light approaching the Sun is decreased to a minimum and is increasing with increasing distance from the Sun until the former value ((43) and (44)). The velocity of light approaching the Sun is decreased to a minimum and increases with increasing distance from the Sun to its former value ((46) and (47)).

     

Gravitation und weitreichende schwache Wechselwirkungen bei Neutrino-Feldern Gedanken zu einer Theorie der solaren Neutrinos

The strange non-evidence of the solar-neutrino current by the experiments of DAVIS et al. postulates a fundamental revision of the theory of weak interactions and of its relations to gravitation theory. (We assume that the astrophysical stellar models are not completely wrong.) – Our paper is based on PAULI 's grand hypothesis about the connection between weak and gravitational interactions. According to PAULI and BLACKETT the (dimensionless) gravitation constant is the square of the (dimensionless) FERMI -interaction constant and according to the hypotheses of PAULI, DE BROGLIE , and JORDAN the RIEMANN -EINSTEIN gravitational metric g_ik is fusioned by the four independent WEYL ian neutrino fields (β-neutrinos and β-antineutrinos, μ-neutrinos and μ-antineutrinos). This fusion gives four reference tetrads h_i^A(x^l) as neutrino-current vectors, firstly. Then, the metric g_ik is defined by the equation g_ik = η_AB h_i^Ah_η^B according to EINSTEIN 's theory of tele-parallelism in RIEMANN ian space-times. The relation of the gravitation field theory to FERMI 's theory of weak interactions becomes evident in our reference-tetrads theory of gravitation (TREDER 1967, 1971). – According to this theory the coupling of the gravitation potential h_i^A with the matter T_ιⁱ is given by a potential-like (FERMI -like) interaction term. In this interaction term two WEYL spinor-fields are operating on the matter-tensor, simultanously. Therefore, the gravitation coupling constant is PAULI 's square of the FERMI -constant. Besides of the fusion of the RIEMANN -EINSTEIN metric g_ik by four WEYL spinors we are able to construct a conformal flat metric ĝ_ik = ϕ²η_ik by fusion from each two WEYL spinors. (This hypothesis is in connection with our interpretation of EINSTEIN 's hermitian field theory as a unified field-theory of the gravitational metric g_ik and a WEYL spinor field [TREDER 1972].) Moreover, from the reference-tetrads theory is resulting that the WEYL spinors in the “new metric” ĝ_ik are interacting with the DIRAC matter current by a FERMI -like interaction term and that these WEYL spinors fulfil a wave equation in the vacuum. Therefore, we have a long-range interaction with the radiced gravitational constant \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt {\frac{{tm^2 }}{{hc}}} $\end{document} as a coupling constant. That means, we have a long-range interaction which is 10¹⁸ times stronger than the gravitation interaction. – However, according to the algebraic structure of the conform-flat this long-range interaction is effective for the neutrino currents, only. And for these neutrinos the interaction is giving an EINSTEIN -like redshift of its frequences. The characteristic quantity of this “EINSTEIN shift” is a second gravitation radius â of each body: N = number of baryons, m = mass of a baryon.) This radius â is 10¹⁸ times larger than the EINSTEIN -SCHWARZSCHILD gravitation radius a = fM/c²: But, this big “weak radius” â has a meaning for the neutrinos, only.–The determination of the exterior and of the interior “metrics” ĝ_ik is given by an “ansatz” which is analogous to the ansatz for determination of strong gravitational fields in our tetrads theory. That is by an ansatz which includes the “self-absorption” of the field by the matter. For all celestial bodies the “weak radius” â is much greater than its geometrical dimension. Therefore, a total EINSTEIN redshift of the neutrino frequences v is resulting according to the geometrical meaning of our long-range weak interaction potential ĝ_ik = ϕ²η_ik. That means, the cosmic neutrino radiation becomes very weak and unable for nuclear reactions. Theoretically, our hypothesis means an ansatz for unitary theory of gravitation and of weak interaction. This unitary field theory is firstly based on EINSTEIN 's hermitian field theory and secondly based on our reference-tetrads theory of gravitation.     

Photoelektrische Untersuchungen des Magnetfeldes und der Helligkeit der Am-Sterne 15 Vul und 68 Tau

The Am stars 15 Vul and 68 Tau have been observed photoelectrically in the UBV system and for determination of the longitudinal magnetic field component. Both the stars show periodical variations of the magnitude and the magnetic field. The periods are determined to 14.0 days for 15 Vul and 57.25 days for 68 Tau. The variations of these Am stars are the same as those of typical Ap stars. The star 68 Tau was found to be a spectroscopical binary. The period of the orbital motion is 57.25 days, too. The rotation of the components is synchronous.     

Zum Einfluß eines Quadrupolmoments der Sonne auf die Bahnlage der Planeten

Formulae are derived for the transformation of the secular perturbations of the elements giving the position of the orbit of a planet, produced by a solar quadrupole moment and related to the equator of the Sun, to perturbations related to the ecliptic. For Mercury, Venus, and Earth the numerical values of the coefficients of the transforming equations are given.     

BIANCHI-I-Kosmen der BRANS-DICKE-Theorie für das Vakuum

The field equations of the BRANS -DICKE theory are solved for a vacuum with the aid of a space-time metric of BIANCHI -I-type. Two solutions are found. One of them corresponds to a generalization of the flat de SITTER -universe. On the other side we have obtained the KASNER -like solution on the basis of original the version of BRANS -DICKE theory.     

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.     

Über periodische Bahnen im eingeschränkten Dreikörperproblem und in der Nähe der Kommensurabilitäten vom Typus (k + 1)/k

The authors, collaborating during the winter 1966/67, performed numerical investigations on form and character of periodic solutions of the restricted problem of three bodies in the Sun–Jupiter-System and in the neighbourhood of the resonances of the (k + 1)/k type. The principal part of these computations which were achieved using a fast IBM-computer refers to the cases 2/1 (Hecuba-gap) and 3/2 (Hilda-group). The results gave new insight into the genealogy of periodic orbits in the regions which do not contain solutions of Poincaré's first genre. Moreover, L. Carpenter tried to develop an analytical theory (here not explicitely described) which leads to convergent trigonometric series for the coordinates of periodic orbits with restricted eccentricities, using the method of general perturbations in rectangular coordinates recently published by P. Musen and himself.     

Die multidimensionale Ungleichung von BERNSTEIN und die Abschätzung der Ableitungen des Gravitationspotentials

In different problems of celestial mechanics it is often necessary to estimate the effect of the truncated higher harmonics of the gravity potential on the motion of a test particle. As a rule the magnitude of this effect is strictly connected with the gravitational acceleration, i.e. partials of the potential. But the mathematical theory of attraction gives the estimations for the potential itself. However, as far as the general term of development (spherical harmonic) possesses a definite reserve of the smoothness, we have succeeded in passing from potential estimations to its partials estimations. The mathematical method based on a multidimensional generalization (obtained here) of an inequality by BERNSTEIN is used. By the way several inequalities connecting different norms of spherical harmonics are proved.     

Beobachtungen der Geminiden und Quadrantiden

Geminids and Quadrantids are probably observed for only about 100 years. Due to perturbations of their orbits rapid variations occur. A change in the Geminid rate profile can not be found from observations. Observations of Geminids and Quadrantids from Arbeitskreis Meteore are compared with Perseid results. Around their activity peaks we find an increasing number of bright meteors. At the same time the population index r decreases for Perseids and Quadrantids, while it increases for Geminids. From this behaviour we estimate the increase of the number density to fainter magnitude classes for the three showers.     

Verwendbarkeit des Prismas auf der Korrektionsplatte des Tautenburger Schmidt-Spiegels bei Positionsbestimmungen

To overcome a possible magnitude equation a weakly refracting prism fitted on the correcting plate of the Tautenburg Schmidt telescope was used, forming a secondary image of every object 3.8 mag weaker than the primary one. Because the distances between these two images are not constant, a polynomial was searched which could reflect these variation in dependence on the magnitude of a star and its position on the plate. For each of the 11 plates tested we have got another polynomial, therefore this way to tide over large magnitude differences is unefficient for astrometric investigations.     

Galaxienbewegung und Frühphase des Kosmos

The eigenbewegungen of the galaxies prevent the existence of a radiation universe in the past, if the present mean mass density is larger than the critical value 10⁻³⁰ g/cm³.     

Erste Ergebnisse der Erprobung des photometrischen Zwillingsreflektors

First measurements of the short time variations of Ap stars with the twin telescope show a nonlinear drift caused by a sensibility of the amplifier depending on temperature. Moreover we found a dependence of the impulse rate on the position of the star image in the diaphragm. Special test measurements with a simple incandescent lamp show that this telescope gives results with an accuracy of ± 0.002 mag after elimination of these effects.     

Lichtkurve und Dimensionsbestimmung des Bedeckungssystems W Delphini

Complete light curves in B and V of this semi-detached system observed 1964 in Sicily are given. The primary minimum has been found to be strongly asymmetric whilst it was symmetric in the years near 1900. It is shown that a gas stream suggested already by Struve from spectroscopic observations may account for the photometric peculiarities like the observed ones, if the enlightening of the bright component by particles of the gas stream hitting this star will be considered. From the light curves photometric solutions are calculated and compared with earlier ones. It is shown that the effect of dissimilarity of the shapes of the components may strongly influence the calculated value of the ratio of radii.     

Lichtwechsel und Extinktion des jungen Sterns RR Tauri

Photoelectric UBV observations of RR Tauri show three components of its brightness variations: permanent short-term fluctuations (range≦ 0.2 mag, duration 10¹ days), slow variations of the “maximum brightness” (range 1 mag, duration 10²…10³ days) and unperiodic minima (range≦ 2 mag, duration 20 days). The hypothesis that these minima are produced by clouds of circumstellar condensation products is suggested. From photometry and spectral-type determination of a number of surrounding stars we conclude, that in “maximum brightness” no circumstellar extinction can be detected, provided the spectral type is B9V.     

Astronomische Längen-und Breitendifferenzen der Basisobservatorien Irkutsk,Potsdam und Simeiz (Mitteilungen des Zentralinstituts für Physik der Erde,Nr. 1180)

In 1980/1981 astronomical observations using a carried DANJON -astrolabe were made at Irkutsk, Potsdam and Simeiz stations in order to determine the longitude and latidute differences. — It is informed about the observations made and the analysis of the results obtained. The formulas required for the astronomical longitude and latitude determination are indicated. Subsequent calculation of the weighted mean serves to stepwise condence the values and, at the same time, to examine them for systematic groupe differences and personal errors. Finally the longitude and latitude differences are derived taking into account the observers' personal equations. Their accuracies range from ±0.0020 s to ±0.0028 s and from ±0.013”︁ to ±0.017”︁, respectively. Russian text ingnor     

Vertikalkreis-Beobachtungen der Aberration des Lichtes von Sternen verschiedenen Spektraltyps

Measurements of 9 stars of high declination generally confirm W. BECKER 's relation between the constant of aberration and the spectral type of the stars. The right ascensions and the declinations of the 9 stars are also determined. The relation between aberration and spectral type cannot be explained by atmospheric dispersion. The relation does not affect measurements of trigonometric parallaxes.     

Photometrische und spektrographische Beobachtungen des magnetischen Sterns HD 98088

For the spectroscopic binary HD 98088 with an Ap component UBV photoelectric lightcurves and four Zeeman-spectrograms were obtained in 1971. The results for the radial velocities and effective magnetic fields confirm the phase relations. The lightcurve in U is shifted in phase about 90° relative to the curves in B and U. The U minimum is in coincidence with the positive maximum of the effective magnetic field. The absence of eclipses was confirmed.     

Geometrie der Raum-Zeit der Maßbestimmung von KOTTLER,WEYL und TREFFTZ

The space-time manifold with the metric tensor of KOTTLER , WEYL and TREFFTZ (KWT) is analytically extended for all the three ranges 2m/a ⩽ 2/3^3/2 and the transformations into Kruskal-coordinates are given. The conformal infinity is represented by Penrose-diagrams. Finally embeddings in three-space are shown of surfaces with KWT-metric in cylindrical and spherical coordinates.     

Lebensdauer und Dichte der CO-Ionen im Kometen Morehouse

A photometry of five photographs of Comet Morehouse 1908 III gives a decay constant for CO⁺ ions of γ = 3.5 × 10⁻⁶s⁻¹ (heliocentric distance of the Comet at the time of observation 1.4 A. U.). In a distance from the nucleus of 1.2 × 10⁶ km the average CO⁺ ion density amounts to 130/cm³.