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.     

Bemerkung zur scheinbaren Entfernungsabhängigkeit der HUBBLE-Konstante

The apparent dependence of the HUBBLE constant on the distance observed by LE DENMAT et al. is obviously caused by the luminosity distribution of the ScI galaxies.     

Astrometrische Verwendung der zweiten kurzen Exposition auf Tautenburger Pilotprogrammplatten

To overcome a possible magnitude equation the Tautenburg Schmidt plates of the Lohrmann programme were taken with a long 20-minute exposure (System A) and a short 20-second exposure (System C) displaced about 0·5 minute of arc in declination from the long exposure. The distance between the two images in dependence on the magnitude of a star and its position on the plate was analysed. The transformation of coordinates from system C to A can be performed by using first order polynomials. No higher order terms were found to be necessary. The coefficients of the polynomials can not be assumed as constant for all plates but must be computed from least squares solutions involving a sufficient number of stars on each plate. For three of four plates investigated significant orthogonal linear terms were detected.     

Helligkeitsschätzungen von 12 quasistellaren Objekten auf photographischen Himmelsaufnahmen

Twelve QSO's have been investigated for variability on plates of the “Sonneberger Himmelsüberwachung”. Besides for 3 C 273 and Ton 616 no variability exceeding the mean error (±0.08 mag for m < 17.0) was found. TON 616 shows variability of 0,4 mag on time scales from hours (1964 Apr. 15) to one year.     

Absolute Eigenbewegungen ausgewählter blauer Objekte in der Nähe des galaktischen Nordpols

Es werden absolute Eigenbewegungen von 74 blauen Objekten der Größenklassen 16_μ^m5 bis 19_μ^m5 und von weiteren 28 schwachen Sternen (17_μ^m5) in der Nähe des galaktischen Nordpols angegeben. Die absoluten Eigenbewegungen wurden in Bezug auf 45 Referenzgalaxien als Mittel aus 5 im B-System aufgenommenen Tautenburger Schmidt-Platten bestimmt. Die mittleren Fehler der Eigenbewegung für einen Stern betragen m̄ = 0_˝″0058 und m̄ = 0_˝″0069. Für ein blaues Objekt mit einer B-Helligkeit zwischen 17_m̄^m0 und 18_m̄^m0 erreichen diese Fehler die Werte m̄ = 0_˝″0059 und m̄ = 0_˝″0051, und sie vergrößern sich mit Abnahme der Helligkeit. Für 16 der untersuchten blauen Objekte konnte mit einer Wahrscheinlichkeit von 0.99 die Existenz von Eigenbewegungen nachgewiesen werden. The absolute proper motions of 74 blue objects (from 16_m̄^m5 up to 19_m̄^m5) and 28 additional faint stars (17_m̄^m5) near the galactic north pole are presented. They were derived with reference to 45 galaxies as the mean value from 5 plates taken in the B-system with the Tautenburg Schmidt telescope. The mean errors of the proper motion of a star are equal to m̄ = 0_˝″0058 and m̄ = 0_˝″0069. The errors of a blue object with a B-magnitude between 17_m̄^m0 and 18_m̄^m0 are m̄ = 0_˝″0059 and m̄ = 0_˝″0051 and increase with decreasing brightness. For 16 of the investigated blue objects it was possible to show that proper motions exist with a probability of 0.99.     

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.     

Singularitäten in der Allgemeinen Relativitätstheorie

“Regular solutions of EINSTEIN 's equations” mean very different things. In the case of the empty-space equations, R_ik = 0, such solutions must be metrics g_ik(x^l) without additionaly singular “field sources” (EINSTEIN 's “Particle problem”). – However the “phenomenological matter” is defined by the EINSTEIN equations R_ik – 1/2g_ikR =–xT_ik itselves. Therefore if 10 regular functions g_ik(x^l) are given (which the inequalities of LORENTZ -signature fulfil) then these g_ik define 10 functions T_ik(x^l) without singularities. But, the matter-tensor T_ik must fulfil the two inequalities T ≥ 0, T ≥ 1/2 T only and therefore the EINSTEIN -equations with “phenomenological matter” mean the two inequalities R ≥ 0, R ≤ 0 which are incompatible with a permanently regular metric with LORENTZ -signature, generally.     

Zur dynamischen Äquivalenz der post-NEWTONSCHEN Näherung für die Planetentheorie in der allgemeinen Relativitätstheorie und in der trägheitsfreien Mechanik mit RIEMANNSchem Gravitationspotential

Proof of the dynamical equivalence of the post-NEWTONian approximations for the LAGRANGAIN representations of planetary motions according to GRT and according to our “RIEMANNian dynamics with MACH EINSTEIN doctrine”. Finally, we discuss the equivalence problem for general post-NEWTONian LAGRANGians of the one-body Problem in celestical mechanics.     

Schwache blaue Objekte in der Nähe des galaktischen Nordpols (Umgebung von M 3)

The results of a complete UBV photometry in a field of 3.1 square degrees to the limiting magnitude B = 20.0 are given. The number of blue objects (with U — B ≤ — 0.4) per square degree brighter than magnitude B is given by the relation log N = (0.66 ± 0.08) (B — 18) — 0.04±0.07. The percentage of the blue objects is 2% of the total number of stars brighter than magnitude V = 19.5. It is not distinguished between WD and QSO.     

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     

Empirische Atmosphärenmodelle zur Erklärung des Lichtwechsels magnetischer Sterne

Empirical model atmospheres on the basis of MIHALAS models were investigated. If the temperature of the outer layers in a spot is higher than in the surrounding normal atmosphere and lower than in the deeper layers, many characteristics of the observed amplitude-wavelength relation of magnetic stars can be explained.     

Zur Abschätzung der Zyklenlänge bei langzyklischen U-Geminorum-Sternen

Several methods for estimating very long mean cycle lengths of U Geminorum type variables and the influence of observational gaps are discussed. The well-observed star SW UMa serves as an example for comparing statistical findings with more direct evalutions; the agreement is not bad.     

Koordinateninvariante Erhaltungssätze in der Schwarzschildgeometrie

Einstein's field equations can be written in a special way to give expressions free of any quantities which cannot be measured. These expressions are fully coordinate invariant but observer dependent. Generalized LORENTZ transformations according to TREDER 's theory serve as connecting links between the measured values of different observer systems. The field equations contain expressions for gravitational energy and stresses which satisfy covariant conservation laws.