Transformation from proper time on Earth to coordinate time in solar system barycentric space-time frame of reference

In order to obtain accurate computed values of Earth-based range and Doppler observables of a beep space probe, an expression is required for the time differencet–, wheret is coordinate time in the solar system barycentric space-time frame of reference and is proper time recorded on a fixed atomic clock on earth. This paper is part 1 of a two-part article which obtains an expression fort– which is suitable for use in obtaining computed values of observations of a spacecraft or celestial body located anywhere in the solar system. The expression can also be used in the computation of Very Long Baseline Interferometry data types. Part 1 obtains an expression fort– which is a function of position and velocity vectors of the major celestial bodies of the solar system and the atomic clock on Earth which reads . In Part 2, this expression will be transformed to a function of time and the Earth-fixed coordinates of the atomic clock.This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under NASA Contract No. NAS 7-100.     

Large-scale collective motion of RFGC galaxies in curved space-time

We consider the large-scale collective motion of flat edge-on spiral galaxies from the Revised Flat Galaxy Catalogue (RFGC) taking into account the curvature of the space-time in the Local Universe at the scale 100h ⁻¹ Mpc. We analyse how the relativistic model of the collective motion should be modified to provide the best possible values of the parameters, the effects that impact these parameters and ways to mitigate them. Evolution of galactic diameters, selection effects, and the difference between isophotal and angular diameter distances are inadequate to explain this impact. At the same time, the measurement error in H i line widths and angular diameters can easily provide such an impact. This is illustrated by a toy model, which allows analytical consideration, and then in the full model using Monte Carlo simulations. The resulting velocity field is very close to that provided by the non-relativistic model of the collective galactic motion. The obtained bulk flow velocity is consistent with the ΛCDM cosmology.     

Why is the space-time curved by gravity?

It is usually regarded that the space-time is curved by gravity, because it is determined by massless spin-2 fields called gravitons. In this Letter it is shown that one must also regard the fact that the gravity is the gauge field of the translation group.     

S-matrix approach to interacting quantum field theory in curved space-time1)

We give an analysis of mutually interacting quantum fields in given unquantized Robertson-Walker universes using an S-matrix approach. Transition probabilities and particle number mean values are discussed in detail with the intention to read off the underlying physics and to apply them to scattering and decay processes.     

Tetrad formulation of the basic equations of type II superconductors in curved space-time

The basic equations of type II superconductors have been obtained by adopting London’s phenomenological approach. The generation of the electromagnetic field in a superconductor at rest in a stationary universe has been investigated using the method of anholonomic frames. The Newtonian formulation of the problem has also been studied. __________ Translated from Astrofizika, Vol. 51, No. 1, pp. 99–107 (February 2008).     

Inertial coordinate systems on the sky

Book review

Inertial coordinate systems on the skySymposium No. 141 of the IAU. Edited by Jay H. Lieske and Victor K. Abalakine, 1990. Kluwer Academic Publishers, 528 pages     

Relations between integrable systems in plane and curved spaces

We consider trajectory isomorphisms between various integrable systems on an n-dimensional sphere S ⁿ and a Euclidean space . Some of the systems are classical integrable problems of Celestial Mechanics in plane and curved spaces. All the systems under consideration have an additional first integral quadratic in momentum and can be integrated analytically by using the separation of variables. We show that some integrable problems in constant curvature spaces are not essentially new from the viewpoint of the theory of integration, and they can be analyzed using known results of classical Celestial Mechanics.     

Rotation of the moon and lunar coordinate systems

The need for precise definition of lunar reference systems is stressed and the principles on which systems of lunar coordinates could be based are established. Differences between coordinate systems defined by the dynamical properties of the lunar configuration and the rotational motion of the lunar globe about its centre of gravity are outlined, and rigorous mathematical formulae relating those systems have been developed. The principles of reduction of measurements are outlined and in the Appendix the absolute coordinates obtained for 700 lunar features are presented.Paper presented to the NATO Advanced Study Institute on Lunar Studies, Patras, Greece, September 1971.     

Cosmological variations in the space-time distribution of absorption systems in quasar spectra

Based on the catalog of Junkkarinen et al. (1991), we analyze the space-time distribution of absorption systems in quasar spectra at cosmological redshifts z=0–3.7. The z distribution of absorbing matter is shown to have a pattern of alternating maxima (peaks) and minima (dips). Within statistical uncertainty, the positions of such peaks and dips do not depend on the direction of observation. We have found a periodicity in the distribution of absorption systems in the functions ln(1+z) and (1+z)^?1/2. We show that the derived sequence of maxima and minima in the space-time distribution of absorbing matter is not a manifestation of the spatial large-scale structure alone, but it is more likely temporal in nature. The most probable source of the putative structure could be an alternation (in the course of cosmological evolution) of pronounced and depressed epochs with a characteristic time interval of 520±160 Myr, depending on the cosmological model chosen.     

The wave equation in a curved space-time: On the consistency of the perturbation expansion about minkowski metric

Eine skalare Wellengleichung wird auf dem Hintergrund eines speziellen Bianchi-Typ-I-Universums, wofür ihre zeitsymmetrische Greensche Funktion exakt angegeben werden kann (NARIAI 1977), betrachtet. Die explizit bekannten Bauelemente dieser Greenschen Funktion werden bis zu einer gewissen Ordnung eines Parameters entwickelt, der die Abweichung der Bianchi-Typ-Metrik von der Minkowskischen markiert. Es wird gezeigt, daß das Resultat mit demjenigen zusammenfällt, das man erhält, wenn man die Bauelemente für die spezielle Bianchi-Typ-I-Metrik nach allgemeinen, durch ein Lorentz-invariantes Störungsverfahren früher (SYNGE 1960, JOHN 1972, 1975) gewonnenen Näherungsformeln in der entsprechenden Ordnung in ε berechnet.     

Post-newtonian gravitational radiation from binary systems in flat space-time theory of gravitation

For a previously studied theory of gravitation in flat space-time a general formula of the gravitational radiation at large distances from a system of bodies is derived. The calculations are carried out through post-Newtonian order within this theory of gravitation. A more explicit formula is given for a binary system. It agrees with the result of general relativity.     

The dependence of the kolmogorov entropy of mappings on coordinate systems

It is now known that the Lyapunov characteristic numbers (LCNs) are a good indicator of stochasticity of mappings or dynamical systems. But the LCNs and the Kolmogorov entropy depend on the norm. In this paper we investigate under what coordinate transformations the LCNs and the Kolmogorov entropy are kept constant and give some numerical examples.     

Zonal comparison of modern selenodetic reference systems

An account is given of the results of a comparison of existing basic selenodetic systems in the equatorial zone of the Moon together with plan and altitude data, which have been provided by means of a specially worked out method, based on the use of the LAC charts of the Moon (scale 1:1000000), and which does not require the presence of common catalogued reference points. It is shown that systematic differences of the form () for different catalogues are, on the whole, relatively small and do not exceed 2. Systematic differences of the form () have a minimum in the region = ± 20° and significantly increase towards the edges of the visible disk, where they may attain a value of 6 between catalogues. Random errors in latitude have on the whole, a similar behaviour in different catalogues, being practically independent of longitude and not exceeding 3. Random errors in longitude significantly increase towards the limb regions in all the studied catalogues, and may reach values of 6 to 8. Author's estimates of the accuracy of absolute heights in selenodetic catalogues is not always sufficiently precise; in certain cases it was found that the accuracy was underestimated by a factor of one and a half. The data on relative heights in the LAC charts are expressed with a vertical step of 300 m, errors in these values are of the order of 250 m for each step in height. As a result of the comparison a set of better points has been obtained forming a catalogue which may be referred to as LPL. The selection was made on the basis of magnitude and character of both the systematic and random errors.     

Formation of a reference coordinate network as a basis for studying the physical parameters of phobos

The national experience of creating a Phobos reference coordinate network based on the Mars Express data, results of studying the libration, and the technology of creating the Digital Terrestrial Model (DTM) with involved structural lines are described. New spheroid parameters for approximating Phobos are derived using the created DTM. All the results are given in comparison with foreign data. The attractive potential is calculated numerically using the created DTM.     

Relativity in astrometry,Celestial mechanics and geodesy

Book review

Relativity in astrometry, Celestial mechanics and geodesySoffel, M. H.: 1989, Springer Verlag, DM 98. (Hardcover) (ISBN 3-540-18906-8)