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.     

On the standardization of the selenodetic frame of reference

Strict solving of various selenodetic and astrometric problems is possible in the case when positions of lunar surface points are given in a common system of reference. Such a system can be realised by composing the fundamental catalogue of selenodetic reference points. Principles of establishing a lunar standard frame of reference are discussed.Communication prepared for the conference on Lunar Dynamics and Observational Coordinate Systems held January 15–17, 1973 at the Lunar Science Institute, Houston, Tex. U.S.A.     

On the orientation of ephemeris reference frames

One may construct complete planetary and lunar ephemerides, referred to the equator and dynamical equinox of some epoch, strictly from ranging data alone. Such an ephemeris would be completely independent from any optical data and therefore independent of any stellar catalogue. By using such an ephemeris to then analyse optical observations, one could theoretically derive many of the pertinent features of the catalogue system to which the optical observations are referred. Such features include the equinox offset, equinox motion and systematic proper motion errors. In practice, the optical observations are used in the fitting process, but essentially the same determinations may be made.This paper presents estimates of the equinox offset and equinox motion of the FK4 as determined by the ephemeris fitting process and compares them with corresponding determinations by Fricke. No significant differences are found. Further, it is indicated how one may also estimate a value for precession and the value of the obliquity from the ephemerides. These' values are also compared with the presently adopted ones.     

On the errors and stability of reference frames

The distribution of systematic errors in the coordinates of 1217 extragalactic radio sources included in the latest version of the ICRF2 (International Celestial Reference Frame) reference catalog has been mapped for the first time by processing VLBI observations from international astrometric and geodetic programs spanning the period 1980–2012. These errors are shown to reach ±1.0 mas (milliarcseconds). However, for a sample of 752 sources observed more than 100 times, these errors do not exceed ±0.2 mas, suggesting that ICRF2 is inhomogeneous. In addition, the individual stability of dozens of extragalactic radio sources and ground-based stations included in the latest version of the International Terrestrial Reference Frame, ITRF2005, has been investigated. Significant linear trends and anomalous shifts reaching ±20 µas (microarcseconds) have been detected for many of the sources. Significant systematic shifts have also been found for some of the reference stations. The results obtained stimulate a search for new methods of analyzing VLBI observations and ways of their global adjustment that would provide greater homogeneity and stability of the ICRF and ITRF. This is needed both to increase the accuracy of determining the astrometric, geodetic, and geodynamic parameters derived from these observations and to facilitate their physical interpretation. The work has been performed with the QUASAR multifunction software package developed at the Institute of Applied Astronomy of the Russian Academy of Sciences.     

Relative deformations of selenodetic nets of coordinates

One of the main problems of selenodesy consists of the construction of a net of basic reference points on the surface of the Moon. At present there exist many catalogues containing the coordinates of selected objects on the Moon. These catalogues differ by the presence of both systematic and accidental errors.The investigations concerning the comparison of catalogues and the elucidation of their systematic differences are of very recent date. Various methods of interpretation of the systematic differences between catalogues have been proposed. Without an attempt to encompass the whole problem in what follows, we shall describe one method for comparative study of catalogues based on the theory of the deformation of continuous media.     

The relativistic blackbody spectrum in inertial and non-inertial reference frames

By invoking inverse temperature as a van Kampen-Israel future-directed timelike 4-vector, this paper derives the Relativistic Blackbody Spectrum, the Relativistic Wien's Displacement Law, and the Relativistic Stefan-Boltzmann Law in inertial and non-inertial reference frames.     

Relativistic reference frames including time scales: Questions and answers

The subject of relativistic reference frames in astronomy is discussed with respect to the problems and needs of the various user groups. For didactical reasons the discussion is presented in form of a sequence of questions and answers.     

System of selenodetic coordinates based on heliometric observations of the Moon at Kazan

On the basis of heliometric observations of the Moon carried out by the author between 1969–1975 a system of the coordinates of 32 lunar craters has been set up which is independent of the scale and orientation. The zero point of these coordinates has been fixed by the position of the crater Mösting A in accordance with Koziel (1967a, b; 1970).     

Combination of terrestrial reference frames based on space geodetic techniques in SHAO: methodology and main issues

Based on years of input from the four geodetic techniques(SLR, GPS, VLBI and DORIS),the strategies of the combination were studied in SHAO to generate a new global terrestrial reference frame as the material realization of the ITRS defined in IERS Conventions. The main input includes the time series of weekly solutions(or fortnightly for SLR 1983–1993) of observational data for satellite techniques and session-wise normal equations for VLBI. The set of estimated unknowns includes 3-dimensional Cartesian coordinates at the reference epoch 2005.0 of the stations distributed globally and their rates as well as the time series of consistent Earth Orientation Parameters(EOPs) at the same epochs as the input. Besides the final solution, namely SOL-2, generated by using all the inputs before 2015.0 obtained from short-term observation processing, another reference solution, namely SOL-1, was also computed by using the input before 2009.0 based on the same combination of procedures for the purpose of comparison with ITRF2008 and DTRF2008 and for evaluating the effect of the latest six more years of data on the combined results. The estimated accuracy of the x-component and y-component of the SOL-1 TRF-origin was better than 0.1 mm at epoch 2005.0 and better than 0.3 mm yr~(-1) in time evolution, either compared with ITRF2008 or DTRF2008. However, the z-component of the translation parameters from SOL-1 to ITRF2008 and DTRF2008 were 3.4 mm and –1.0 mm, respectively. It seems that the z-component of the SOL-1 TRF-origin was much closer to the one in DTRF2008 than the one in ITRF2008. The translation parameters from SOL-2 to ITRF2014 were 2.2,-1.8 and 0.9 mm in the x-, y-and z-components respectively with rates smaller than 0.4 mm yr~(-1). Similarly, the scale factor transformed from SOL-1 to DTRF2008 was much smaller than that to ITRF2008. The scale parameter from SOL-2 to ITRF2014 was –0.31 ppb with a rate lower than 0.01 ppb yr~(-1). The external precision(WRMS) compared with IERS EOP 08 C04 of the combined EOP series was smaller than 0.06 mas for the polar motions, smaller than 0.01 ms for the UT1-UTC and smaller than 0.02 ms for the LODs. The precision of the EOPs in SOL-2 was slightly higher than that of SOL-1.     

Ideal frames for perturbed Keplerian motions

Cartan's exterior calculus is used to refer a perturbed Keplerian motion to an ideal frame by means of either the Eulerian parameters or the Eulerian angles, in which case the equations are given a Hamiltonian form. The results are compared with the corresponding systems in the orbital and nodal frames.     

Orientation of the hipparcos frame with respect to the reference frames of the DE403/LE403 and DE405/LE405 ephemerides based on asteroid observations

Highly accurate observations of 116 asteroids are used to determine the orientation of the Hipparcos frame with respect to the reference frames of the DE403/LE403 and DE405/LE405 majorplanet ephemerides. These observations include the photographic observations of 15 asteroids obtained as part of the programs for observing selected asteroids and reduced to the Hipparcos frame using dependences, the space observations of 48 asteroids obtained by the Hipparcos satellite, and the presentday observations of 116 asteroid performed in the frame of the ACT catlog. The total number of observations used is more than 50 000 in the interval 1949–2007. Processing this series has yielded the following estimates of the orientation parameters: ω _x = 0.12 ± 0.08 mas yr^?1, ω _y = 0.66 ± 0.09 mas yr^?1, and ω _z = ?0.56 ± 0.16 mas yr^?1. This rotation may be attributable to a peculiarity of the transition from the reference frame of the DE200/LE200 ephemerides to that of DE403/LE403 ephemerides (since October 1, 1988, to J2000) that consists in the the assumption that the former reference frame has no rotation relative to the ICRF.     

Precision astrometry with SuperCOSMOS

We describe the new, fast, high-precision microdensitometer SuperCOSMOS. Some aspects of hardware and software design that enable high-precision astrometry from photographic plates are explained. We show that the positioning repeatability of the measuring machine is less than 0.1 μ μ m standard error in either coordinate, and the absolute positional accuracy is about 0.15 μ m standard error. Furthermore, measurements of the same plate in different orientations show that the sampling errors are small (e.g. ∼ 0.2 μ m, rising to ∼ 1.0 μ m at the plate limit, for stellar images in a IIIaJ emulsion), thus allowing the extraction of relative positional information from Schmidt plates at accuracies less than 1 μ m. We demonstrate that SuperCOSMOS is capable of measuring the positions of bright stars (i.e. those more than ∼ 4 mag above the plate limit) to a precision ∼ 0.5 μ m with survey–grade photographic plates employing fine–grained emulsions.     

Potential of the VLTI for linking stellar frames to ICRF

The question of positioning the optical counterparts of the ICRF quasars is outlined in the perspective of future space astrometry missions, which ultimately will bring a new realization of the ICRS in the optical range. Ground-based interferometry with a dual-field observing mode (PRIMA/VLTI),together with the missions DIVA and FAME, will have a key role in building an extragalactic reference frame in the optical/near-IR range with about the same accuracy as that of the present (VLBI) primary frame. This revised version was published online in July 2006 with corrections to the Cover Date.     

General covariance,accelarated frames and the particle concept

The definition of particle states in various accelerated frames is considered. It is shown that in any realistically accelerated system, quantum field theory can be formulated without any ambiguity. We further show that the definition of a particle based on Green's function techniques does not always agree with the definition based on explicit quantization. We analyse the standard accelerated detector results from this point of view and show that the uncertainty principle imposes a rigorous bound on these detection processes.     

Precision of diffuse 21-cm lensing

We study the limits of accuracy for weak lensing maps of dark matter using diffuse 21-cm radiation from the pre-reionization epoch using simulations. We improve on previous 'optimal' quadratic lensing estimators by using shear and convergence instead of deflection angles. This is a generalization of the deflection estimator, and is more optimal for non-Gaussian sources. The cross-power spectrum of shear and convergence is an unbiased estimator of lensing power spectrum which does not require knowledge of the source four-point function. We find that non-Gaussianity provides a limit to the accuracy of weak lensing reconstruction, even if instrumental noise is reduced to zero. The best reconstruction result is equivalent to Gaussian sources with effective independent cell of side length  2.0  h ⁻¹ Mpc  . Using a source full map from z = 10 to 20, this limiting sensitivity allows mapping of dark matter at a signal-to-noise ratio greater than 1 out to l ≲ 6000, which is better than any other proposed technique for large-area weak lensing mapping.     

低纬子午环应有的观测精度

本文介绍了在拟定总体设计方案时针对实际需要与可能提出的基本要求 ;对各种误差的测定方法与传统子午环作了比较 ,并且列出了低纬子午环新增加的仪器误差 ;文章根据在仪器较稳定条件下各种误差的测定精度 ,对该仪器的应有观测精度作了估计 ,指出每颗天体位置的单次测定精度不应低于± 0 .1 0″,最后还分析了目前尚未达到应有精度的原因。     

卫星双向定时精度分析

介绍了Compass卫星双向定时的基本原理,在讨论双向定时计算模型的基础上,给出了考虑Sagnac效应项的详细计算模型,并计算了Sagnac效应项在几个代表性地区的影响,结果表明:对于距离中心站较远地区的用户,这种影响可达几十个纳秒。最后,对Compass卫星双向定时理论精度进行了分析,并采用几个地区的试验结果进行了验证。