The proper reference frame comoving with a system of mass-points is defined as a general relativistic extension of the relative coordinate system in the Newtonian mechanics. The coordinate transformation connecting this and the background coordinate systems is presented explicitly in the post-Newtonian formalism. The conversion formulas of some physical quantities caused by this coordinate transformation are discussed. The concept of the rotating coordinate system is reexamined within the relativistic framework. A modification of the introduced proper reference frame named the Natural Coordinate System (NCS) is proposed as the basic coordinate system in the astrometry. By means of the concept of the natural coordinate system, the relation between the solar system barycentric coordinate system and the terrestrial coordinate system is given explicitly. To illustrate the concept of NCS, we quote in the following the definition of the non-rotating NCS comoving with the Earth, i.e. the Terrestrial Coordinate System (TCS) (Fukushima et al., 1986a, 1986b):

1) Consider a fictitious spacetime with the metric obtained by subtracting the direct terms due to the Earth from the true metric in the solar system Barycentric Coordinate System (BCS).

2) The time coordinate axis of the TCS is defined as the worldline of the geocenter, i.e. the timelike geodesic of the geocenter in the above ficititious spacetime.

3) The unit of time in the TCS, terrestrial second sT, is defined as the unit of time in the BCS, barycentric second, multiplied by a certain factor so that there exist periodic differences only between the time coordinate of any event in the TCS, i.e. TDT, and the corresponding time coordinate in the BCS, i.e. TDB.

4) The space coordinate axes of the TCS are defined as three geometrically straight lines satisfying that they and the time coordinate axis of the TCS are orthogonal to each other at the geocenter in the above fictitious spacetime, and that the coordinate triad constructed by them is symmetric.

5) The unit of length in the TCS, terrestrial meter mT, is defined as the length so that c = 299792458 mT/sT.

A new realization of the BIH Terrestrial System, using space information (VLBI, LLR, SLR, Doppler), was published in the BIH Annual Report for 1984, under the name BTS 84. Details about the analysis, as well as comparisons between BTS 84 and BTS 85, and between BTS 85 and other individual systems, are presented. A study of origin, scale and orientation characteristics of BTS with regard to other systems is given. Further improvements of the model, taking time-like variations into account, are also outlined.

From a combination of 1) the location of McDonald Observatory from Lunar Laser Ranging, 2) relative station locations obtained from Very Long Baseline Interferometry (VLBI) measurements, and 3) a short tie by traditional geodesy, the geocentric coordinates of the 64 m antennas of the NASA/JPL Deep Space Network are obtained with an orientation which is related to the planetary ephemerides and to the celestial radio reference frame. Comparison with the geocentric positions of the same antennas obtained from tracking of interplanetary spacecraft shows that the two methods agree to 20 cm in distance off the spin axis and in relative longitude. The orientation difference of a 1 meter rotation about the spin axis is consistent with the error introduced into the tracking station locations due to an error in the ephemeris of Jupiter.

In order to obtain coordinate transformations between our CDP-VLBI terrestrial coordinate frame and the corresponding frames used by the Goddard Space Flight Center SLR group, the University of Texas Center for Space Research SLR group, and Deep Space Network, we obtained geocentric, Cartesian coordinates and formal errors of five locations in our system and those of the two SLR groups, and of three locations in our system and that of the Deep Space Network. After transformation we found that both SLR coordinate sets agree at the 20 to 30 mm level with our values. The Deep Space Network values, with higher formal errors than the other sets, agree at the half meter level.

Since 1975, the Defense Mapping Agency (DMA) has been determining polar motion as a byproduct of computing the precise orbits of the Navy Navigation Satellite System (NNSS) satellites. The orbit determination process currently incorporates the NSWC 9Z2 terrestrial reference system and the NWL 10E-1 Earth Gravitational Model (EGM) to degree 28 and order 27. The World Geodetic System 1984 (WGS 84), developed by DMA, will replace the NSWC 9Z2/10E-1 system for NNSS orbit determination. The WGS 84 EGM to degree and order 41 will be utilized. This paper presents the results of two experiments which compared pole positions computed in the two systems. These comparisons indicate that use of WGS 84 improves agreement between pole position values resulting from the Nova-class satellite orbit solutions and the values determined by other modern techniques.

A package of computer programs for the analysis of satellite laser ranging data has been written at the Royal Greenwich Observatory. The methods used are described, and the Earth rotation parameters and station coordinates derived from the MERIT Lageos data are given, with comparisons with other determinations. The uncertainty of the absolute value of the z-coordinate of the stations is discussed, and a method of short-arc analysis for determining baselines is described.

The proposed earth rotation service and the related efforts to monitor the terrestral reference frame will employ instrumental and computational techniques of widely different kinds. It has already been demonstrated that the results produced by these techniques are sensitive to systematic errors occurring at the level of a few millimeters. As a result it will be extremely important to verify the performance of the different systems by making comparative observations at the same sites. Only mobile laser-ranging systems are currently in a position to perform this kind of service. To demonstrate the status of laser ranging during co-location, this paper presents a proposal for a controlled collocation experiment involving U.S. and European stations of the IRIS network.

The earth rotation parameters and coordinates of optical astrometric stations from 1962. O to 1986. O are estimated simultaneously on the assumption that the system of selected standard stations does not rotate. Longitudes and latitudes of the stations are determined every 2 months. Disagreement of the ERPs with those obtained by the space techniques decreased much compared with the published ERPs of the IPMS. It is expected that the ERPs in the whole period are also improved significantly.

Results from Lunar Laser Ranging data analysis are presented: (a) the values and statistics of UT1 determined by three stations are given; (b) the lunar tidal acceleration n is found to be −24.9 ± 1.0 arc sec/century2; (c) the tidal-effect coefficient k/C for UT1 is shown to be in strong agreement with the theoretical value; and (d) corrections to the IAU values of precession and nutation are estimated.

In this paper a comparison is presented between near-real-time earth orientation parameters, produced on-site by the McDonald Laser Ranging System (MLRS) at McDonald Observatory, using observations to the Apollo 15 lunar retroreflector, and those results which are obtained after the fact at the University of Texas at Austin and elsewhere, as well as the results obtained from other techniques. The MLRS data set which is included in this study spans the interval from the commencement of on-site earth orientation solutions at MLRS in February 1985, through the present time, September 1986. This research is supported by the National Aeronautics and Space Administration under Grant NAG5-754 and Contract NAS5-29404 to McDonald Observatory and the University of Texas at Austin from the Goddard Space Flight Center in Greenbelt, Maryland.

Two series of UT1 data determined by VLBI within Project IRIS at 5 day intervals respectively on a daily basis have been subjected to an iterative spectral analysis. Various significant oscillations with periods less than two months could be detected in the IRIS UT1 data. Most of the periods between 18 and 63 days obviously correspond to short-period variations in global atmospheric data. The other significant variations with periods shorter than 35 days can be clearly identified as being due to the influence of zonal tides on the rotation of the earth. The results of the spectral analysis are compared with the theoretical periods and phases and with the amplitudes given by Yoder et al. (1981). The spectral analysis reveals very clearly the monthly (27.6d) and the fortnightly (13.7d) terms and also the smaller variations at 14.77 days and 9.13 days. A similar analysis of 8 subsets, each with two months of the daily UT1 determinations, indicates that the small 7.10 day term can already be extracted from the VLBI observations.

The combined POLARIS-IRIS Earth orientation time series now span nearly a full cycle of the Chandler-annual beat period, beginning in late 1980. Since April 1985 there is also a nearly continuous coverage of UT1 at daily intervals. We have fit a simple model, consisting of circular 14-month and annual components and a linear drift to the polar motion series, then computed the “along-track” and “cross-track” residuals. Both sets of residuals display structure with amplitudes of tens of milliseconds of arc on time scales of months, but Fourier analysis reveals no significant peaks at shorter periods, including the 40-60 day period found in the UT1 time series.

During September, 1986, we introduced a new “quick-look” UT1 time series. The values are typically available within 7 days. The accuracy, which depends strongly on the accuracy of the X and Y pole coordinates used in the computations, ranged from 0.3 to 0.7 milliseconds during the first two weeks, but improved to about 0.1 milliseconds during the latter two weeks of the month. We plan to continue the quick-look UT1 series as a standard product of the IRIS Earth orientation monitoring service.

This study compares the earth orientation results obtained by the NASA CDP and the NGS IRIS experiments. The results agree at about one combined formal error (two milliarcseconds) after small biases (one to three milliarcseconds) have been removed from each component. Furthermore the biases are found to correspond to small rotations between the reference frames, principally the terrestrial frame, for the two sets of experiments. In the past the CDP data has not been used in combined solutions of earth orientation parameters prepared by the data centers at the U.S.N.O. and the B.I.H. The authors propose that these data should be included because they are distinct from the IRIS data and represent an important supplement to those data. We also point out that the total number of observations is about equal in the CDP and IRIS experiment sets.

The first high accuracy VLBI measurements with the Hartebeesthoek Radio Astronomy Observatory (HartRAO) at the southern end of the African tectonic plate were made possible at the beginning of 1986 through the loan of a MARK III DAT to HartRAO by the US National Geodetic Survey. Six twenty-four hour experiments spread over thirty-three days were used to precisely determine the HartRAO station position and to measure baseline lengths to Europe and North America. Interleaved between these multi-station experiments, a single baseline from Wettzell to HartRAO was used for two hours on a daily basis in order to measure pole positions. The formal errors of the x and y pole component determinations for each day are about ±2 mas and ±1 mas respectively, but an offset of about 6 mas from the IRIS values remains to be investigated.

For more than a dozen years, Doppler tracking of the Navy Navigation Satellite System (NNSS) has demonstrated the ability to give solutions for polar motion as a byproduct of precise ephemerides generation. The polar motion estimation process at the Defense Mapping Agency is reviewed and comparisons of the Doppler results with the polar motion series of the newer observational techniques and the Bureau International de l'Heure (BIH) Circular-D are made. This paper extends the analyses and comparisons done during the MERIT Main Campaign for one additional Chandler period.

Radio-interferometric tracking of the Global Positioning System (GPS) satellites offers a new technique for regular monitoring of variations in the earth's rotation. The observations are sensitive to pole position and length-of-day, at a level of precision which may make this technique competitive with satellite and lunar laser ranging and very long baseline interferometry (VLBI). The present limitations are the number of satellites and tracking stations available and inadequate modeling of non-gravitational forces on the satellites. The potential advantages are rapid turn-around and minimal incremental cost. We have performed a preliminary analysis using six days of observations from a four-station network. Comparison of earth rotation values from our GPS analysis with values obtained by VLBI and laser ranging reveals differences after five days of 0.9 ms in UT1, 0.04″ in x and 0.07″ in y. These differences reflect errors in the GPS determinations due primarily to inadequate modeling of non-gravitational forces.

Least-squares collocation is a powerful method for combining interpolation, filtering and parameter determination in one single computational step. We show that the method is applicable to the computation of polar motion values from a very large set of basic observational data. In this study, we use the ILS observations from 1900 to 1978.

We present a set of spectrum analysis techniques described by Thomson (1982) in which the discrete Fourier transform (DFT) is windowed by an expanding set of prolate spheroidal wave functions. The homogeneous ILS polar motion series was chosen for the presentation because of its interesting spectrum. It contains lines at the annual and semi-annual frequencies, a band of uncertain width and structure around Chandler's frequency, and evidence for a 30-year periodicity. None has been measured with great certainty by traditional single-taper DFT spectrum analysis. Here, a multi-taper algorithm significantly improves the bias control and consistency of high-resolution DFT spectrum estimates. An analysis of variance is performed to locate significant harmonic lines, and jackknifed statistics are used as additional cross-checks on the stability of the results. In addition, multi-tapered coherence estimates confirm a previously noted correlation between a meteorological forcing function and a polar motion excitation derived from the ILS series.

It is generally recognised that the Working Group on the Rotation of the Earth that was set up after IAU Symposium No. 82 has successfully achieved its principal objectives, namely: “to make recommendations on … future international services on earth-rotation” and “to obtain and analyse data on earth-rotation by both current and new methods …”. In particular, by organising Project MERIT, it has stimulated the development and use of new techniques and it has brought together in fruitful collaboration scientists from many countries and disciplines. Other subsidiary objectives have also been achieved and the project has been extended through cooperation with the COTES Working Group on the terrestrial reference system. The possible reasons for this success are also reviewed in the expectation that the conclusions will be relevant to other future projects.

Simulation experiments have been performed in order to compare the Earth Rotation Parameter (ERP) results obtained from a) individual observational systems, b) the weighted mean of the results from a), and c) all of the observational data, via the combination of the normal equations obtained in a). These experiments included the use of 15 days of simulated Lunar Laser Ranging (LLR), Satellite Laser Ranging (SLR) to Lageos, and Very Long Baseline Interferometry (VLBI) data using realistic station positions and accuracies. Under the assumptions chosen, the normal equation combination solutions usually provide the best ERP over recovery periods of 6 and 12 hours, and 1, 2, and 5 days. However, solutions by the weighted mean (and even by VLBI alone) provide results that are nearly as good, i.e., within a factor of one to two in accuracy. Complete details are presented in [Archinal, 1987].