Modern astrometric techniques lead to large, linear systems solved by the precepts of least-squares. These systems are usually sparse, and one should take advantage of the sparsity to facilitate their solution. As long as the matrix A of the equations of condition possesses the weak Hall property, characteristic of linear systems derived from astrometric reductions, it is possible to find a sparse Cholesky factor. Before the equations of condition are accumulated, by use of the fast Givens transformation, a symbolic factorization of A using Tewarson’s length of intersection technique determines the ordering of the columns of A that result in low fill-in. The non-null elements are stored in a sparse, dynamic data structure by use of dynamic hashing. Numerical experimentation shows that this competes well with alternatives such as nested dissection, and large, but sparse, linear systems with several thousand unknowns can be solved in a reasonable amount of time, even on personal computers.

The operational work of the Interplanetary Solar Stereoscopic Observatory (ISSO) may continue for 11 years. The ISSO Project is designed to insert two spacecraft (SC) into Lagrangian triangular libration points of the “Sun + barycenter (the Earth + the Moon)” system. The Project scientific program consists of two sets of experiments related to solar physics and to dynamical astronomy, respectively.

Various options of the astronomical observation program are possible. We discuss the option where the stereoscopic mode is applied to the direct triangulation observations of the solar system objects with respect to the ICRS coordinate frame.

The stereoscopic mode with the baseline equal to appears to be suitable for receiving the three-dimensional (3-D) measurement series for planets during the ISSO’s lifetime. Extended investigation of the planetary aberration based on the observations of major and minor planets, the direct distance determinations for minor planets and Kuiper’s belt objects, and the new set of star parallaxes may be used for constructing a new fundamental ephemeris and establishing an alternative scale of stellar distances. The accuracy of the angular measurements is expected to attain the milliarcsecond level.

The adoption of the International Celestial Reference System (ICRS) by the IAU in use since 1 January 1998, and the accuracy achieved by the most recent models and observations of Earth rotation call for a redefinition of the Earth Orientation Parameters (EOP). First, the precession-nutation parameters and Greenwich sidereal time, which are currently defined in the FK5 System, have to be re-defined to be consistent with the ICRS. Second, the current definition of the Celestial Ephemeris Pole (CEP) has to be extended in order to be consistent with the most recent models for nutation and polar motion at a microarsecond accuracy including diurnal and sub-diurnal components, as well as with new strategies of observations. Such issues have been under consideration by the subgroup T5 named “Computational Consequences” of the IAU Working Group “ICRS”. This paper gives, as the basis for future recommendations, the preliminary proposals of the subgroup T5 for a modern definition of the CEP, for the definition of more basic EOP in the ICRS and for the choice of a new origin on the equator of the CEP in place of the equinox. Then, the paper emphasizes the use of the Celestial Ephemeris Origin (CEO) which is defined as the “non-rotating origin” in the celestial frame on the equator of the CEP.

We show how the study of variations in orientation of a terrestrial reference system (TRS) in space may be done directly in terms of the motion of the pole of the TRS and rotation around it, and how a separation of these variations into low frequency and high frequency (retrograde and prograde diurnal, semidiurnal, · · · ) bands enables one to characterize and model variations belonging to the various bands and to estimate them simultaneously from observational data by a uniform procedure. Introduction of the Celestial Ephemeris Pole (CEP) or other Celestial Intermediate Pole (IP) is not only unnecessary, but also gives rise to needless debate as to whether variations due to particular causes are to be included in the celestial motion of the IP or in its terrestrial motion, and leaves the question of estimation of high-frequency signals in either frame unresolved. In regard to UT1, we point out that the “correction terms” through which the concept of the nonrotating origin is implemented emerge naturally from fundamental kinematical relations, and use this observation to identify the correction terms to be employed when the Earth orientation parameters are defined in relation to the pole of the TRS rather than an IP.

This paper discusses the short-period terms of nutation which are included in the recent theories of nutation for a rigid Earth. We argue that these terms should be expressed as terrestrial perturbations, that is as polar motion, and describe how such a transformation can be accomplished in practice. Based on the available rigid-Earth amplitudes, we estimate this lunisolar effect in polar motion for an elastic Earth with liquid core, and compare it to the oceanic and atmospheric perturbations at similar frequencies.

High precision astrometry has a long history of making fundamental contributions to geodesy and geophysics extending centuries into the past, and has provided the foundation for many exciting developments in geophysics in the last several decades. In the 1970s, geodetic VLBI and laser ranging provided the first direct measurement of plate tectonic deformation of the crust. These techniques have also revolutionized the study of Earth rotation by providing sufficient precision to measure climate variability, internal structure, and physical properties. Astrometry will continue to be important in a variety of geophysical problems because of its unique ability to determine Earth orientation relative to a stable celestial frame.

Despite the fact that the main causes of the differences between the observed Earth nutation and that derived from analytical calculations come from geophysical effects associated with nonrigidity (core flattening, core-mantle interactions, oceans, etc…), efforts have been made recently to compute the nutation of the Earth when it is considered to be a rigid body, giving birth to several “rigid Earth nutation models.” The reason for these efforts is that any coefficient of nutation for a realistic Earth (including effects due to nonrigidity) is calculated starting from a coefficient for a rigid-Earth model, using a frequency-dependent transfer function. Therefore it is important to achieve high quality in the determination of rigid-Earth nutation coefficients, in order to isolate the nonrigid effects still not well-modeled.

After reviewing various rigid-Earth nutation models which have been established recently and their relative improvement with respect to older ones, we discuss their specifics and their degree of agreement.

The nonrigid Earth nutation series adopted by the IAU (International Astronomical Union) are based on the works of Kinoshita (1977) and Wahr (1979). In the first one, the rigid Earth nutation series were calculated by the application of the Hamiltonian canonical equations to the rotation of the rigid and elliptical Earth. In the second one, the transfer function for the nutations of an elliptical, elastic and oceanless Earth with fluid core and a solid inner core was obtained. The nonrigid Earth nutation coefficients were derived from the convolution between Wahr’s transfer function and Kinoshita’s rigid Earth nutation series.

The improvement in the accuracy of the techniques as a Very Long Baseline (VLBI), Lunar Laser Ranging (LLR) and Global Positioning System (GPS) has led in this decade to the extension of Kinoshita’s theory and more precise determination of Wahr’s transfer function. In the present paper and starting from Kinoshita’s work (1977), we present the different steps carried out, during this last decade, to obtain the sub-microarcsecond rigid Earth nutation series REN 2000 from the Hamiltonian study of the rotation of a rigid Earth (Souchay et al., 1999).

The last precession-nutation model adopted by the IAU (International Astronomical Union) in 1980 is the nutation series built on Wahr’s Earth transfer function for the nutations of an oceanless elastic Earth (Wahr, 1979, 1981), and on Kinoshita’s rigid-Earth precession-nutation series (Kinoshita, 1977; Kinoshita et al., 1979). The resulting precession and nonrigid-Earth nutation series have been used since that time and have been compared with observations. This comparison, which has been done by different teams all-over the world, shows that the theoretical series must be improved to meet observational precision. A Working Group (WG) was set up to examine the possibility of adopting a new nonrigid-Earth nutation series and to study the existing possibilities. On the one hand, the rigid-Earth nutation series have been improved (three new series) and the mutual differences have been shown to be less than a few hundreds of microarcseconds. On the other hand, new Earth transfer functions have been derived based on additional physical considerations within the Earth. The problem with these transfer functions however is that there is no reliable, independent information about the geophysical parameters needed to improve a theoretical model. Instead, the discrepancies with the nutation observations themselves are used to infer those parameters. Recent fits of geophysical parameters to the observed nutations have provided a series that is suitable for practical use, and is also a source of important information on the physics of the Earth’s interior. This paper reviews the recent work of the WG and establishes the reasons and criteria for the choice of the new model ‘IAU 2000’ which is proposed for adoption at the next IAU General Assembly.

The modeling of nutations and precession has advanced to the point where the rms of residuals between theory and the observational estimates from the VLBI data of the past decade is only 0.16 mas in Δψ sin є0 as well as in Δє. Such a fit is provided by the MHB2000 nutation series (Mathews et al., 2000) based on geophysical theory with a few basic Earth parameters estimated by a fit to nutation-precession data, and its accompanying precession rate. A brief account of the series is presented, along with an outline of the theoretical background and of the geophysical information of interest obtained in the process of constructing the series. A series due to Shirai and Fukushima (2000) also gives a somewhat comparable fit to data, improving on the IERS 1996 series, but it is essentially empirical and provides no geophysical insights.

From the analysis of VLBI observational data compiled by USNO (U.S. Naval Observatory) from MJD 44089.994 to 51618.250 (McCarthy, 2000), we showed that a strong peak around –400 sidereal days in the spectrum of its differences from the IERS96 nutation theory could be explained by adding a model Free Core Nutation (FCN) term in the form of a single damped oscillation. Then we developed a new analytical theory of the nonrigid-Earth nutation including the derived FCN model. We adopted RDAN98 (Roosbeek and Dehant, 1998) as the rigid Earth nutation theory. It was convolved with a transfer function using numerical convolution in the time domain (Shirai and Fukushima, 2000). The form of the transfer function was the same as that of Herring (1995). However, its free parameters such as the complex amplitude and frequency of the FCN were readjusted by fitting to the above VLBI data. Even after truncating the forced nutation series so as to contain only 180 terms, the WRMS (Weighted Root Mean Square) of the complex residuals for the new nutation series is 0.312 mas, which is significantly smaller than 0.325 mas, that of the IERS96 nutation theory. As for the FCN term, we estimated its oscillatory period as –430.8±0.6 sidereal days, and its Q-value as 16200 ± 1600. Also we estimated the correction of the precession constants as −0.29297±0.00047”/cy in longitude and −0.02430±0.00019”/cy in obliquity, respectively.

The accuracy of the rigid-Earth solution SMART97 is 2 μas over the time interval (1968, 2023). To obtain a nonrigid-Earth solution, we use the transfer function of Mathews (1999). The perturbations of the third component of the angular velocity vector are taken into account.

Investigations of nonrigid-Earth rotation usually rely on the convolution of a transfer function with a rigid-Earth solution. A possible alternative is to develop a unified theory to encompass in only one body both rigid and nonrigid effects. It is represented in the Hamiltonian theory by Getino and Ferrándiz (GF). This theory combines the convenience of being a really analytical theory with good practical performance, since the residuals with respect to observations are also at the same ±1 mas level as the present IERS series.

We report on more recent results we obtained in the last year, not collected in the “Considerations” paper of the WGN (joint IAU/IUGG Working Group on Nutations).

By integrating the truncated complex scalar gravitational motion equations for an anelastic, rotating, slightly elliptical Earth, the complex frequency dependent Earth transfer functions are computed directly. Unlike the conventional method, the effects of both oceanic loads and tidal currents are included via outer surface boundary conditions, all of which are expanded to second order in ellipticity. A modified ellipticity profile in second order accuracy for the non-hydrostatic Earth is obtained from Clairaut’s equation and the PREM Earth model by adjusting both the ellipticity of the core-mantle boundary and the global dynamical ellipticity to modern observations. The effects of different Earth models, anelastic models, and ocean models are computed and compared. The atmospheric contributions to prograde annual, retrograde annual and retrograde semiannual nutation are also included as oceanic effects. Finally, a complete new nutation series of more than 340 periods, including in-phase and out-of-phase parts of longitude and obliquity terms, for a more realistic Earth, is obtained and compared with other available nutation series and observations.

The most recent solution of Earth orientation parameters from the observations made by optical astrometry in 1899.7-1992.0 at 33 observatories is used to estimate the corrections of the present IAU model of precession-nutation. Since the resolution of the solution is about five days, only the terms with periods of 14 days and longer are considered. The results are compared with VLBI-based corrections of the standard precession-nutation model, and the differences are discussed.

The currently adopted strategy of EOP estimation from VLBI is to estimate six parameters: UT1, UT1 rate, pole positions and nutation offsets for each 24-hour session independently. Then the resulting time series of raw Earth orientation parameters are filtered and a regression analysis is performed in order to obtain nutation coefficients, polhode of the pole and other physical parameters. Thus, the latter parameters are obtained indirectly in two stages. An alternative approach of direct estimation of the final Earth orientation parameters is presented. Pole coordinates and UT1 are considered as a sum of three components: the low-period component which is modeled by a cubic spline, the harmonic component which includes forced nutation, precession and sub-daily variations of EOP, and the stochastic component which is modeled by a linear spline with segment length 1-2 hours. All parameters are obtained in a single LSQ solution using all available data.

Very Long Baseline Interferometry (VLBI) provides information about the Earth’s rotation. Various observational programs have operated for different specific purposes since 1983. The purpose of the NEOS-Intensive program is to make observations of Universal Time (UT1–UTC). Short observational sessions (1-2 hours) include only the transcontinental baseline (Wettzell - NRAO20). 20–30 individual scans are performed during the observational time. Only five parameters, wet delay for the reference station, wet delay for the second station, clock offset for the second station, clock rate for the second station, and UT1–UTC are considered in the parametric model.

The purpose of this paper is to investigate the influence of the adopted nutation model on the UT1–UTC estimates. VLBI data from the NEOS-Intensives have been analyzed using the OCCAM 3.4 software. All reduction calculations are in accordance with the IERS Conventions 1996 (McCarthy, 1996).

After a short introduction into experimental foundations of general relativity, an overview of modern relativistic modelling of astronomical observations is given. The principal relativistic effects in various kind of observations are reviewed, and the problems for increasing accuracy of the astrometric catalogs due to general relativity are formulated.

The BIPM/IAU Joint Committee on relativity for space-time reference systems and metrology (JCR) has worked in collaboration with the IAU Working Group on relativity for celestial mechanics and astrometry (RCMA) on the problems of astronomical relativistic space-time reference frames and the RCMA has proposed to the IAU a consistent framework for defining the barycentric and geocentric celestial reference systems at the first post-Newtonian level. Because new clock technology and space missions will necessitate the application of this framework for time and frequency measurements in the solar system, practical resolutions are proposed by the JCR to the IAU to allow a consistent treatment of these measurements. The paper outlines the conclusions of the work which resulted in the proposed IAU resolutions.