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A numerical solution to the Earth's precession in a relativistic framework for a long time span is presented here. We obtain the motion of the solar system in the Barycentric Celestial Reference System by numerical integration with a symplectic integrator. Special Newtonian corrections accounting for tidal dissipation are included in the force model. The part representing Earth's rotation is calculated in the Geocentric Celestial Reference System by integrating the post-Newtonian equations of motion published by Klioner et al. All the main relativistic effects are included following Klioner et al. In particular, we consider several relativistic reference systems with corresponding time scales, scaled constants and parameters. Approximate expressions for Earth's precession in the interval +/- 1 Myr around J2000.0 are provided. In the interval +/- 2000 years around J2000.0, the difference compared to the P03 precession theory is only several arcseconds and the results are consistent with other long-term precession theories.

Present accuracy of satellite laser ranging is at the millimeter level. The current time-delay equation of satellite laser ranging given by International Earth Rotation and Reference Systems Service is in agreement with this accuracy. Prospectively, the accuracy of satellite laser ranging will be improved to sub-millimeter in the future (Pearlman et al. 2007). In this paper, for theoretical interest and applications in future satellite-laser-ranging data processing, we develop a relativistic time-delay model for satellite laser ranging by the time-transfer-function method, and investigate all possible relativistic effects on the light propagation between a station and a satellite. The accuracy of our model arrives at the micrometer ( ${\sim}0.01~\mbox{ps}$ ) level. For achieving such accuracy, only the quadrupole moment of the Earth needs to be taken into account compared with the existing model. This micrometer-level model should be useful in tests of the gravitation theory, high accuracy orbital determination of satellites and geodesy in the future.

This article applies a new scheme of the first post-Newtonian theory (Damour et al., 1991-1994) to the problem of gauge in relativistic reference systems. Choosing and fixing gauge are necessary when the precision of time measurement and application needs to reach the 2PN level (10(-16) or better). We present a general method for fixing the gauges of both the global and local coordinate systems, and for determining the expressions of gravitational potentials and coordinate transformations. The results relevant are consistent with the newest IAU resolutions, therefore they can be applied to astronomical practice.

According to one of the resolutions of the 24th IAU General Assembly, the IAU 2000 precession-nutation model should be adopted from 2003 January 1 on. The one-epoch expressions of seven frequently used precession quantities of the model are given in the IERS Conventions (in 2003). In 2003, Capitaine et al. improved on the model and the improved model is known as the post IAU 2000 precession-nutation model. Based on this work, the two-epoch expressions of the precession quantities in the two models are obtained. When the two-epoch expressions are applied to the coordinate transformation, the accuracies over the years 1800 to 2200 are in accordance with the original models, reaching 1 mas and 1 μ as, respectively. Since the expressions of the precession quantities have the same form as the IAU 1976 precession model except as regards the order of expansion, it provides a convenient tool for practical applications. The results have been applied to the calculation and compilation of the Chinese Astronomical Ephemeris.

Applying the Damour–Soffel–Xu framework of general-relativistic celestial mechanics, the theory of relativistic rigid body presented by Thorne and Gürsel is extended and developed in this paper. We successfully construct a quasi-rigid body model in the full post-Newtonian framework for the first time. This model has some simple properties in a similar way to the Newtonian rigid body, and it could be applied in geodynamics and astronomy, for example, to solve problems on rotation or precession of celestial bodies when relativistic effects are not negligible.

Since 1976 the International Astronomical Union (IAU) has made a series of resolutions on the reference systems and time scales for high precision data processing in the frame- work of general relativity. This article reviews those resolutions that closely relate with the ASTROD project. We give our comments on how to meet the IAU resolutions in the future ASTROD data processing and what kind of works that need to be done further. For example, the self-gravitation terms should be included in the motion equation of the Earth, which is not included in the present DE ephemerides. And the effect of the Sun's figure on the motion of photons should be considered, which is partly neglected in the IAU metric. We also give the metric and the motion equations for both planets and photons in the parameterized post-Newtonian (PPN) formalism. A further improvement of the framework to the second post-Newtonian (2PN) precision would be necessary for the ASTROD project.

With a new theory on the 1PN celestial mechanics recently developed by Damour, Soffel and Xu (1991,1992,1993,1994), definitions and expressions of the 1PN spin angular momentum are investigated and analysed. The total spin angular momentum of a system of extended bodies such as the solar system is calculated and expressed as the function of local parameters and observables under reasonable assumptions, which would find its application in the evolution and dynamics of systems of celestial bodies.

This paper describes a numerical simulation of the rigid rotation of the Moon in a relativistic framework. Following a resolution passed by the International Astronomical Union (IAU) in 2000, we construct a kinematically non-rotating reference system named the Selenocentric Celestial Reference System (SCRS) and give the time transformation between the Selenocentric Coordinate Time (TCS) and Barycentric Coordinate Time (TCB). The post-Newtonian equations of the Moon's rotation are written in the SCRS, and they are integrated numerically. We calculate the correction to the rotation of the Moon due to total relativistic torque which includes post-Newtonian and gravitomagnetic torques as well as geodetic precession. We find two dominant periods associated with this correction: 18.6yr and 80.1 yr. In addition, the precession of the rotating axes caused by fourth-degree and fifth-degree harmonics of the Moon is also analyzed, and we have found that the main periods of this precession are 27.3d, 2.9 yr, 18.6 yr and 80.1 yr.

The Dyson realization of the quantum group SU(1,1)q is constructed and the transformation matrix, which turns the Dyson realization into the Holstein–Primakoff realization, is given. The coherent state for the Dyson realization is discussed and is found to be the q-deformed Weyl–Heisenberg coherent state.

ASTROD I is the first step of ASTROD (Astrodynamical Space Test of Relativity using Optical Devices). This mission concept has one spacecraft carrying a payload of a telescope, five lasers, and a clock together with ground stations (ODSN: Optical Deep Space Network) to test the optical scheme of interferometric and pulse ranging and yet give important scientific results. These scientific results include a better measurement of the relativistic parameters, a better sensitivity in using optical Doppler tracking method for detecting gravitational waves, and measurement of many solar system parameters more precisely. The weight of this spacecraft is estimated to be about 300-350 kg with a payload of about 100-120 kg. The spacecraft is to be launched with initial period about 290 days and to pass by Venus twice to receive gravity-assistance for achieving shorter periods. For a launch on August 4, 2010, after two encounters with Venus, the orbital period can be shortened to 165 days. After about 370 days from launch, the spacecraft will arrive at the other side of the Sun for the determination of relativistic parameters.

In this paper, we construct for the first time, in the first post-Newtonian (1PN) approximation, a complete model of a quasirigid body by means of a new constraint on the mass current density and mass density. In our 1PN quasirigid body model most of the relations, such as the spin vector proportional to the angular velocity, the definition of the moment of inertia tensor, the key relation between the mass quadrupole moment and the moment of inertia tensor, the rigid rotating formulas for the mass quadrupole moment, and the moment of inertia tensor, are just an extension of the main relations in the Newtonian rigid body model. When all of the 1/c(2) terms are neglected, the 1PN quasirigid body model and the corresponding formulas reduce to the Newtonian version. A key relation is obtained in this paper for the first time, which might be very useful in future applications to problems in geodynamics and astronomy.