ROTATIONAL MOTION OF CELESTIAL BODIES IN THE RELATIVISTIC FRAMEWORK SERGEI A. KLIONER and MICHAEL SOFFEL Lohrmann Observatory, Dresden Technical University, 01062 Dresden, Germany e-mail: klioner(soffel)@rcs.urz.tu-dresden.de There are several important reasons to consider relativistic effects in rotational motion of celestial bodies. General Relativity is now recommended by the Inter- national Astronomical Union and International Union of Geodesy and Geophysics as a theoretical framework for modeling of high-precision observational data. On the other hand, various geodynamical observations provide data which are widely used for testing General Relativity itself. In Newtonian mechanics it is well known how to describe rotational motion of an extended body. In General Relativity this is a rather subtle issue. The concept of a precessing extended rigid body in general relativity encounters fundamental difficulties and cannot be introduced even in the first post-Newtonian approxima- tion. From a practical point of view, however, the rotational motion of the Earth even at the Newtonian level is defined operationally through the time-dependence of geocentric quasi-inertial coordinates of observing sites. An analogous opera- tional definition can be applied in general relativity. To this end, we need a set of physically adequate reference systems. Nowadays there are two well-developed formalisms for the construction of rel- ativistic astronomical reference systems: the Brumberg-Kopeikin formalism (see, e.g., Brumberg, 1991) and the DSX formalism (Damour, Soffel, Xu, 1991, 1992, 1993). The two reference systems needed to model the Earth rotation are the barycentric reference system of the solar system and the local geocentric reference system, where the influence of the external masses reduces to tidal effects. Each reference system is defined by the structure of its metric tensor. In the local geocentric reference system one can derive rotational equations of motion of the extended deformable arbitrarily-shaped Earth, which take the same form as in Newtonian physics where S l is the post-Newtonian spin, and L % is the post-Newtonian tidal torque (Damour, Soffel, Xu, 1993; Klioner, 1996). Eq. (1) is sufficient to discuss precession and nutation of the spin. To consider precession and nutation of the angular velocity and figure axis, we need a relativistic definition of the tensor of inertia and angular velocity. A variety of theoretical approaches (from restricted rigid body models (Soffel, 1994) to relativistic Tisserand-like axes of deformable Earth (Klioner, 1996)) lead to the same post-Newtonian definition of the tensor of inertia C^. The 435 J. Henrard and S. Ferrai-Mello (eds.), Impact of Modern Dynamics in Astronomy, 435-436. © 1999 Kluwer Academic Publishers. Printed in the Netherlands. of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0252921100073048 Downloaded from https://www.cambridge.org/core. IP address: 207.241.231.81, on 29 Apr 2019 at 13:28:26, subject to the Cambridge Core terms