Physically adequate proper reference system of a test observer and relativistic description of the GAIA attitude

A relativistic definition of the physically adequate proper reference system of a test observer is suggested within the framework of the PPN formalism. According to the nomenclature accepted within the GAIA project this reference system is called Center-of-Mass Reference System (CoMRS). The interrelation between the suggested definition of the CoMRS and the Resolutions 2000 on relativity of the International Astronomical Union (IAU) are elucidated. The tetrad representation of the CoMRS at its origin is also explicated. It is demonstrated how to use that tetrad representation to calculate the relation between the observed direction of a light ray and the corresponding coordinate direction in the Barycentric Celestial Reference System of the IAU. It is argued that the kinematically non-rotating CoMRS is the natural choice of the reference system where the attitude of the observer (e.g. of the GAIA satellite) should be modeled. The relativistic equations of rotational motion of a satellite relative to its CoMRS are briefly discussed. A simple algorithm for the attitude description of the satellite is proposed.Comment: 16 page

Relativistic scaling of astronomical quantities and the system of astronomical units

For relativistic modelling of high-accuracy astronomical data several time scales are used: barycentric and geocentric coordinate times, TCB and TCG, as well as two additional time scales, TDB and TT, that are defined as linear functions of TCB and TCG, respectively. The paper is devoted to a concise but still detailed explanation of the reasons and the implications of the relativistic scalings of astronomical quantities induced by the time scales TDB and TT. We consequently distinguish between quantities and their numerical values expressed in some units. It is argued that the scaled time scales, the scaled spatial coordinates and the scaled masses should be considered as distinct quantities which themselves can be expressed in any units, and not as numerical values of the same quantities expressed in some different, non-SI units (``TDB units'' and ``TT units''). Along the same lines of argumentation the system of astronomical units is discussed in the relativistic framework. The whole freedom in the definitions of the systems of astronomical units for TCB and TDB is demonstrated. A number of possible ways to freeze the freedom are shown and discussed. It is argued that in the future one should think about converting AU into a defined quantity by fixing its value in SI meters

Analysis of astrometric catalogues with vector spherical harmonics

Comparison of stellar catalogues with position and proper motion components using a decomposition on a set of orthogonal vector spherical harmonics. We show the theoretical and practical advantages of this technique as a result of invariance properties and the independence of the decomposition from a prior model. We describe the mathematical principles used to perform the spectral decomposition, evaluate the level of significance of the multipolar components and examine the transformation properties under space rotation. The principles are illustrated with a characterisation of the systematic effects in the FK5 catalogue compared to Hipparcos and with an application to the extraction of the rotation and dipole acceleration in the astrometric solution of QSOs expected from Gaia.Comment: accepted for publication in Astronomy & Astrophysic