Orbiting frames and satellite attitudes in relativistic astrometry

Space-born measuring devices require an accurate determination of the satellite rest frame. This frame consists of a clock and a triad of orthonormal axes which provide a local Cartesian reference system. The aim of this paper is to find the mathematical representation of this triad in two cases which may correspond to actual satellite attitudes. First we construct a Fermi frame which can be operationally fixed by a set of three mutually orthogonal gyroscopes, then we find a frame which corresponds to the expected attitude of the satellite GAIA which was ESA approved to fly not later than 2012. In the latter case, we were able to find an analytical solution accurate to (v/c)3. In order to exploit this solution in the treatment of GAIA's astrometrical observations, we illustrate all the steps needed to deduce the components of this triad of vectors.