  In this article we outline the structure of a general relativistic
astrometric model which has been developed to deduce the position and proper
motion of stars from 1-microarcsecond optical observations made by an
astrometric satellite orbiting around the Sun. The basic assumption of our
model is that the Solar System is the only source of gravity, hence we show how
we modeled the satellite observations in a many-body perturbative approach
limiting ourselves to the order of accuracy of $(v/c)^2$. The microarcsecond
observing scenario outlined is that for the GAIA astrometric mission.
