General relativistic satellite astrometry - II. Modeling parallax and proper motion

The non-perturbative general relativistic approach to global astrometry int roduced by de Felice et al. (1998) is here extended to account for the star motions on the Schwarzschild celestial sphere. A new expression of the obs ervables, i.e. angular distances among stars, is provided, which takes into account the effects of parallax and proper motions. This dynamical model i s then tested on an end-to-end simulation of the global astrometry mission GAIA. The results confirm the findings of our earlier work, which applied t o the case of a static (angular coordinates only) sphere. In particular, me asurements of large arcs among stars (each measurement good to similar to 1 00 mu arcsec, as expected for V similar to 17 mag stars) repeated over an o bserving period comparable to the mission lifetime foreseen for GAIA, can b e modeled to yield estimates of positions, parallaxes, and annual proper mo tions good to similar to 15 mu arcsec. This second round of experiments con firms, within the limitations of the simulation and the assumptions of the current relativistic model, that the space-born global astrometry initiated with Hipparcos can be pushed down to the 10(-5) arcsec accuracy level prop osed with the GAIA mission. Finally, the simplified case we have solved can be used as reference for testing the limiting behavior of more realistic m odels as they become available.