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

The non-perturbative general relativistic approach to global astrometry introduced 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 observables, i.e. angular distances among stars, is provided, which takes into account the effects of parallax and proper motions. This dynamical model is 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 to the case of a static (angular coordinates only) sphere. In particular, measurements of large arcs among stars (each measurement good to similar to 100 mu arcsec, as expected for V similar to 17 mag stars) repeated over an observing period comparable to the mission lifetime foreseen for GAIA, can be modeled to yield estimates of positions, parallaxes, and annual proper motions good to similar to 15 mu arcsec. This second round of experiments confirms, 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 proposed with the GAIA mission. Finally, the simplified case we have solved can be used as reference for testing the limiting behavior of more realistic models as they become available.