Differential astrometry with <i>Gaia</i>

In this paper we develop a differential astrometric framework that is appropriate for scanning space satellite such as Gaia. We apply it to the first of GAREQ fields, which fruit dedicated efforts within Gaia project focused on measuring relativistic deflection light close Jupiter's limb. This provides preliminary assessment of: a) observability Jupiter, and, b) Gaia's capabilities under extremely difficult conditions those around bright extended object. Inputs our model are CCD transit times measured by IDU system, transformed field angles via AGIS geometric calibrations, and commanded/nominal spacecraft attitude. [abridged] To illustrate analyze measurements after their calibration through latest cyclic EDR3/DR3 processing event Feb 2017. use observations closest target star successfully observed several in proximity Jupiter surrounding reference stars brighter than G<13 mag transits leading up time approach subsequent transits. The signal detected with S/N 50 at star. combined effect due Sun, mainly dominated monopole, demonstrating scientific performance extreme observational conditions. It an unprecedented detection following reasons: ever limb (~7") optical, highest any wavelength. Finally, work sets stage investigations into disentangling quadrupole future measurements.