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In this paper we develop a differential astrometric framework that isappropriate for a scanning space satellite such as Gaia. We apply it to thefirst of the GAREQ fields, which is the fruit of dedicated efforts within theGaia project focused on measuring the relativistic deflection of light close toJupiter's limb. This provides a preliminary assessment of: a) the observabilityof the relativistic deflection of light close to Jupiter, and, b) Gaia'sastrometric capabilities under extremely difficult conditions such as thosearound a bright extended object. Inputs to our differential astrometric modelare the CCD transit times as measured by the IDU system, transformed to fieldangles via AGIS geometric calibrations, and the commanded/nominal spacecraftattitude. [abridged] To illustrate the model we analyze Gaia astrometricmeasurements after their calibration through the latest cyclic EDR3/DR3processing of the GAREQ event of Feb 2017. We use observations of the closestbright target star successfully observed several times by Gaia in closeproximity to Jupiter and surrounding reference stars brighter than G<13 mag intransits leading up to the time of closest approach and on subsequent transits.The relativistic deflection signal is detected with a S/N of 50 at closestapproach by the target star. This signal is the combined effect due to Jupiterand the Sun, mainly dominated by Jupiter's monopole, demonstrating Gaia'sscientific performance under extreme observational conditions. It is anunprecedented detection for the following reasons: a) closest ever to Jupiter'slimb (~7") in the optical, and, b) highest S/N at any wavelength. Finally, thiswork sets the stage for investigations into disentangling the relativisticquadrupole deflection due to Jupiter with future Gaia astrometric measurements.

Differential Astrometry with Gaia: Investigating relativistic light deflection close to Jupiter