Differential astrometric framework for the Jupiter relativistic experiment with Gaia

We employ differential astrometric methods to establish a small field reference frame stable at the microarcsecond (μas) level on short time-scales using high-cadence simulated observations taken by Gaia in 2017 February of a bright star close to the limb of Jupiter, as part of the relativistic experiment on Jupiter's quadrupole. We achieve subμas-level precision along scan through a suitable transformation of the field angles into a small-field tangent plane and a least-squares fit over several overlapping frames for estimating the plate and geometric calibration parameters with tens of reference stars that lie within ∼0.5 deg from the target star, assuming perfect knowledge of stellar proper motions and parallaxes. Furthermore, we study the effects of unmodelled astrometric parameters on the residuals and find that proper motions have a stronger effect than unmodelled parallaxes, e.g. unmodelled Gaia DR2 proper motions introduce extra residuals of ∼23 μas (AL) and 69 μas (AC) versus the ∼5 μas (AL) and 17 μas (AC) due to unmodelled parallaxes. On the other hand, assuming catalogue errors in the proper motions and parallaxes such as those from Gaia DR2 has a minimal impact on the stability introducing subμas and μas level residuals in the along and across scanning direction, respectively. Finally, the effect of a coarse knowledge in the satellite velocity components (with time-dependent errors of 10 μas s-1) is capable of enlarging the size of the residuals to roughly 0.2 mas