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Register a new userDifferential Astrometric Framework for the Jupiter Relativistic Experiment with Gaia
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Authors
Ummi Abbas
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We employ differential astrometric methods to establish a small field reference frame stable at the micro-arcsecond ($mu$as) level on short timescales using high-cadence simulated observations taken by Gaia in February 2017 of a bright star close to the limb of Jupiter, as part of the relativistic experiment on Jupiters quadrupole. We achieve sub$mu$as-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 $sim$0.5 degs from the target star, assuming perfect knowledge of stellar proper motions and parallaxes. Furthermore, we study the effects of unmodeled astrometric parameters on the residuals and find that proper motions have a stronger effect than unmodeled parallaxes. For e.g., unmodeled Gaia DR2 proper motions introduce extra residuals of $sim$23$mu$as (AL) and 69$mu$as (AC) versus the $sim$5$mu$as (AL) and 17$mu$as (AC) due to unmodeled parallaxes. On the other hand, assuming catalog errors in the proper motions such as those from Gaia DR2 has a minimal impact on the stability introducing sub$mu$as and $mu$as 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$mu$as) is capable of enlarging the size of the residuals to roughly 0.2 mas.
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A tool for representation of the one-dimensional astrometric signal of Gaia is described and investigated in terms of fit discrepancy and astrometric performance with respect to number of parameters required. The proposed basis function is based on the aberration free response of the ideal telescope and its derivatives, weighted by the source spectral distribution. The influence of relative position of the detector pixel array with respect to the optical image is analysed, as well as the variation induced by the source spectral emission. The number of parameters required for micro-arcsec level consistency of the reconstructed function with the detected signal is found to be 11. Some considerations are devoted to the issue of calibration of the instrument response representation, taking into account the relevant aspects of source spectrum and focal plane sampling. Additional investigations and other applications are also suggested.
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