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We compared positions of the Gaia first data release (DR1) secondary data setat its faint limit with CCD positions of stars in 20 fields observed with theVLT/FORS2 camera. The FORS2 position uncertainties are smaller than onemilli-arcsecond (mas) and allowed us to perform an independent verification ofthe DR1 astrometric precision. In the fields that we observed with FORS2, weprojected the Gaia DR1 positions into the CCD plane, performed a polynomial fitbetween the two sets of matching stars, and carried out statistical analyses ofthe residuals in positions. The residual RMS roughly matches the expectationsgiven by the Gaia DR1 uncertainties, where we identified three regimes in termsof Gaia DR1 precision: for G = 17-20 stars we found that the formal DR1position uncertainties of stars with DR1 precisions in the range of 0.5-5 masare underestimated by 63 +/- 5\%, whereas the DR1 uncertainties of stars in therange 7-10 mas are overestimated by a factor of two. For the best-measured andgenerally brighter G = 16-18 stars with DR1 positional uncertainties of <0.5mas, we detected 0.44 +/- 0.13 mas excess noise in the residual RMS, whoseorigin can be in both FORS2 and Gaia DR1. By adopting Gaia DR1 as the absolutereference frame we refined the pixel scale determination of FORS2, leading tominor updates to the parallaxes of 20 ultracool dwarfs that we publishedpreviously. We also updated the FORS2 absolute parallax of the Luhman 16 binarybrown dwarf system to 501.42 +/- 0.11 mas

Gaia and VLT astrometry of faint stars: Precision of Gaia DR1 positions and updated VLT parallaxes of ultracool dwarfs