Astrometric (left) and spectroscopic (right) 1σ statistical measurement uncertainties of S2 over time. Left panel: almost 100-fold improvement in astrometric precision in RA and Dec, from the early period of speckle imagery with SHARP on the 3.5 m NTT (until 2001), then the AO imagery with NACO on the 8 m VLT (> 2002), and then, since 2016.7, the interferometric astrometry of GRAVITY combining all four 8 m telescopes of the VLT. The grey vertical lines are the two pericentre passages (2002.33 and 2018.38) covered by our data set.