Theoretical expectations for the effect of the Schwarzschild precession on the orbit of the star S2. Here we took the best-fit parameters of the S2 orbit, and computed two model orbits, one for f_SP = 0 (Newton, plus Rømer effect, plus SRT, plus RS), and one for f_SP = 1 (Eq. (C.1)). The grey (2018.38) and blue (2002.34) vertical lines are the pericentre times. We arbitrarily set the precession angle of the SP orbit to 0 during apocentre 2010.35. Top panels: residuals of δvz (left) and δφ (right) between the f_SP = 1 and f_SP = 0 orbits. Bottom panels: same for δRA (left) and δDec (right). Middle panels: vz (left) and φ (right) as a function of time. Here, φ is the position angle of the star on the sky, φ = arctan(RA/Dec), running from 359° when the star is straight north, or north-west of centre, to 180° when it is straight south, to > 0° when it is just north-north east of centre. The most fundamental aspect of the precession is seen in the top right panel as a change in δφ by ≈14′ between two apocentres. Because the precession strongly depends on radius, the precession is very fast around pericentre (2018.38) in a highly elliptical orbit, so that within ≈1 year of pericentre ≈75% of the precession has occurred. To first order, the precession leads to a change in time when the star is found at a given angle φ on the sky, relative to the non-precessing orbit. Because the functional form of φ(t) is close to a step function, the differencing δφ(t) = φ_SP = 1(t)−φ_SP = 0(t) is close to a differentiation dφ/dt, which thus results in a sharp δ-function in the residuals δφ(t) near pericentre. In velocity space a similar effect occurs in the residuals as well, although vz(t) is not as symmetric in t relative to t_peri. Finally in δRA and δDec (bottom panels), the effect of the precession results in a “kink” in the orbit coordinate time slope. Because of the variations in the foreshortening of the RA and Dec coordinates of the apocentre values of the δRA, δDec and δφ the SP = 1 vs. SP = 0 curves vary over time (Fig. B.1). The projected precession on the sky between the apocentres 2010.35 and 2026.5 is ≈14′.