Example orbits of allowed IMBHs in the Galactic Centre. The left panel shows the on-sky orbits of S2 and three IMBH solutions around Sgr A^* (indicated by the cross). The right panels show the time evolution of the RA, Dec, and radial velocity. The solid grey and dashed black curves show the orbit of S2 with and without an IMBH, respectively. The IMBHs are shown in blue and correspond to the parameters given in Table 2. The data points show the last 30 years of observations of S2. The black points correspond to adaptive optics measurements with NACO and early speckle imagery with SHARP. The red points correspond to GRAVITY interferometric measurements. The black and red radial velocity observations correspond, respectively, to SINFONI – KECK and GNIRS spectral measurements of the line-of-sight velocity.