The highly elliptical , 16-year-period orbit of the star S2 around the massive black hole candidate Sgr A* is a sensitive probe of the gravitational field in the Galactic centre .
Near pericentre at 120 \mathrm { AU } { \approx } 1400 Schwarzschild radii , the star has an orbital speed of { \approx } 7650 \mathrm { km / s } , such that the first-order effects of Special and General Relativity have now become detectable with current capabilities .
Over the past 26 years , we have monitored the radial velocity and motion on the sky of S2 , mainly with the SINFONI and NACO adaptive optics instruments on the ESO Very Large Telescope , and since 2016 and leading up to the pericentre approach in May 2018 , with the four-telescope interferometric beam-combiner instrument GRAVITY .
From data up to and including pericentre , we robustly detect the combined gravitational redshift and relativistic transverse Doppler effect for S2 of z = \Delta \lambda / \lambda { \approx } 200 \mathrm { km / s } / c with different statistical analysis methods .
When parameterising the post-Newtonian contribution from these effects by a factor f , with f = 0 and f = 1 corresponding to the Newtonian and general relativistic limits , respectively , we find from posterior fitting with different weighting schemes f = 0.90 \pm 0.09 | _ { \mathrm { stat } } \pm 0.15 | _ { \mathrm { sys } } .
The S2 data are inconsistent with pure Newtonian dynamics .