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The highly elliptical, 16-year-period orbit of the star S2 around the massiveblack hole candidate Sgr A* is a sensitive probe of the gravitational field inthe Galactic centre. Near pericentre at 120 AU, ~1400 Schwarzschild radii, thestar has an orbital speed of ~7650 km/s, such that the first-order effects ofSpecial and General Relativity have now become detectable with currentcapabilities. Over the past 26 years, we have monitored the radial velocity andmotion on the sky of S2, mainly with the SINFONI and NACO adaptive opticsinstruments on the ESO Very Large Telescope, and since 2016 and leading up tothe pericentre approach in May 2018, with the four-telescope interferometricbeam-combiner instrument GRAVITY. From data up to and including pericentre, werobustly detect the combined gravitational redshift and relativistic transverseDoppler effect for S2 of z ~ 200 km/s / c with different statistical analysismethods. When parameterising the post-Newtonian contribution from these effectsby a factor f, with f = 0 and f = 1 corresponding to the Newtonian and generalrelativistic limits, respectively, we find from posterior fitting withdifferent weighting schemes f = 0.90 +/- 0.09 (stat) +\- 0.15 (sys). The S2data are inconsistent with pure Newtonian dynamics.

Detection of the gravitational redshift in the orbit of the star S2 near the Galactic centre massive black hole