The star S2 orbiting the compact radio source Sgr A* is a precision probe of the gravitational field around the closest massive black hole ( candidate ) .
Over the last 2.7 decades we have monitored the star ’ s radial velocity and motion on the sky , mainly with the SINFONI and NACO adaptive optics ( AO ) instruments on the ESO VLT , and since 2017 , with the four-telescope interferometric beam combiner instrument GRAVITY .
In this paper we report the first detection of the General Relativity ( GR ) Schwarzschild Precession ( SP ) in S2 ’ s orbit .
Owing to its highly elliptical orbit ( e = 0.88 ) , S2 ’ s SP is mainly a kink between the pre-and post-pericentre directions of motion \approx \pm 1 year around pericentre passage , relative to the corresponding Kepler orbit .
The superb 2017-2019 astrometry of GRAVITY defines the pericentre passage and outgoing direction .
The incoming direction is anchored by 118 NACO-AO measurements of S2 ’ s position in the infrared reference frame , with an additional 75 direct measurements of the S2-Sgr A* separation during bright states ( ‘ flares ’ ) of Sgr A* .
Our 14-parameter model fits for the distance , central mass , the position and motion of the reference frame of the AO astrometry relative to the mass , the six parameters of the orbit , as well as a dimensionless parameter f _ { \mathrm { SP } } for the SP ( f _ { \mathrm { SP } } = 0 for Newton and 1 for GR ) .
From data up to the end of 2019 we robustly detect the SP of S2 , \delta \phi \approx 12 ^ { \prime } per orbital period .
From posterior fitting and MCMC Bayesian analysis with different weighting schemes and bootstrapping we find f _ { \mathrm { SP } } = 1.10 \pm 0.19 .
The S2 data are fully consistent with GR .
Any extended mass inside S2 ’ s orbit can not exceed \approx 0.1 % of the central mass .
Any compact third mass inside the central arcsecond must be less than about 1000 M _ { \odot } .