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 AU ≈ 1400 Schwarzschild radii, the star has an orbital speed of ≈7650 km s⁻¹, 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 ofz= Δλ/λ≈ 200 km s⁻¹/cwith different statistical analysis methods. When parameterising the post-Newtonian contribution from these effects by a factorf, withf= 0 andf= 1 corresponding to the Newtonian and general relativistic limits, respectively, we find from posterior fitting with different weighting schemesf= 0.90 ± 0.09|_stat± 0.15|_sys. The S2 data are inconsistent with pure Newtonian dynamics.

We present a 0.16% precise and 0.27% accurate determination of R₀, the distance to the Galactic center. Our measurement uses the star S2 on its 16-year orbit around the massive black hole Sgr A* that we followed astrometrically and spectroscopically for 27 years. Since 2017, we added near-infrared interferometry with the VLTI beam combiner GRAVITY, yielding a direct measurement of the separation vector between S2 and Sgr A* with an accuracy as good as 20 μas in the best cases. S2 passed the pericenter of its highly eccentric orbit in May 2018, and we followed the passage with dense sampling throughout the year. Together with our spectroscopy, in the best cases with an error of 7 km s⁻¹, this yields a geometric distance estimate of R₀ = 8178 ± 13_stat. ± 22_sys. pc. This work updates our previous publication, in which we reported the first detection of the gravitational redshift in the S2 data. The redshift term is now detected with a significance level of 20σ with f_redshift = 1.04 ± 0.05.

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 Letter 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 ≈±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_SP for the SP (f_SP = 0 for Newton and 1 for GR). From data up to the end of 2019 we robustly detect the SP of S2, δϕ ≈ 12′ per orbital period. From posterior fitting and MCMC Bayesian analysis with different weighting schemes and bootstrapping we find f_SP = 1.10 ± 0.19. The S2 data are fully consistent with GR. Any extended mass inside S2’s orbit cannot exceed ≈0.1% of the central mass. Any compact third mass inside the central arcsecond must be less than about 1000 M_⊙.

GRAVITY is a new instrument to coherently combine the light of the European Southern Observatory Very Large Telescope Interferometer to form a telescope with an equivalent 130 m diameter angular resolution and a collecting area of 200 m². The instrument comprises fiber fed integrated optics beam combination, high resolution spectroscopy, built-in beam analysis and control, near-infrared wavefront sensing, phase-tracking, dual-beam operation, and laser metrology. GRAVITY opens up to optical/infrared interferometry the techniques of phase referenced imaging and narrow angle astrometry, in many aspects following the concepts of radio interferometry. This article gives an overview of GRAVITY and reports on the performance and the first astronomical observations during commissioning in 2015/16. We demonstrate phase-tracking on stars as faint asm_K≈ 10 mag, phase-referenced interferometry of objects fainter thanm_K≈ 15 mag with a limiting magnitude ofm_K≈ 17 mag, minute long coherent integrations, a visibility accuracy of better than 0.25%, and spectro-differential phase and closure phase accuracy better than 0.5°, corresponding to a differential astrometric precision of better than ten microarcseconds (μas). The dual-beam astrometry, measuring the phase difference of two objects with laser metrology, is still under commissioning. First observations show residuals as low as 50μas when following objects over several months. We illustrate the instrument performance with the observations of archetypical objects for the different instrument modes. Examples include the Galactic center supermassive black hole and its fast orbiting star S2 for phase referenced dual-beam observations and infrared wavefront sensing, the high mass X-ray binary BP Cru and the active galactic nucleus of PDS 456 for a fewμas spectro-differential astrometry, the T Tauri star S CrA for a spectro-differential visibility analysis,ξ Tel and 24 Cap for high accuracy visibility observations, andηCar for interferometric imaging with GRAVITY.

The GRAVITY instrument on the ESO VLTI pioneers the field of high-precision near-infrared interferometry by providing astrometry at the 10−100 μas level. Measurements at this high precision crucially depend on the control of systematic effects. We investigate how aberrations introduced by small optical imperfections along the path from the telescope to the detector affect the astrometry. We develop an analytical model that describes the effect of these aberrations on the measurement of complex visibilities. Our formalism accounts for pupil-plane and focal-plane aberrations, as well as for the interplay between static and turbulent aberrations, and it successfully reproduces calibration measurements of a binary star. The Galactic Center observations with GRAVITY in 2017 and 2018, when both Sgr A* and the star S2 were targeted in a single fiber pointing, are affected by these aberrations at a level lower than 0.5 mas. Removal of these effects brings the measurement in harmony with the dual-beam observations of 2019 and 2020, which are not affected by these aberrations. This also resolves the small systematic discrepancies between the derived distance R₀ to the Galactic Center that were reported previously.