Abstract
The GRAVITY instrument on the ESO VLTI pioneers the field of high-precision near-infrared interferometry by providing astrometry at the 10-100 mu as 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 R-0 to the Galactic Center that were reported previously.

Abstract
We present K-band interferometric observations of the PDS 70 protoplanets along with their host star using VLTI/GRAVITY. We obtained K-band spectra and 100 mu as precision astrometry of both PDS 70 b and c in two epochs, as well as spatially resolving the hot inner disk around the star. Rejecting unstable orbits, we found a nonzero eccentricity for PDS 70 b of 0.17 0.06, a near-circular orbit for PDS 70 c, and an orbital configuration that is consistent with the planets migrating into a 2:1 mean motion resonance. Enforcing dynamical stability, we obtained a 95% upper limit on the mass of PDS 70 b of 10 M-Jup, while the mass of PDS 70 c was unconstrained. The GRAVITY K-band spectra rules out pure blackbody models for the photospheres of both planets. Instead, the models with the most support from the data are planetary atmospheres that are dusty, but the nature of the dust is unclear. Any circumplanetary dust around these planets is not well constrained by the planets' 1-5 mu m spectral energy distributions (SEDs) and requires longer wavelength data to probe with SED analysis. However with VLTI/GRAVITY, we made the first observations of a circumplanetary environment with sub-astronomical-unit spatial resolution, placing an upper limit of 0.3 au on the size of a bright disk around PDS 70 b.

Abstract
The spin of the supermassive black hole that resides at the Galactic Center can, in principle, be measured by accurate measurements of the orbits of stars that are much closer to Sgr A* than S2, the orbit of which recently provided the measurement of the gravitational redshift and the Schwarzschild precession. The GRAVITY near-infrared interferometric instrument combining the four 8m telescopes of the VLT provides a spatial resolution of 2-4 mas, breaking the confusion barrier for adaptive-optics-assisted imaging with a single 8-10m telescope. We used GRAVITY to observe Sgr A* over a period of six months in 2019 and employed interferometric reconstruction methods developed in radio astronomy to search for faint objects near Sgr A*. This revealed a slowly moving star of magnitude 18.9 in the K-band within 30 mas of Sgr A*. The position and proper motion of the star are consistent with the previously known star S62, which is at a substantially greater physical distance, but in projection passes close to Sgr A*. Observations in August and September 2019 detected S29 easily, with K-magnitude of 16.6, at approximately 130 mas from Sgr A*. The planned upgrades of GRAVITY, and further improvements in the calibration, offer greater chances of finding stars fainter than K-magnitude of 19.

Abstract
Context. T Tauri stars are surrounded by dust and gas disks. As material reservoirs from which matter is accreted onto the central star and planets are built, these protoplanetary disks play a central role in star and planet formation. Aims. We aim at spatially resolving at sub-astronomical unit (sub-au) scales the innermost regions of the protoplanetary disks around a sample of T Tauri stars to better understand their morphology and composition. Methods. Thanks to the sensitivity and the better spatial frequency coverage of the GRAVITY instrument of the Very Large Telescope Interferometer, we extended our homogeneous data set of 27 Herbig stars and collected near-infrared K-band interferometric observations of 17 T Tauri stars, spanning effective temperatures and luminosities in the ranges of similar to 4000-6000 K and similar to 0.4-10 L-circle dot, respectively. We focus on the continuum emission and develop semi-physical geometrical models to fit the interferometric data and search for trends between the properties of the disk and the central star. Results. As for those of their more massive counterparts, the Herbig Ae/Be stars, the best-fit models of the inner rim of the T Tauri disks correspond to wide rings. The GRAVITY measurements extend the radius-luminosity relation toward the smallest luminosities (0.4-10 L-circle dot). As observed previously, in this range of luminosities, the R proportional to L-1/2 trend line is no longer valid, and the K-band sizes measured with GRAVITY appear to be larger than the predicted sizes derived from sublimation radius computation. We do not see a clear correlation between the K-band half-flux radius and the mass accretion rate onto the central star. Besides, having magnetic truncation radii in agreement with the K-band GRAVITY sizes would require magnetic fields as strong as a few kG, which should have been detected, suggesting that accretion is not the main process governing the location of the half-flux radius of the inner dusty disk. The GRAVITY measurements agree with models that take into account the scattered light, which could be as important as thermal emission in the K band for these cool stars. The N-to-K band size ratio may be a proxy for disentangling disks with silicate features in emission from disks with weak and/or in absorption silicate features (i.e., disks with depleted inner regions and/or with large gaps). The GRAVITY data also provide inclinations and position angles of the inner disks. When compared to those of the outer disks derived from ALMA images of nine objects of our sample, we detect clear misalignments between both disks for four objects. Conclusions. The combination of improved data quality with a significant and homogeneous sample of young stellar objects allows us to revisit the pioneering works done on the protoplanetary disks by K-band interferometry and to test inner disk physics such as the inner rim morphology and location.

Abstract
Using VLTI/GRAVITY and SINFONI data, we investigate the subparsec gas and dust structure around the nearby type 1 active galactic nucleus (AGN) hosted by NGC 3783. The K-band coverage of GRAVITY uniquely allows simultaneous analysis of the size and kinematics of the broad line region (BLR), the size and structure of the near-infrared(near-IR)-continuum-emitting hot dust, and the size of the coronal line region (CLR). We find the BLR, probed through broad Br gamma emission, to be well described by a rotating, thick disc with a radial distribution of clouds peaking in the inner region. In our BLR model, the physical mean radius of 16 light-days is nearly twice the ten-day time-lag that would be measured, which closely matches the ten-day time-lag that has been measured by reverberation mapping. We measure a hot dust full-width at half-maximum (FWHM) size of 0.74 mas (0.14 pc) and further reconstruct an image of the hot dust, which reveals a faint (5% of the total flux) offset cloud that we interpret as an accreting or outflowing cloud heated by the central AGN. Finally, we directly measure the FWHM size of the nuclear CLR as traced by the [Ca VIII] and narrow Br gamma line. We find a FWHM size of 2.2 mas (0.4 pc), fully in line with the expectation of the CLR located between the BLR and narrow line region. Combining all of these measurements together with larger scale near-IR integral field unit and mid-IR interferometry data, we are able to comprehensively map the structure and dynamics of gas and dust from 0.01 to 100 pc.

Abstract
Context. 51 Oph is a Herbig Ae/Be star that exhibits strong near-infrared CO ro-vibrational emission at 2.3 mu m, most likely originating in the innermost regions of a circumstellar disc.Aims. We aim to obtain the physical and geometrical properties of the system by spatially resolving the circumstellar environment of the inner gaseous disc.Methods. We used the second-generation Very Large Telescope Interferometer instrument GRAVITY to spatially resolve the continuum and the CO overtone emission. We obtained data over 12 baselines with the auxiliary telescopes and derive visibilities, and the differential and closure phases as a function of wavelength. We used a simple local thermal equilibrium ring model of the CO emission to reproduce the spectrum and CO line displacements.Results. Our interferometric data show that the star is marginally resolved at our spatial resolution, with a radius of similar to 10.58 2.65R(circle dot). The K-band continuum emission from the disc is inclined by 63 degrees +/- 1 degrees, with a position angle of 116 degrees +/- 1 degrees, and 4 +/- 0.8 mas (0.5 +/- 0.1 au) across. The visibilities increase within the CO line emission, indicating that the CO is emitted within the dust-sublimation radius. By modelling the CO bandhead spectrum, we derive that the CO is emitted from a hot (T = 1900-2800 K) and dense (N-CO = (0.9-9) x 10(21) cm(-2)) gas. The analysis of the CO line displacement with respect to the continuum allows us to infer that the CO is emitted from a region 0.10 +/- 0.02 au across, well within the dust-sublimation radius. The inclination and position angle of the CO line emitting region is consistent with that of the dusty disc.Conclusions. Our spatially resolved interferometric observations confirm the CO ro-vibrational emission within the dust-free region of the inner disc. Conventional disc models exclude the presence of CO in the dust-depleted regions of Herbig AeBe stars. Ad hoc models of the innermost disc regions, that can compute the properties of the dust-free inner disc, are therefore required.