Abstract
We report the time-resolved spectral analysis of a bright near-infrared and moderate X-ray flare of Sgr A(*). We obtained light curves in the M, K, and H bands in the mid- and near-infrared and in the 2 - 8 keV and 2 - 70 keV bands in the X-ray. The observed spectral slope in the near-infrared band is nu L-nu proportional to proportional to nu(0.5 +/- 0.2); the spectral slope observed in the X-ray band is nu L-nu proportional to nu(-0.7 +/- 0.5). Using a fast numerical implementation of a synchrotron sphere with a constant radius, magnetic field, and electron density (i.e., a one-zone model), we tested various synchrotron and synchrotron self-Compton scenarios. The observed near-infrared brightness and X-ray faintness, together with the observed spectral slopes, pose challenges for all models explored. We rule out a scenario in which the near-infrared emission is synchrotron emission and the X-ray emission is synchrotron self-Compton. Two realizations of the one-zone model can explain the observed flare and its temporal correlation: one-zone model in which the near-infrared and X-ray luminosity are produced by synchrotron self-Compton and a model in which the luminosity stems from a cooled synchrotron spectrum. Both models can describe the mean spectral energy distribution (SED) and temporal evolution similarly well. In order to describe the mean SED, both models require specific values of the maximum Lorentz factor gamma(max), which differ by roughly two orders of magnitude. The synchrotron self-Compton model suggests that electrons are accelerated to gamma(max)similar to 500, while cooled synchrotron model requires acceleration up to gamma(max)similar to 5 x 10(4). The synchrotron self-Compton scenario requires electron densities of 10(10) cm(-3) that are much larger than typical ambient densities in the accretion flow. Furthermore, it requires a variation of the particle density that is inconsistent with the average mass-flow rate inferred from polarization measurements and can therefore only be realized in an extraordinary accretion event. In contrast, assuming a source size of 1 R-S, the cooled synchrotron scenario can be realized with densities and magnetic fields comparable with the ambient accretion flow. For both models, the temporal evolution is regulated through the maximum acceleration factor gamma(max), implying that sustained particle acceleration is required to explain at least a part of the temporal evolution of the flare.

Abstract
Sky survey telescopes and powerful targeted telescopes play complementary roles in astronomy. In order to investigate the nature and characteristics of the motions of very faint objects, a flexibly-pointed instrument capable of high astrometric accuracy is an ideal complement to current astrometric surveys and a unique tool for precision astrophysics. Such a space-based mission will push the frontier of precision astrometry from evidence of Earth-mass habitable worlds around the nearest stars, to distant Milky Way objects, and out to the Local Group of galaxies. As we enter the era of the James Webb Space Telescope and the new ground-based, adaptive-optics-enabled giant telescopes, by obtaining these high precision measurements on key objects that Gaia could not reach, a mission that focuses on high precision astrometry science can consolidate our theoretical understanding of the local Universe, enable extrapolation of physical processes to remote redshifts, and derive a much more consistent picture of cosmological evolution and the likely fate of our cosmos. Already several missions have been proposed to address the science case of faint objects in motion using high precision astrometry missions: NEAT proposed for the ESA M3 opportunity, micro-NEAT for the S1 opportunity, and Theia for the M4 and M5 opportunities. Additional new mission configurations adapted with technological innovations could be envisioned to pursue accurate measurements of these extremely small motions. The goal of this White Paper is to address the fundamental science questions that are at stake when we focus on the motions of faint sky objects and to briefly review instrumentation and mission profiles.

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.