Abstract
Context. The formation and evolution of planetary systems impact the evolution of the primordial accretion disk in its dust and gas content. HD 141569 is a peculiar object in this context as it is the only known pre-main sequence star characterized by a hybrid disk. Observations with 8 m class telescopes probed the outer-disk structure showing a complex system of multiple rings and outer spirals. Furthermore, interferometric observations attempted to characterize its inner 5 au region, but derived limited constraints. Aims. The goal of this work was to explore with new high-resolution interferometric observations the geometry, properties, and dynamics of the dust and gas in the internal regions of HD 141569. Methods. We observed HD 141569 on milliarcsecond scales with GRAVITY/VLTI in the near-infrared (IR) at low (R similar to 20) and high (R similar to 4000) spectral resolution. We interpreted the interferometric visibilities and spectral energy distribution with geometrical models and through radiative transfer techniques using the code MCMax to constrain the dust emission. We analyzed the high spectral resolution quantities (visibilities and differential phases) to investigate the properties of the Brackett-gamma (Br gamma) line emitting region. Results. Thanks to the combination of three different epochs, GRAVITY resolves the inner dusty disk in the K band with squared visibilities down to V-2 similar to 0.8. A differential phase signal is also detected in the region of the Br gamma line along most of the six baselines. Data modeling shows that an IR excess of about 6% is spatially resolved and that the origin of this emission is confined in a ring of material located at a radius of similar to 1 au from the star with a width less than or similar to 0.3 au. The MCMax modeling suggests that this emission could originate from a small amount (1.4 x 10(-8) M-circle plus) of quantum-heated particles, while large silicate grain models cannot reproduce at the same time the observational constraints on the properties of near-IR and mid-IR fluxes. The high spectral resolution differential phases in the Br gamma line clearly show an S-shape that can be best reproduced with a gaseous disk in Keplerian rotation, confined within 0.09 au (or 12.9 R-star). This is also hinted at by the double-peaked Br gamma emission line shape, known from previous observations and confirmed by GRAVITY. The modeling of the continuum and gas emission shows that the inclination and position angle of these two components are consistent with a system showing relatively coplanar rings on all scales. Conclusions. With a new and unique observational dataset on HD 141569, we show that the complex disk of this source is composed of a multitude of rings on all scales. This aspect makes HD 141569 a potentially unique source to investigate planet formation and disk evolution in intermediate-mass pre-main sequence stars.

Abstract
Context. GCIRS 7, the brightest star in the Galactic central parsec, formed 6 2 Myr ago together with dozens of massive stars in a disk orbiting the central black-hole. It has been argued that GCIRS 7 is a pulsating body, on the basis of photometric variability.Aims. Our goal is to confirm photospheric pulsations based on interferometric size measurements to better understand how the mass loss from these massive stars enriches the local interstellar medium.Methods. We present the first medium-resolution (R = 500), K-band spectro-interferometric observations of GCIRS 7, using the GRAVITY instrument with the four auxiliary telescopes of the ESO VLTI. We looked for variations using two epochs, namely 2017 and 2019.Results. We find GCIRS 7 to be moderately resolved with a uniform-disk photospheric diameter of theta (*)(UD)=1.55 +/- 0.03 theta UD*=1.55 +/- 0.03 mas ( R-UD(*)=1368 +/- 26 RUD*=1368 +/- 26 R-circle dot) in the K-band continuum. The narrow-band uniform-disk diameter increases above 2.3 mu m, with a clear correlation with the CO band heads in the spectrum. This correlation is aptly modeled by a hot (T-L = 2368 +/- 37 K), geometrically thin molecular shell with a diameter of theta (L) = 1.74 +/- 0.03 mas, as measured in 2017. The shell diameter increased (theta (L) = 1.89 +/- 0.03 mas), while its temperature decreased (T-L = 2140 +/- 42 K) in 2019. In contrast, the photospheric diameter theta (*)(UD)theta UD* and the extinction up to the photosphere of GCIRS 7 ( AKS=3.18 +/- 0.16KS=3.18 +/- 0.16 ) have the same value within uncertainties at the two epochs.Conclusions. In the context of previous interferometric and photo-spectrometric measurements, the GRAVITY data allow for an interpretation in terms of photospheric pulsations. The photospheric diameter measured in 2017 and 2019 is significantly larger than previously reported using the PIONIER instrument (theta * = 1.076 +/- 0.093 mas in 2013 in the H band). The parameters of the photosphere and molecular shell of GCIRS 7 are comparable to those of other red supergiants that have previously been studied using interferometry. The extinction we measured here is lower than previous estimates in the direction of GCIRS 7 but typical for the central parsec region.

Abstract
Aims. We aim to demonstrate that the presence and mass of an exoplanet can now be effectively derived from the astrometry of another exoplanet. Methods. We combined previous astrometry of beta Pictoris b with a new set of observations from the GRAVITY interferometer. The orbital motion of beta Pictoris b is fit using Markov chain Monte Carlo simulations in Jacobi coordinates. The inner planet, beta Pictoris c, was also reobserved at a separation of 96 mas, confirming the previous orbital estimations. Results. From the astrometry of planet b only, we can (i) detect the presence of beta Pictoris c and (ii) constrain its mass to 10.04(-3.10)(+4.53) M-Jup . If one adds the astrometry of beta Pictoris c, the mass is narrowed down to 9.15(-1.06)(+1.08) M-Jup. The inclusion of radial velocity measurements does not affect the orbital parameters significantly, but it does slightly decrease the mass estimate to 8.89(-0.75)(+0.75) M-Jup.With a semimajor axis of 2.68 +/- 0.02 au, a period of 1221 +/- 15 days, and an eccentricity of 0.32 +/- 0.02, the orbital parameters of beta Pictoris c are now constrained as precisely as those of beta Pictoris b. The orbital configuration is compatible with a high-order mean-motion resonance (7:1). The impact of the resonance on the planets' dynamics would then be negligible with respect to the secular perturbations, which might have played an important role in the eccentricity excitation of the outer planet.

Abstract
The angular size of the broad line region (BLR) of the nearby active galactic nucleus NGC 3783 has been spatially resolved by recent observations with VLTI/GRAVITY. A reverberation mapping (RM) campaign has also recently obtained high quality light curves and measured the linear size of the BLR in a way that is complementary to the GRAVITY measurement. The size and kinematics of the BLR can be better constrained by a joint analysis that combines both GRAVITY and RM data. This, in turn, allows us to obtain the mass of the supermassive black hole in NGC 3783 with an accuracy that is about a factor of two better than that inferred from GRAVITY data alone. We derive M-BH = 2.54(-0.72)(+0.90) x 10(7) M-circle dot. Finally, and perhaps most notably, we are able to measure a geometric distance to NGC 3783 of 39.9(-11.9)(+14.5) Mpc. We are able to test the robustness of the BLR-based geometric distance with measurements based on the Tully-Fisher relation and other indirect methods. We find the geometric distance is consistent with other methods within their scatter. We explore the potential of BLR-based geometric distances to directly constrain the Hubble constant, H-0, and identify differential phase uncertainties as the current dominant limitation to the H-0 measurement precision for individual sources.

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.