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.

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.