Abstract
The detection of low-mass planets orbiting the nearest stars is a central stake of exoplanetary science, as they can be directly characterized much more easily than their distant counterparts. Here, we present the results of our long-term astrometric observations of the nearest binary M-dwarf Gliese 65 AB (GJ65), located at a distance of only 2.67 pc. We monitored the relative astrometry of the two components from 2016 to 2023 with the VLTI/GRAVITY interferometric instrument. We derived highly accurate orbital parameters for the stellar system, along with the dynamical masses of the two red dwarfs. The GRAVITY measurements exhibit a mean accuracy per epoch of 50-60 ms in 1.5 h of observing time using the 1.8 m Auxiliary Telescopes. The residuals of the two-body orbital fit enable us to search for the presence of companions orbiting one of the two stars (S-type orbit) through the reflex motion they imprint on the differential A-B astrometry. We detected a Neptune-mass candidate companion with an orbital period of p = 156 +/- 1 d and a mass of mp = 36 +/- 7 M circle plus. The best-fit orbit is within the dynamical stability region of the stellar pair. It has a low eccentricity, e = 0.1 - 0.3, and the planetary orbit plane has a moderate-to-high inclination of i > 30 degrees with respect to the stellar pair, with further observations required to confirm these values. These observations demonstrate the capability of interferometric astrometry to reach microarcsecond accuracy in the narrow-angle regime for planet detection by reflex motion from the ground. This capability offers new perspectives and potential synergies with Gaia in the pursuit of low-mass exoplanets in the solar neighborhood.

Abstract
The dark compact object at the centre of the Milky Way is well established to be a supermassive black hole with mass M-center dot similar to 4.3 x 10(6) M-circle dot, but the nature of its environment is still under debate. In this work, we used astrometric and spectroscopic measurements of the motion of the star S2, one of the closest stars to the massive black hole, to determine an upper limit on an extended mass composed of a massive vector field around Sagittarius A*. For a vector with effective mass 10(-19) (less than or similar to) m(s less than or similar to) 10(-18) eV, our Markov chain Monte Carlo analysis shows no evidence for such a cloud, placing an upper bound M-cloud (less than or similar to) 0.1 % M-center dot at 3 sigma confidence level. We show that dynamical friction exerted by the medium on S2 motion plays no role in the analysis performed in this and previous works, and can be neglected thus.

Abstract
By using the GRAVITY instrument with the near-infrared (NIR) Very Large Telescope Interferometer (VLTI), the structure of the broad (emission-)line region (BLR) in active galactic nuclei (AGNs) can be spatially resolved, allowing the central black hole (BH) mass to be determined. This work reports new NIR VLTI/GRAVITY interferometric spectra for four type 1 AGNs (Mrk 509, PDS 456, Mrk 1239, and IC 4329A) with resolved broad-line emission. Dynamical modelling of interferometric data constrains the BLR radius and central BH mass measurements for our targets and reveals outflow-dominated BLRs for Mrk 509 and PDS 456. We present an updated radius-luminosity (R-L) relation independent of that derived with reverberation mapping (RM) measurements using all the GRAVITY-observed AGNs. We find our R-L relation to be largely consistent with that derived from RM measurements except at high luminosity, where BLR radii seem to be smaller than predicted. This is consistent with RM-based claims that high Eddington ratio AGNs show consistently smaller BLR sizes. The BH masses of our targets are also consistent with the standard MBH-sigma* relation. Model-independent photocentre fitting shows spatial offsets between the hot dust continuum and the BLR photocentres (ranging from similar to 17 mu as to 140 mu as) that are generally perpendicular to the alignment of the red- and blueshifted BLR photocentres. These offsets are found to be related to the AGN luminosity and could be caused by asymmetric K-band emission of the hot dust, shifting the dust photocentre. We discuss various possible scenarios that can explain this phenomenon.

Abstract
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 approximate to 1400 Schwarzschild radii, the star has an orbital speed of approximate to 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 of z = Delta lambda/lambda approximate to 200 km s(-1)/c with different statistical analysis methods. When parameterising the post-Newtonian contribution from these effects by a factor f, with f = 0 and f = 1 corresponding to the Newtonian and general relativistic limits, respectively, we find from posterior fitting with different weighting schemes f = 0.90 +/- 0.09 vertical bar(stat) +/- 0.151 vertical bar(sys). The S2 data are inconsistent with pure Newtonian dynamics.

Abstract
The Mid-Infrared ELT Imager and Spectrograph (METIS) is one of the first generation science instruments on ESO's 39m Extremely Large Telescope (ELT). METIS will provide diffraction-limited imaging and medium resolution slit-spectroscopy from 3 - 13 microns (L, M, and N bands), as well as high resolution (R similar to 100,000) integral field spectroscopy from 2.9 - 5.3 microns. Both imaging and IFU spectroscopy can be combined with coronagraphic techniques. After passing its preliminary design review (PDR) in May 2019, and the final design review (FDR) of its optical system in June 2021, METIS is now preparing for the FDR of its entire system in the fall of 2022, while the procurements of many optical components have already started. First light at the telescope is expected in 2028, after a comprehensive assembly integration and test phase. In this paper we focus mainly on the various design aspects, and present a status update on the final optical and mechanical design of METIS. We describe the conceptual setup of METIS, its key functional components, and the resulting observing modes. Last but not least, we present the expected scientific performance, in terms of sensitivity, adaptive optics, and high contrast imaging performance.

Abstract
Hexapods are very common in astronomy as a mechanism to provide a stiff mount or a precision alignment tool. Here, we present a lumped model for a general symmetric hexapod that allows us to compute the load distribution under external forces, the hexapod's resolution, and the identification of singularity loci within the workspace. We also developed a script to analyze this parametric model, which is publicly available. We use this model to develop and design a hexapod for mid-infrared ELT imager and spectrograph, one of the extremely large telescope's first light instruments. The designed hexapod solution can survive strict earthquake conditions that can go up to 5g, and position and align the 11 ton instrument with submillimetric and arcsecond precisions. Although the model presented is not as precise or as realistic as a finite element WO analysis, it provides, in a fraction of a second, a very good first approximation. Therefore, unlike Eh methods, the model is able to study many geometries in a short time. (C) 2021 Society of Photo-Optical Instrumentation Engineers (SPIE)