The Araucaria project: High-precision orbital parallaxes and masses of binary stars I. VLTI/GRAVITY observations of ten double-lined spectroscopic binaries

Aims. We aim to measure very precise and accurate model-independent masses and distances of detached binary stars. Precise masses at the < 1% level are necessary to test and calibrate stellar interior and evolution models, while precise and independent orbital parallaxes are essential to check for the next Gaia data releases.Methods. We combined RV measurements with interferometric observations to determine orbital and physical parameters of ten double-lined spectroscopic systems. We report new relative astrometry from VLTI/GRAVITY and, for some systems, new VLT/UVES spectra to determine the radial velocities of each component.Results. We measured the distance of ten binary systems and the mass of their components with a precision as high as 0.03% (average level 0.2%). They are combined with other stellar parameters (effective temperatures, radii, flux ratios, etc.) to fit stellar isochrones and determine their evolution stage and age. We also compared our orbital parallaxes with Gaia and showed that half of the stars are beyond 1s with our orbital parallaxes; although, their RUWE is below the frequently used cutoff of 1.4 for reliable Gaia astrometry. By fitting the telluric features in the GRAVITY spectra, we also estimated the accuracy of the wavelength calibration to be similar to 0.02% in high and medium spectral resolution modes.Conclusions. We demonstrate that combining spectroscopic and interferometric observations of binary stars provides extremely precise and accurate dynamical masses and orbital parallaxes. As they are detached binaries, they can be used as benchmark stars to calibrate stellar evolution models and test the Gaia parallaxes.