The µ Herculis system solved after nearly three centuries

Context . µ Herculis is a bright, nearby quadruple system. Its brightest member, µ Her Aa, displays solar-like oscillations, establishing the system as a crucial benchmark for asteroseismology, provided that its mass can be determined independently of stellar models. Aims . We aim to resolve the full hierarchical architecture of the system and determine precise, model-independent dynamical masses for all four components (Aa, Ab, B, and C), along with a consistent astrometric solution for the system’s centre of mass. Methods . We performed a joint fit of radial velocities, relative astrometry and absolute astrometry from H IPPARCOS , Gaia DR3, and ground-based catalogues, spanning nearly three centuries. Our forward-modelling framework simultaneously constrains the Keplerian orbits of the inner Aa–Ab and B–C subsystems, the wide A–BC orbit, and the sky motion and parallax of the total centre of mass. Results . Leveraging several complementary datasets and the decisive 2023 periastron passage of the Aa–Ab pair, we precisely determine all orbital parameters and obtain sub-percent precision on the component masses: M Aa = 1.134 ± 0.007 M ⊙ , M Ab = 0.2286±0.0006 M ⊙ , M C = 0.445±0.005 M ⊙ , and M B = 0.417±0.005 M ⊙ . We derive a system parallax of ϖ CM = 120.069±0.089 mas that reconciles and improves upon the individual H IPPARCOS and Gaia DR3 values.