SIMBAD references

The mutual inclination ψ between orbits within multi-planetary systems is difficult to measure directly. Through a joint analysis of radial velocities, Hipparcos-Gaia absolute astrometry and relative astrometry of JWST, D. C. Bardalez Gagliuffi et al. recently found two possible values of ${\psi }_{\,\rm{bc}\,}=3{2}_{-15.1}^{+13.6}{^\circ} $ and ${\psi }_{\,\rm{bc}\,}=145.{0}_{-11.1}^{+15.8}{^\circ} $ for the nearby, non-transiting planet system, 14 Her. By incorporating additional astrometry from Gaia second data release (DR2), we have further constrained the orbital orientation of 14 Her b, resulting in a definitive and unambiguous mutual inclination of ${\psi }_{\,\rm{bc}\,}=35.{3}_{-7.3}^{+6.8}{^\circ} $. The unusual misaligned orbital architecture of 14 Her system may serve as a benchmark for dynamical studies.