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The orbit and physical parameters of the eclipsing binary system $\zeta$~Aur\-igae (K4 Ib + B5 V) have been determined from an analysis of recent observations with the Goddard High Resolution Spectrograph of the Hubble Space Telescope, interferometric observations from the NRL/USNO Optical Interferometer Project, and photometric observations from the literature. The GHRS data in the far ultraviolet near 1200 \AA, obtained at several orbital phases, yield (for the first time) an accurate solution of the B star radial velocity curve, and an accurate mass ratio for the system. The interferometry yields the orbital inclination, and this allows the individual masses to be recovered. The interferometric observations also give the angular sizes of the K star and of the orbit (the B star is unresolved), and therefore $a/R_K$, the ratio of the semi-major axis to the K star radius. This ratio is also derived from photometric observations of the eclipse. Since the radial velocity curves yield the physical size of the orbit $a= a_1 + a_2$, the distance to the system is obtained. Finally, we compute a model atmosphere of the B star secondary, assuming $T_{\rm eff}= 15450$~K and $\log g= 3.86$ (Bennett et al.\ 1994), and infer the B star angular diameter and the interstellar extinction by fitting the model spectrum to the observed GHRS fluxes.
