$mu$ Cassiopeiae is a nearby, high-velocity, metal-poor ($rm[Fe/H]=-0.81$) visual binary. We have used high-resolution imaging with the Hubble Space Telescope (HST), obtained over nearly two decades, to determine the period (21.568 yr) and precise orbital elements. Combining these with published ground- and space-based astrometry, we determined dynamical masses for both components of $mu$ Cas: $0.7440pm0.0122,M_odot$ for the G5 V primary, and $0.1728pm0.0035,M_odot$ for its faint dM companion. We detect no significant perturbations in the HST astrometry due to a third body in the system. The primary aim of our program was to determine, with the aid of stellar models, the helium content and age of the metal-deficient primary star, $mu$ Cas A. Although we now have a precise mass, there remain uncertainties about other parameters, including its effective temperature. Moreover, a re-examination of archival interferometric observations leads to a suspicion that the angular diameter was overestimated by a few percent. In the absolute magnitude versus color plane, $mu$ Cas A lies slightly cooler and more luminous than the main sequence of the globular cluster 47 Tucanae; this may imply that the star has a lower helium content, and/or is older, and/or has a higher metallicity, than the cluster. Our best estimates for the helium content and age of $mu$ Cas A are $Y=0.255pm0.014$ and $12.7pm2.7$ Gyr--making $mu$ Cas possibly the oldest star in the sky visible to the naked eye. Improved measurements of the absolute parallax of the system, the effective temperature of $mu$ Cas A, and its angular diameter would provide tighter constraints.
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