Proper Motions of Dwarf Spheroidal Galaxies from Hubble Space Telescope Imaging. V: Final Measurement for Fornax

The measured proper motion of Fornax, expressed in the equatorial coordinate system, is $(\mu_{\alpha},\mu_{\delta})=(47.6\pm 4.6,-36.0\pm 4.1)$ mas century$^{-1}$. This proper motion is a weighted mean of four independent measurements for three distinct fields. Each measurement uses a quasi-stellar object as a reference point. Removing the contribution of the motion of the Sun and of the Local Standard of Rest to the measured proper motion produces a Galactic rest-frame proper motion of $(\mu_{\alpha}^{\mbox{\tiny{Grf}}}, \mu_{\delta}^{\mbox{\tiny{Grf}}}) = (24.4\pm 4.6,-14.3\pm 4.1)$ mas century$^{-1}$. The implied space velocity with respect to the Galactic center has a radial component of $V_{r}=-31.8 \pm 1.7$ km s$^{-1}$ and a tangential component of $V_{t}=196 \pm 29$ km s$^{-1}$. Integrating the motion of Fornax in a realistic potential for the Milky Way produces orbital elements. The perigalacticon and apogalacticon are 118 (66, 137) kpc and 152 (144, 242) kpc, respectively, where the values in the parentheses represent the 95% confidence intervals derived from Monte Carlo experiments. The eccentricity of the orbit is 0.13 (0.11, 0.38), and the orbital period is 3.2 (2.5, 4.6) Gyr. The orbit is retrograde and inclined by $101^{\circ}$ ($94^{\circ}$, $107^{\circ}$) to the Galactic plane. Fornax could be a member of a proposed ``stream'' of galaxies and globular clusters, however the membership of another proposed galaxy in the stream, Sculptor, has been previously ruled out. Fornax is in the Kroupa-Theis-Boily plane that contains eleven of the Galactic satellite galaxies, but its orbit will take it out of that plane.