A Mass for the Extrasolar Planet Gl 876b Determined from Hubble Space Telescope Fine Guidance Sensor 3 Astrometry and High-Precision Radial Velocities

We report the first astrometrically determined mass of an extrasolar planet, a companion previously detected by Doppler spectroscopy. Radial velocities first provided an ephemeris with which to schedule a significant fraction of the {\it HST} observations near companion peri- and apastron. The astrometry residuals at these orbital phases exhibit a systematic deviation consistent with a perturbation due to a planetary mass companion. Combining {\it HST} astrometry with radial velocities, we solve for the proper motion, parallax, perturbation size, inclination, and position angle of the line of nodes, while constraining period, velocity amplitude, longitude of periastron, and eccentricity to values determined from radial velocities. We find a perturbation semi-major axis and inclination, $\alpha$ = 0.25 $\pm$ 0.06 mas, $i$ = 84\arcdeg $\pm$6\arcdeg, and Gl 876 absolute parallax, $\pi_{abs}= 214.6 \pm$ 0.2 mas. Assuming that the mass of the primary star is $M_* = 0.32M_{\sun}$, we find the mass of the planet, Gl 876b, $M_b = 1.89\pm0.34M_{Jup}$