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Hubble Space Telescope observations of the nearby (3.22 pc), K2 V star epsilon Eridani have been combined with ground-based astrometric and radial velocity data to determine the mass of its known companion. We model the astrometric and radial velocity measurements simultaneously to obtain the parallax, proper motion, perturbation period, perturbation inclination, and perturbation size. Because of the long period of the companion, \eps b, we extend our astrometric coverage to a total of 14.94 years (including the three year span of the \HST data) by including lower-precision ground-based astrometry from the Allegheny Multichannel Astrometric Photometer. Radial velocities now span 1980.8 -- 2006.3. We obtain a perturbation period, P = 6.85 +/- 0.03 yr, semi-major axis, alpha =1.88 +/- 0.20 mas, and inclination i = 30.1 +/- 3.8 degrees. This inclination is consistent with a previously measured dust disk inclination, suggesting coplanarity. Assuming a primary mass M_* = 0.83 M_{\sun}, we obtain a companion mass M = 1.55 +/- 0.24 M_{Jup}. Given the relatively young age of epsilon Eri (~800 Myr), this accurate exoplanet mass and orbit can usefully inform future direct imaging attempts. We predict the next periastron at 2007.3 with a total separation, rho = 0.3 arcsec at position angle, p.a. = -27 degrees. Orbit orientation and geometry dictate that epsilon Eri b will appear brightest in reflected light very nearly at periastron. Radial velocities spanning over 25 years indicate an acceleration consistent with a Jupiter-mass object with a period in excess of 50 years, possibly responsible for one feature of the dust morphology, the inner cavity.

We report on the detection of a planetary companion in orbit around the primary star of the binary system $\gamma$ Cephei. High precision radial velocity measurements using 4 independent data sets spanning the time interval 1981--2002 reveal long-lived residual radial velocity variations superimposed on the binary orbit that are coherent in phase and amplitude with a period or 2.48 years (906 days) and a semi-amplitude of 27.5 m s$^{-1}$. We performed a careful analysis of our Ca II H & K S-index measurements, spectral line bisectors, and {\it Hipparcos} photometry. We found no significant variations in these quantities with the 906-d period. We also re-analyzed the Ca II $\lambda$8662 {\AA} measurements of Walker et al. (1992) which showed possible periodic variations with the ``planet'' period when first published. This analysis shows that periodic Ca II equivalent width variations were only present during 1986.5 -- 1992 and absent during 1981--1986.5. Furthermore, a refined period for the Ca II $\lambda$8662 {\AA} variations is 2.14 yrs, significantly less than residual radial velocity period. The most likely explanation of the residual radial velocity variations is a planetary mass companion with $M$ sin $i$ = 1.7 $M_{Jupiter}$ and an orbital semi-major axis of $a_2$ $=$ 2.13 AU. This supports the planet hypothesis for the residual radial velocity variations for $\gamma$ Cep first suggested by Walker et al. (1992). With an estimated binary orbital period of 57 years $\gamma$ Cep is the shortest period binary system in which an extrasolar planet has been found. This system may provide insights into the relationship between planetary and binary star formation., Comment: 19 pages, 15 figures, accepted in Ap. J. Includes additional data and improved orbital solution