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The bright K1 III-IV star gamma Cep has been reported previously to have acompanion in a 2.5-yr orbit that is possibly substellar, and also has a stellarcompanion at a larger separation that has never been seen. Here we determinefor the first time the three-dimensional orbit of the stellar companionaccounting also for the perturbation from the closer object. We combine new andexisting radial velocity measurements (of both classical precision and highprecision) with intermediate astrometric data from the Hipparcos mission(abscissa residuals) as well as ground-based positional observations going backmore than a century. The orbit of the secondary star is eccentric and has aperiod of 66.8 yr. We establish the primary star to be on the first ascent ofthe giant branch, and to have a mass of 1.18 M_Sun, an effective temperature of4800 K, and an age around 6.6 Gyr (for an assumed metallicity [Fe/H] = +0.01).The unseen secondary star is found to be an M4 dwarf with a mass of 0.362M_Sun, and is expected to be about 6.4 mag fainter than the primary in K. Theminimum mass of the putative planetary companion is M_p sin i = 1.43 M_Jup.Taking advantage again of the high-precision Hipparcos observations we are ableto place a dynamical upper limit on this mass of 13.3 M_Jup (95% confidencelevel) and 16.9 M_Jup (99.73%, or 3 sigma) thus confirming that it is indeedsubstellar in nature. (Abridged)Comment: 28 pages in emulateapj style, including tables and figures. Accepted  for publication in Ap

The Planet Host Star γ Cephei: Physical Properties, the Binary Orbit, and the Mass of the Substellar Companion