Model atmosphere fits to high-resolution optical spectra of Wray 977 confirm the B hypergiant classification of the massive companion to the X-ray pulsar GX301-2. The models give a radius of 62 Rsun, an effective temperature of 18,100 K and a luminosity of 5 x 10^^5 Lsun. The deduced mass-loss rate and terminal velocity of the stellar wind are 10^^-5 Msun/yr and 305 km/s, respectively. The interstellar Na I D absorption indicates that Wray 977 is located behind the first intersection with the Sagittarius-Carina spiral arm (1-2.5 kpc) and probably belongs to the stellar population of the Norma spiral arm at a distance of 3-4 kpc. The spectra obtained with UVES on the Very Large Telescope (VLT) cover a full orbit of the system, including periastron passage, from which we derive the radial-velocity curve of the B hypergiant. The measured radial-velocity amplitude is 10 +/-3 km/s yielding a mass ratio q = 0.046 +/- 0.014. The absence of an X-ray eclipse results in a lower limit to the mass of Wray 977 of 39 Msun. An upper limit of 53 Msun is derived for the mass of Wray 977 adopting a maximum neutron star mass of 2.5 Msun. The ``spectroscopic mass of Wray 977 is 43 +/- 10 Msun, consistent with the range in mass derived from the binarity constraints. The mass of the neutron star is 1.85 +/- 0.6 Msun. Time series of spectral lines formed in the dense stellar wind indicate the presence of a gas stream trailing the neutron star in its orbit. The long-term behaviour of the H alpha equivalent width exhibits strong variations in wind strength; the sampling of the data is insufficient to conclude whether a relation exists between wind mass-loss rate and pulsar spin period.
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