We measured the radial-velocity curve of HD77581, the B-supergiant companion of the X-ray pulsar Vela X-1, using 183 high-resolution optical spectra obtained in a nine-month campaign. We derive radial-velocity amplitudes for different lines and wavelength regions, and find all are consistent with each other, as well as with values found in previous analyses. We show that one apparent exception, an anomalously low value derived from ultra-violet spectra obtained with the IUE, was due to an error in the analysis procedures. We re-analyse all IUE spectra, and combine the resulting velocities with the ones derived from the new optical spectra presented here, as well as those derived from optical spectra published earlier. As in previous analyses, the radial velocities show strong deviations from those expected for a pure Keplerian orbit. The deviations likely are related to the pronounced line-profile variations seen in our spectra. It turns out that systematic deviations as a function of orbital phase are present. Our best estimate of the radial-velocity amplitude, Kopt = 21.7 +/- 1.6 km/s, has an uncertainty not much reduced to that found in previous analyses, in which the systematic deviations had not been taken into account. Combining our velocity amplitude with the accurate orbital elements of the X-ray pulsar, we infer M_ns sin^3i = 1.78 +/- 0.15 Msun.
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