  Context. Despite the thorough work of van Leeuwen (2007), the parallax of
alpha Centauri is still far from being carved in stone. Any derivation of the
individual masses is therefore uncertain, if not questionable. And yet, that
does not prevent this system from being used for calibration purpose in several
studies. Aims. Obtaining more accurate model-free parallax and individual
masses of this system. Methods. With HARPS, the radial velocities are not only
precise but also accurate. Ten years of HARPS data are enough to derive the
complement of the visual orbit for a full 3D orbit of alpha Cen. Results. We
locate alpha Cen (743 mas) right where Hipparcos (ESA 1997) had put it, i.e.
slightly further away than derived by Soderhjelm (1999). The components are
thus a bit more massive than previously thought (1.13 and 0.97 Msun for A and B
respectively). These values are now in excellent agreement with the latest
asteroseismologic results.

Solar and Stellar Astrophysics