  For late-type non-active stars, gravitational redshifts and convective
blueshifts are the main source of biases in the determination of radial
velocities. If ignored, these effects can introduce systematic errors of the
order of ~ 0.5 km/s. We demonstrate that three-dimensional hydrodynamical
simulations of solar surface convection can be used to predict the convective
blue-shifts of weak spectral lines in solar-like stars to ~ 0.070 km/s. Using
accurate trigonometric parallaxes and stellar evolution models, the
gravitational redshifts can be constrained with a similar uncertainty, leading
to absolute radial velocities accurate to better than ~ 0.1 km/s.
