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High-precision astrometric and radial-velocity observations require accuratemodelling of stellar motions in order to extrapolate measurements over longtime intervals, and to detect deviations from uniform motion caused for exampleby unseen companions. We aim to explore the simplest possible kinematic modelof stellar motions, namely that of uniform rectilinear motion relative to theSolar System Barycentre, in terms of observable quantities including errorpropagation. The apparent path equation for uniform rectilinear motion issolved analytically in a classical (special-relativistic) framework, leading torigorous expressions which relate the (apparent) astrometric parameters andradial velocity to the (true) kinematic parameters of the star in thebarycentric reference system. We present rigorous and explicit formulae for thetransformation of stellar positions, parallaxes, proper motions, and radialvelocities from one epoch to another, assuming uniform rectilinear motion andtaking into account light-time effects. The Jacobian matrix of thetransformation is also given, allowing accurate and reversible propagation oferrors over arbitrary time intervals. The light-time effects are generally verysmall but exceeds 0.1 mas or 0.1 m/s over 100 yr for at least 33 stars in theHipparcos Catalogue. For high-velocity stars within a few tens of pc from theSun light-time effects are generally more important than the effects of thecurvature of their orbits in the Galactic potential.

Rigorous treatment of barycentric stellar motion: Perspective and light-time effects in astrometric and radial velocity data