  Under certain conditions, stellar radial velocities can be determined from
astrometry, without any use of spectroscopy. This enables us to identify
phenomena, other than the Doppler effect, that are displacing spectral lines.
The change of stellar proper motions over time (perspective acceleration) is
used to determine radial velocities from accurate astrometric data, which are
now available from the Gaia and Hipparcos missions. Positions and proper
motions at the epoch of Hipparcos are compared with values propagated back from
the epoch of the Gaia Early Data Release 3. This propagation depends on the
radial velocity, which obtains its value from an optimal fit assuming uniform
space motion relative to the solar system barycentre. For 930 nearby stars we
obtain astrometric radial velocities with formal uncertainties better than 100
km/s; for 55 stars the uncertainty is below 10 km/s, and for seven it is below
1 km/s. Most stars that are not components of double or multiple systems show
good agreement with available spectroscopic radial velocities. Astrometry
offers geometric methods to determine stellar radial velocity, irrespective of
complexities in stellar spectra. This enables us to segregate wavelength
displacements caused by the radial motion of the stellar centre-of-mass from
those induced by other effects, such as gravitational redshifts in white
dwarfs.
