  The Doppler effect is commonly used to infer the velocity difference between
stars based on the relative shifts in the rest-frame wavelengths of their
spectral features. In dynamically-cold systems with a low velocity dispersion,
such as wide binaries, loose star clusters, cold stellar streams or
cosmological mini-halos, the scatter in the gravitational redshift from the
surface of the constituent stars needs to be taken into account as well.
Gravitational redshifts could be important for wide binaries composed of main
sequence stars with separations >0.01 pc or in mini-halos with velocity
dispersions <1 km/s. Variable redshift could also lead to a spurious
"detection" of low-mass planets around a star with periodic photospheric radius
variations.
