The radial velocities for stars caused by planets orbiting around them
measured using the Doppler shift of spectral lines. The technique is sometimes called
the Doppler wobble method, since it uses the Doppler shift to detect a tiny
wobbling motion of the parent star caused by the gravity of the unseen planet.
An Example: 51 Pegasi
The following figure shows the shift in radial velocity observed for the star 51 Pegasi.
In this plot the average radial velocity of 51 Pegasi relative to us has been subtracted. The
oscillation around a radial velocity of zero then represents some additional motion
superposed on its average motion. This periodic variation is interpreted as the effect of a
planet revolving around 51 Pegasi, pulling it
first away from us and then toward us with a period
of about 4 days.
Quantitative analysis of this data indicates that
the unseen companion has
approximately the mass of Jupiter.
Precision of the Measurements
Measurements to detect extrasolar planets typically
require that variations in the radial velocity
of order 10 meters per second be detected relative to an average radial velocity that is
10-100 kilometers per second (in the above example, the shift in radial
velocity is about plus or minus 50 meters per second, which is relatively large).
For example, the wobble of the Sun's motion because of the gravitational influence of Jupiter
as seen by an observer thirty light years away corresponds to a circular motion on the sky
of diameter around 0.001 arc seconds.
This is a remarkably small effect (see the right panel). It would correspond to a periodic
shift, first toward and then away from the observer, of no more than 13 meters per second.