Doppler Wobble

The radial velocities for stars caused by planets orbiting around them are typically 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 often 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 Doppler shift, first toward and then away from the observer, of no more than 13 meters per second.