The radial velocity or line-of-sight velocity of a target with respect to an observer is the rate of change of the vector displacement between the two points. It is formulated as the vector projection of the target-observer relative velocity onto the relative direction or line-of-sight (LOS) connecting the two points.
The radial velocity method to detect exoplanets
Doppler spectroscopy is an indirect method for finding extrasolar planets and brown dwarfs from radial-velocity measurements via observation of Doppler shifts in the spectrum of the planet's parent star.
As of November 2022, about 19.5% of known extrasolar planets have been discovered using Doppler spectroscopy.
Doppler spectroscopy detects periodic shifts in radial velocity by recording variations in the color of light from the host star. When a star moves towards the Earth, its spectrum is blueshifted, while it is redshifted when it moves away from us. By analyzing these spectral shifts, astronomers can deduce the gravitational influence of extrasolar planets.