Final answer:
The Doppler method measures the velocities of stars to detect planets by observing changes in star's radial velocity resulting from gravitational interactions with orbiting planets, using shifts in the star's spectrum.
Step-by-step explanation:
The Doppler method seeks to detect planets by precisely measuring the velocities of stars moving toward and away from us. The presence of a planet can induce a wobble in the star due to gravitational interaction, altering the star's radial velocity as observed from Earth. This can be observed through the Doppler effect—in shifts in the star's spectrum. A blue shift indicates the star is moving toward us, while a red shift indicates it is moving away. High-resolution stellar spectroscopy is utilized to measure these slight changes, which provide insights into the planet's mass and orbital period. The technique is most sensitive to large planets close to their host stars and has been successful in detecting hundreds of planets, such as one orbiting Proxima Centauri.