Final answer:
Finding extrasolar planets through radial velocity variations involves measuring the Doppler shifts in the spectrum of a star as it wobbles due to the gravitational pull of an orbiting planet. This allows the determination of the planet's mass and orbital period. High-resolution stellar spectroscopy is crucial for detecting these small changes.
Step-by-step explanation:
The method for finding extrasolar planets by radial velocity variations works by detecting the wobble of a star caused by the gravitational influence of an orbiting planet. This stellar wobble induces changes in the radial velocity of the star as observed from Earth, which can be measured using high-resolution stellar spectroscopy and the Doppler effect. As the star moves towards us, its spectrum appears slightly blue shifted, and as it moves away, the spectrum is redshifted. The Doppler shifts are extremely small and require sophisticated equipment to detect. By analyzing these periodical shifts in the spectrum of the star, astronomers can infer the existence of a planet, its mass, and its orbital period around the star. This method has led to the detection of hundreds of exoplanets, including those orbiting stars such as Proxima Centauri.