Final answer:
Doppler spectroscopy is a true indirect method for finding extrasolar planets and brown dwarfs by measuring radial-velocity changes in the star's spectrum caused by an orbiting planet's gravitational force.
Step-by-step explanation:
Doppler spectroscopy is indeed an indirect method for detecting extrasolar planets and brown dwarfs through radial-velocity measurements. The method involves observing Doppler shifts in the spectrum of a planet's parent star. The stellar movement around a common center of mass with an orbiting planet causes a redshift when the star moves away from us and a blueshift when it moves toward us. This change in the wavelength corresponds to the star's changing speed, and while the shifts are minute, they can be measured with sophisticated equipment.
The first technique yielding many planet detections, high-resolution stellar spectroscopy, exploits the Doppler effect to measure a star's radial velocity. The presence of a planet induces a small but measurable wobble in the star due to its gravitational influence. By analyzing this wobble, we can deduce the mass and orbital period of the planet. As the technology to measure smaller Doppler shifts improves, more distant and less massive planets can also be revealed using this technique.
This detection method has been employed using large ground-based telescopes, which have discovered hundreds of planets, including one around Proxima Centauri, the closest star to the Sun. Although more sensitive to large planets near their stars, this approach can decipher entire planetary systems by disentangling multiple planets' contributions to radial velocity variations.