Final answer:
The mass of a planet can be estimated by measuring the amplitude of the star's velocity curve, which reflects the wobble caused by the gravitational pull of the planet on the star, as detected through the Doppler shift in the star's spectral lines.
Step-by-step explanation:
The Doppler method can be used to measure the mass of a planet by observing the star's motion due to the gravitational pull of an orbiting planet. When a planet orbits a star, it exerts a gravitational force causing the star to wobble slightly around a common center of mass. This wobble can be detected as variations in the star's radial velocity, with one side of the star moving towards us and the other moving away, producing redshifts and blueshifts in its spectral lines as detected by high-resolution stellar spectroscopy. The amplitude of the star's velocity curve from these Doppler shifts can then be used to estimate the planet's mass. Combining this with transit methods, which provide the size of the planet, allows astronomers to calculate the planet's density and composition.
The Doppler method can be used to measure the mass of a planet by measuring the speed at which the star orbits the mutual center-of-mass of the star and planet. When the star is moving away from us, it shows a tiny redshift in its spectrum; when it is moving toward us, it shows a tiny blueshift. By measuring these changes in color (wavelength), which are caused by the Doppler effect, astronomers can determine the speed and direction of the star's motion. These measurements can then be used to calculate the mass of the planet.