How do astronomers derive orbital parameters for spectroscopic binaries using the Doppler effect?

By measuring the shift in light spectra due to radial velocity changes

Spectroscopic binaries consist of stars that are too closely spaced or too distant to be visually resolved as separate points of light through a telescope. In these cases, astronomers rely on the light emitted by the stars. As the stars trace their orbital paths, one star alternately moves toward the Earth (causing its light spectrum to shift toward the blue end—a blueshift) while the other moves away (causing its spectrum to shift toward the red end—a redshift). This cyclical pattern is the familiar Doppler shift applied to light. By meticulously tracking these shifts in the absorption lines of the star's light spectra, astronomers can calculate the stars' radial velocities, which are essential components for determining the orbital parameters, including the period and the velocity curves necessary for mass calculations.