How can a spectroscope be use to find out if a star is moving?

A spectroscope can determine if a star is moving by analyzing the light spectrum emitted by the star. When a star moves away from Earth, its light is redshifted, meaning the wavelengths are stretched and appear longer. Conversely, if the star is moving towards Earth, its light is blueshifted, with shorter wavelengths. By measuring these shifts in the spectral lines, astronomers can quantify the star's velocity relative to Earth.