Final answer:
The rotation rate of distant objects is measured using the Doppler effect, where changes in wavelength of light due to rotation result in line broadening of spectral lines, allowing astronomers to calculate rotation speeds.
Step-by-step explanation:
Light can reveal the rotation rate of distant objects through an effect known as the Doppler effect. When a star rotates, one edge moves towards us while the other edge moves away. The Doppler effect causes the spectral lines of light from the approaching edge to shift towards shorter wavelengths (blue shift), while the receding edge's spectral lines shift towards longer wavelengths (red shift). This phenomenon, called line broadening, can be observed using spectrographs. By analyzing the broadened spectral lines, astronomers can determine the star's rotation speed. Additionally, this method is not limited by distance as long as we can obtain a good spectrum of the star's light.
For example, even though the radial velocity changes caused by a star's rotation or the gravitational influence of orbiting bodies like Jupiter might be subtle, modern spectrographs enable astronomers to measure these changes accurately. Thus, the detection of a star's rotational speed is not affected by its distance from Earth, enabling astronomers to apply the Doppler effect technique universally with adequate observational equipment.