Final answer:
The spectral lines from a galaxy's stars are subject to Doppler shifts due to their motions, which leads to line broadening. By analyzing these shifts, astronomers can learn about the star's velocity and the galaxy's mass. A comparison of rest and shifted wavelengths yields information about the relative motion of the stars.
Step-by-step explanation:
The spectral lines emitted from the same star in a galaxy can be affected by different motions of the stars within the galaxy. This phenomenon is known as Doppler shifts and results in line broadening. The redshift and blueshift of these lines reflect the motion of the stars toward or away from us, which is influenced by the star's velocity around the galaxy's center of mass and by the gravitational force within the galaxy. By analyzing the amount by which the spectral lines are broadened, astronomers can determine the range of speeds at which stars are moving and, subsequently, calculate the mass of the galaxy.
If we take a rest wavelength of 410 nm from a stationary star and compare it to the observed shifted wavelength of 492 nm from the moving star, we can quantify the Doppler shift. This comparison can potentially reveal the relative motion of the star and contribute to our understanding of the galaxy's dynamics.