Final answer:
One can determine if one star is moving away faster than another by examining their relative redshifts, with a greater redshift indicating a faster recession velocity. This is based on the Doppler effect, where light from objects moving away is redshifted.
Step-by-step explanation:
If several stars are moving away from Earth, one can determine if one is moving away faster than another by examining their relative redshifts. Yes, their relative redshifts determine their speed. Because the universe is expanding, distant stars and galaxies appear to be moving away from us, and their light is redshifted. This redshift is directly proportional to their velocity relative to Earth. A greater redshift indicates that an object is moving away faster, while a smaller redshift indicates a slower speed.
For example, if we observe two stars exhibiting different amounts of redshift, we can infer that the one with the larger redshift is receding at a higher velocity. This conclusion is based on the Doppler effect, which also applies to sound waves but is used in astronomy with light waves. When an object moves away, its spectral lines move towards the red end of the spectrum, hence the term 'redshift'.
To illustrate this, consider three hypothetical stars moving at the same speed in different directions relative to Earth. Star A, moving perpendicular to our line of sight, would have no Doppler shift since it is neither moving towards nor away from us. Star B, moving directly away, would show the greatest Doppler shift, and Star C, moving at an angle, would have a Doppler shift less than Star B but greater than Star A.