Final answer:
The speed at which stars are moving away from the Earth is determined using the Doppler effect, with a greater redshift indicating a faster velocity. Stars are ranked from the smallest to largest observed wavelength shift indicating their relative speeds, from slowest to fastest.
Step-by-step explanation:
To determine the speed at which stars are moving away from Earth based on their wavelengths, we apply the Doppler effect principle. The greater the redshift (the shift of the spectral lines toward the longer wavelength end of the spectrum), the faster the star is moving away from us. Therefore, to rank the stars by speed, we look at the magnitude of the shift from the normal wavelength to the observed wavelength.
As the wavelength increases, so does the Doppler shift, which corresponds to a higher velocity away from Earth. If three stars show shifted wavelengths, with star A having the smallest shift, star B having an intermediate shift, and star C the largest shift, then star A is moving away the slowest, star B at an intermediate speed, and star C at the fastest speed.
Using the formulas provided, we could determine the actual speeds if we had specific wavelength values for the stars in question. For example, suppose a star's hydrogen spectral line is normally at 500 nm, but we observe it at 500.1 nm. In that case, we can calculate its speed using the observed change in wavelength. But without specific wavelength values, we can only rank their speeds relative to each other by the extent of their redshift.