Final answer:
Cepheid variables are essential for measuring cosmic distances due to the direct relationship between their pulsation periods and absolute magnitudes, which remains consistent regardless of their distance from us.
Step-by-step explanation:
Cepheid variables make good standard candles because their period is closely related to their absolute magnitude. The period-luminosity relation observed in Cepheid variables is a fundamental tool in astronomy for measuring cosmic distances. The remarkable discovery of this relationship, thanks to astronomers like Henrietta Swan Leavitt, allows us to measure the period of the star with some basic astronomical equipment, and using the established mathematical relationship to then compute the star's luminosity.
With the star's luminosity known, comparisons between the luminosity and the apparent brightness observed from Earth allow us to calculate the star's distance. This is because the apparent brightness of a star diminishes with distance according to the inverse square law, while the absolute brightness remains constant. Therefore, Cepheid variables, with their predictable luminosity changes, are excellent indicators of distance in space.