Astronomers use the period-luminosity relationship of Cepheid variables and the distance modulus formula, m−M=5log_10(d)−5 , to determine the distances to far-away stars and galaxies. In the formula, m represents a star's apparent magnitude, M represents its absolute magnitude, and d represents the distance in parsecs. A Cepheid variable has an apparent magnitude m=9.0 and an absolute magnitude M=−1.0 What is the distance to the star?
Substitute the magnitudes into the distance modulus: m − M = 9.0 − (−1.0) = 10. Then 10 = 5log₁₀(d) − 5, so 15 = 5log₁₀(d) and log₁₀(d) = 3. Therefore d = 10³ = 1,000 parsecs, which is choice A.
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