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=12.0 and is located 1,000 parsecs from Earth. What is its absolute magnitude?
Substitute the distance of 1,000 parsecs into the distance modulus formula: m − M = 5log₁₀(1,000) − 5 = 5(3) − 5 = 10. Since m = 12.0, this gives 12.0 − M = 10, so M = 2.0. The absolute magnitude is 2.0, choice D.
AI-written and checked against the verified answer.