Apparent magnitude depends on distance, so it cannot be used to compare how powerful stars really are. The absolute magnitude, M, of a star is defined as the apparent magnitude it would have if it were at a distance of 10 parsecs from Earth. Comparing absolute magnitudes compares the stars' actual power outputs (luminosities).Apparent magnitude m, absolute magnitude M and distance d are linked by:m − M = 5 log (d / 10) where d is in parsecs and log is to base 10. The quantity m − M is sometimes called the distance modulus.
• a star exactly 10 pc away has m equal to M
• a star further than 10 pc has m greater than M (it looks fainter than it would at 10 pc)
• a star closer than 10 pc has m less than MWorked example 1: a star at 100 pc has m = 3.0. Find M.
m − M = 5 log (100/10) = 5 log 10 = 5
M = 3.0 − 5 = −2.0Worked example 2: a star has m = 10.0 and M = 0.0. Find d.
10.0 = 5 log (d/10), so log (d/10) = 2
d/10 = 100, so d = 1000 pcThe Sun has m = −26.7 but M ≈ +4.8: it only looks so bright because it is very close. If we know M for a type of star, measuring m gives its distance.
• a star exactly 10 pc away has m equal to M
• a star further than 10 pc has m greater than M (it looks fainter than it would at 10 pc)
• a star closer than 10 pc has m less than MWorked example 1: a star at 100 pc has m = 3.0. Find M.
m − M = 5 log (100/10) = 5 log 10 = 5
M = 3.0 − 5 = −2.0Worked example 2: a star has m = 10.0 and M = 0.0. Find d.
10.0 = 5 log (d/10), so log (d/10) = 2
d/10 = 100, so d = 1000 pcThe Sun has m = −26.7 but M ≈ +4.8: it only looks so bright because it is very close. If we know M for a type of star, measuring m gives its distance.