Astronomers often use the apparent magnitude m as a means of comparing the visual brightness of stars and relating the comparison to the luminosity and distance to “standard” stars, such as the Sun (see Equation 13-9). The difference in the apparent magnitudes of two stars m₁ and m₂ is defined as m₂ - m₁ = 2.5 log (f₁/f₂), a relation based on the logarithmic response of the human eye to the brightness of objects. Pollux, one of the “twins” in the constellation Gemini, has apparent magnitude 1.16 and is 12 pc away.

Betelgeuse, the star at Orion’s right shoulder, has apparent magnitude 0.41. How far away is Betelgeuse if they have the same luminosity?

100(-M)/5 F10 pc F R 10 pc 2 13-9