The full moon has an apparent magnitude of approximately -12.6. What would be the apparent magnitude of a star that was 14 times brighter than the full moon?
A) -15.47
B) 9.73
C) 2.87
D) 0.46

Question

Quizplus · Accepted Answer

The magnitude scale is logarithmic, with a difference of 5 magnitudes corresponding to a brightness factor of 100. To find the magnitude difference for a brightness factor of 14, we use the formula $ \Delta m = 2.5 \log_{10}(B_2/B_1) $, where $B_2/B_1$ is the brightness ratio. Plugging in 14, we get $ \Delta m \approx 2.87 $. Since the star is brighter, we subtract this from the moon's magnitude: -12.6 - 2.87 = -15.47.

The Full Moon Has an Apparent Magnitude of Approximately -12