A star is at such a distance that its apparent magnitude (m) is 10 magnitudes fainter than its absolute magnitude (M). How far away is it?
A) 10 pc
B) 100 pc
C) 1000 pc
D) 10,000 pc

Question

Quizplus · Accepted Answer

The distance modulus formula, which relates a star's apparent magnitude (m) to its absolute magnitude (M) and its distance in parsecs (d), is given by $m - M = 5 \log_{10}(d) - 5$. Given that $m - M = 10$, we can solve for $d$: $10 = 5 \log_{10}(d) - 5$, which simplifies to $15 = 5 \log_{10}(d)$, and further to $\log_{10}(d) = 3$. Therefore, $d = 10^3 = 1000$ parsecs.

A Star Is at Such a Distance That Its Apparent