A solar-type star is observed with an apparent magnitude of 12.7.How far away is it? Recall that the absolute magnitude of the Sun is 4.7.
A)10 parsec
B)40 parsecs
C)400 parsecs
D)1000 parsecs

Question

Quizplus · Accepted Answer

The distance to a star can be calculated using the distance modulus formula, which relates the apparent magnitude (m), absolute magnitude (M), and distance in parsecs (d): $m - M = 5 \log_{10}(d) - 5$. Given that the apparent magnitude $m = 12.7$ and the absolute magnitude $M = 4.7$ for a solar-type star (like the Sun), we can solve for $d$. Rearranging the formula gives $\log_{10}(d) = (m - M + 5) / 5$, which simplifies to $\log_{10}(d) = (12.7 - 4.7 + 5) / 5 = 2.6$. Solving for $d$ gives $d = 10^{2.6} \approx 400$ parsecs.

A Solar-Type Star Is Observed with an Apparent Magnitude of 12.7.How