A star has absolute luminosity equal to that of the sun but is 10 pc away from the Earth. By what factor will it appear dimmer than the sun? The earth is $1.5 \times 10 ^ { 8 } \mathrm {~km}$ from the sun, and 1 parsec is equal to $3.09 \times 10 ^ { 16 } \mathrm {~m}$.
A) $2 \times 10 ^ { - 9 }$
B) $2 \times 10 ^ { - 11 }$
C) $2 \times 10 ^ { - 15 }$
D) $2 \times 10 ^ { - 13 }$

Question

Quizplus · Accepted Answer

The apparent brightness of a star is inversely proportional to the square of its distance. The distance to the star is 10 parsecs, which is $10 \times 3.09 \times 10^{16} \, \text{m}$. The distance to the sun is $1.5 \times 10^8 \, \text{km} = 1.5 \times 10^{11} \, \text{m}$. The factor by which the star appears dimmer is $(1.5 \times 10^{11} / (10 \times 3.09 \times 10^{16}))^2 = 2 \times 10^{-13}$.

A Star Has Absolute Luminosity Equal to That of the Sun