The sun has apparent brightness $B$ at the earth, which is $1.5 \times 10^{8} \mathrm {~km}$ away. What would be the apparent brightness of the sun at Pluto, which is $6.0 \times 10 ^ { 9 } \mathrm {~km}$ from the sun?
A) $0.025 \mathrm {~B}$
B) $0.00063 B$
C) $0.25 B$
D) $0.063 \mathrm {~B}$

Question

Quizplus · Accepted Answer

The apparent brightness of a source (like the Sun) decreases with the square of the distance from the source. This is described by the inverse square law. Given that Pluto is $6.0 \times 10^9 \mathrm{~km}$ away from the Sun, and Earth is $1.5 \times 10^8 \mathrm{~km}$ away, the distance ratio squared is $\left(\frac{1.5 \times 10^8}{6.0 \times 10^9}\right)^2 = \left(\frac{1}{40}\right)^2 = \frac{1}{1600}$. Therefore, the apparent brightness at Pluto would be $B/1600 = 0.000625 B$, which rounds to $0.00063 B$, option B.

The Sun Has Apparent Brightness BBB At the Earth, Which Is 1.5×108 km1.5 \times 10^{8} \mathrm {~km}1.5×108 km

The Sun Has Apparent Brightness $B$ At the Earth, Which Is $1.5 \times 10^{8} \mathrm {~km}$