Question

$b=\frac{L}{4\pi d^2}$
The brightness of a celestial body, like a star, decreases as you move away from it. In contrast, the luminosity of a celestial body is a constant number that represents its intrinsic brightness. The inverse square law, shown is used to find the brightness, $b$, of a celestial body when you know its luminosity, $L$, and the distance $d$, in meters to the body. Which equation shows the distance to a celestial body, given its brightness and luminosity?

• A. $d=\frac{1}{2}\sqrt{\frac{L}{\pi b}}$
• B. $d=\sqrt{\frac{L}{2\pi b}}$
• C. $d=\frac{\sqrt{L}}{2\pi b}$
• D. $d=\frac{L}{2\sqrt{\pi b}}$

Answer 1

The correct option is A $d=\frac{1}{2}\sqrt{\frac{L}{\pi b}}$

Isolate $d^2:d^2=\frac{L}{4\pi b}$
Taking square roots away,
$d=\frac{1}{2}\sqrt{\frac{L}{\pi b}}$