Question

If the distance between a star and an observer is increased by four times, the brightness of the star will be:A. unchangedB. increased by 4 timesC. decreased by 4 timesD. decreased by 16 times

Answer 1

The brightness of a source with luminosity L is given by:

$b=\frac{L}{4\pi d^2}$

Suppose that expression represents the original brightness if we increase the distance four times, then the new brightness is given by:

$b^{\prime}=\frac{L}{4\pi(4d^)^2}=\frac{L}{16(4\pi d^2)}=\frac{1}{16}b$

This means that the brightness will decrease by 16 times. Therefore, the answer is D.