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. decrea…

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asked Jul 22, 2023 215k views

1 Answer

DIEGO CARRASCAL · Answer 1 · 2023-07-27T22:38:22+0000

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

$b=(L)/(4\pi d^2)$

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

$b^(\prime)=(L)/(4\pi(4d^)^2)=(L)/(16(4\pi d^2))=(1)/(16)b$

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