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A star is moved to ten times its present distance from us. How much fainter does it look?
A100 times fainter
B10 times fainter
C20 times fainter
D50 times fainter
Answer & Solution
Correct answer: A. 100 times fainter
1. Light leaving a star spreads over an ever larger shell as it travels.
2. The area of that shell grows as the square of the distance.
3. So the light collected in a fixed area falls off as the square of the distance.
4. Ten times the distance means ten squared, which is one hundred.
5. The star therefore appears 100 times fainter.
6. Answering 10 times fainter uses the distance itself and forgets to square it.
7. Answering 20 times fainter doubles the distance factor instead of squaring it.
8. Answering 50 times fainter matches no step in the calculation at all.
_Source: OpenStax Astronomy (CC BY 4.0), Ch 4 "Earth, Moon, and Sky" and Ch 5 "Radiation and Spectra", section 5.1 The Behavior of Light_
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