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If one star is at a distance of 100 light years, how far away would a second star that is 9 times as luminous, have to be to appear at the same brightness as the first?

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    You need to make the second star appear 9 times dimmer than it would at 100 l.y. distance. Since the received light is inversely proportional to the distance squared, that means you must triple the distance. That will put it 300 light years away.

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