The light is spread over an area four times larger, and it will be only one-fourth as bright as when the projector was half as far away. If you move the projector three times farther away, the light will cover 9 square feet and appear only one-ninth as bright.
If a star measured in this manner happens to be part of a distant cluster, we can assume that all of those stars are the same distance, and we can add them to the library of standard candles.
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How stars are measured.
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