Note 7 — Chapter I · Exploring the Sky

For instance, Cepheids whose light fluctuates in a period of 40 hours have approximately a luminosity 250 times that of the sun, and so are of 8 × 10²⁹ candle-power; a period of ten days indicates a luminosity 1600 times that of the sun, or a candle-power of 5·17 × 10³⁰, and so on. If a star in a distant astronomical object is observed to fluctuate with a period of ten days, and the quality of its fluctuations shew it to be a Cepheid variable, we know that its actual candle-power must be 5·17 × 10³⁰. Its apparent brightness is observed to be that of a star of, say, magnitude 16, which, stripped of technicalities, means that we receive as much light from it as from a single candle at a distance of 570 miles. The difference between one candle and 5·17 × 10³⁰ candles accordingly corresponds to the difference between 570 miles and the distance of the object in question, whence, since light falls off as the inverse square of the distance, we calculate that the distance of the object must be

√5·17 × 10³⁰ × 570 miles

or about 220,000 light-years.