Thread: Math trivia
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Old 08-18-2017, 11:27 PM
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ceptimus ceptimus is offline
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Default Re: Math trivia

In 1856, Norman Robert Pogson defined the system we use to measure the apparent brightness of stars, as seen from here on Earth.

He came up with the wonderfully arcane system where a higher number means a dimmer star, and each whole number of the scale indicates a star that is 2.512 times dimmer than the number before. The number 2.512 is now known as Pogson's ratio in his honor.

So a magnitude 4 star is 2.512 times dimmer than a magnitude 3 star, and a magnitude 5 star is another 2.512 times dimmer - so that's a total of 2.512 squared or 6.31 times dimmer. On this scale, the brightest object in the sky, the Sun, has an apparent magnitude of -27.

In fairness to Pogson, he didn't invent this system just to be awkward - he was just trying to rationalize a system devised by the Ancient Greeks who had a scale from 1 to 6 for stars in the night sky where magnitude 1 stars were the brightest and magnitude 6 stars were the faintest that could be seen with the naked eye - which, of course, was the only observing instrument available to the Greeks at that time.

The Greeks reckoned that each magnitude represented a halving in the brightness of the stars, which would make a magnitude 6 star 1/32 as bright as a magnitude 1 star, but by Pogson's time there were instruments that could measure the actual amount of light received from stars and he found that the stars called magnitude 6 by the Greeks were nearer a hundred times dimmer than the brightest magnitude 1 stars.

So Pogson decreed that a magnitude 1 star was exactly 100 times brighter than a magnitude 6 one, and that's where his ratio of 2.512 comes from - to make the 6 different magnitudes cover a range of one to one hundredth, the ratio between each magnitude number has to be the fifth root of a hundred.
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Last edited by ceptimus; 08-18-2017 at 11:39 PM.
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