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I understand that each scale you go up on the absolute magnitude scale, the luminosity decreases by the fifth root of 100, or around 2.512. Is there a name for the constant 2.512, or not. Also, is the fifth root of 100 rational, or irrational?

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The fifth root of 100 is occasionally referred to as "Pogson's Ratio" after Norman Pogson who systematized the magnitude system. I'd recommend not using this as it doesn't save any space or time and only serves to disguise a value that actually is a fifth root.

As 100 is not a fifth power, the fifth root of 100 is irrational. All roots of integers are either irrationals or integers.

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    $\begingroup$ Another reason not to use the term "Pogson's ratio": A survey among nine astronomer colleagues yielded zero astronomers who had ever heard the term before :) $\endgroup$
    – pela
    Apr 4 at 9:56
  • $\begingroup$ Do you have the resource where you found this? I find this very interesting and couldn't find anything online. Thanks for sharing the fun fact :) $\endgroup$
    – Astrovis
    May 9 at 4:38
  • $\begingroup$ Yes, linked in the question mathworld.wolfram.com/PogsonsRatio.html $\endgroup$
    – James K
    May 9 at 4:41

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