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I understand this is an icky subject, but I recently got interested in units for large distances for applications in cosmology and what not (after hearing about the redefinition of the kilo and kelvin), and I was surprised to see many very weird units which seem difficult to use.

So I was thinking in astronomy distances only get larger and larger, so I looked to see if I could find any logarithmic scale for distances and I couldn't find any. Then again, I'm not an astronomer and not suited to argue anything.

Are there any logarithmic scales for larger distances, and if so why aren't they being used? And if non exist, is there a reason why(is it simply a bad idea)? Or is it simply a matter of keeping historical background?

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    $\begingroup$ Could you give an example of what you mean by "logarithmic" here? $\endgroup$
    – Steve Linton
    Jan 9, 2019 at 15:08
  • $\begingroup$ @SteveLinton I mean something like the pH scale where say something like theoretical Q is the unit used, 1Q = 1m, 2Q = 10m, 3Q = 100m. Thats just an example. Although I dont know much I was thinking to myself at least that it would be easier to express larger distances that way $\endgroup$
    – Julian A Avar C
    Jan 9, 2019 at 15:17

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Having some experience with the only logarithmic unit in regular use (the dB, for sound intensity), I have to say: please, no.

A logarithmic representation can be handy in some cases. This chart is an excellent example of what can be done if you choose the scale on your image correctly.

enter image description here

Note that this has been done without introducing a new unit for distance, it just plots log(x) instead of x on the vertical scale.

But if you were to use a logarithm in the fundamental unit for distance, you'd introduce some problems:

  • cosmological distances no longer match other distance units and any conversion between them involves using a log function.
  • calculations involving cosmological distances get more complicated because you've now got to use log() everywhere.
  • you lose the linear relationship between numbers: object X is twice as far away as object Y, but the difference in your unit becomes log(2) making distances far less intuitive.
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  • $\begingroup$ Apart from the decibel scale, a logarithmic scale that should immediately spring to everyone's mind on an astronomy site is apparent magnitude. The pH scale and several seismic moment magnitude scales (e.g. Richter's) are logarithmic too. $\endgroup$
    – Chappo Hasn't Forgotten Monica
    Jan 10, 2019 at 4:54

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