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On closer inspection of the absolute visual magnitude and the apparent visual magnitude of the sun, I noticed that their magnitude range (4.83 + 26.74 = 31.57) exactly matches the human eye. The already no longer healthy brightness (-26.74) in 1 AU and just visible with the naked eye (4.83) in 10 parsec. In addition, these approx. 30 mag are also represented by the entire brightness range from the dimmest (e.g. LHS 2924 with 20) to the brightest fixed star (-9). So could it be that when the standard distance was set at 10 parsecs, the visible distance of the sun was taken into account or is there another objective reason?

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The various units used in astronomy are, essentially, practical units. The first distances to stars were measured in the 19th century. As only the nearest stars could be measured in this way, by 1895 only 28 stars had had their parallax measured, with values found to be between 0.187 and 0.054 arcseconds.

In 1902, the Dutch astronomer Julius Kapteyn defined "absolute magnitude". He wrote:

We further define the absolute magnitude (M) of a star, of which the parallax is π and the distance r as the apparent magnitude that star would have if transferred to a distance from the sun corresponding to a parallax of 0.1 [arcseconds].

His choice of "0.1" is not explained, but it seems to be entirely practical. It is close to the median of parallax values of stars that had had their parallax measured at the time. A parallax of 0.1 arcseconds corresponds (in terminology that did not exist in 1902) to a distance of 10 parsecs.

It is worth noting that there were other proposals. Hertzsprung did calculations of brightness using one parsec as his standard. There were multiple proposals for distance scales for stars that have since been forgotten (who knows what a "Andromede", a "metron" or a "Siriusweite" are now?) This naturally led to the potential for confusion. It was therefore down to the IAU, in 1922, to adopt a standard, and Kapteyn's convention of 10 parsecs was chosen.

So the choice of 10 parsecs seems simply to be because that was close to the average distance of stars whose distances were known in 1902.

The history is described in The Introduction of Absolute Magnitude (1902 - 1922) by David Hughes.

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  • $\begingroup$ +1 for pointing out the general arbitrariness of those units. I guess there is a typo in "Sirusweite" - it should be "Siriusweite" (distance to Sirius). $\endgroup$
    – Chieron
    Commented Feb 24 at 16:45
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    $\begingroup$ Yes, a typo. The actual defintion of a Siriusweite was a parallax of 0.2 arcseconds, or about 16.3 light years. This was the measured parallax of Sirius at the time. In fact it is closer, about 8 light years. On the other hand, an andromede was thought to be between 1600 and 8000 light years, in fact is it 2100000 ly $\endgroup$
    – James K
    Commented Feb 24 at 17:36
  • $\begingroup$ is there any info why IAU chose it over alternatives? $\endgroup$ Commented Feb 25 at 14:07
  • $\begingroup$ They probably felt that it was the alternative that had the most use, and was becoming a de facto standard. To get evidence for that, you'd probably have to read through the minutes of the meetings from 1922.... which I have no huge desire to do. $\endgroup$
    – James K
    Commented Feb 25 at 17:32

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