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    Average altitude of a celestial sight
    From: Frank Reed
    Date: 2020 Aug 17, 00:04 -0700

    I was thinking about that graphical arc error sextant certificate. It could be summarized by a simple table with values every 15° and an assumption of linearity between those altitudes:
    0°    0.0'
    15°  0.2'
    30°  0.4'
    45°  0.4'
    60°  0.6'
    75°  0.2'
    90°  0.2'

    I suspect that's what was actually measured, and the curve was drawn in to display those values as if on a smooth curve.

    Now suppose you wanted to represent this table by one single number. You apply your index correction, which is independent of arc error. Then you want to apply some number that would capture some sort of "average" of all of the arc error values above. What would that be? It's not a simple average. After all, the band of the sky from 0-15° is about 7.5 times bigger (in terms of "square degrees") than the band from 75-90°. If you throw darts at the sky at random, you're much more likely to hit the 15° band near the horizon than the 15° band near the zenith. In addition, we only rarely shoot altitudes below about 5°, and most navigators avoid altitudes above 80°. So what constitues an "average" altitude?? And what weights would you apply to the values in the above table to generate an average arc error value from them? My guess for the best "average arc error" from the table above is in the range from 0.35' to 0.40'. A simple average of the list would be 0.28'.

    Frank Reed

       
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