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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2025 Jan 22, 11:12 -0800
As with your index error tests, there are two ways to do this. You can either place the Sun's image "on top of itself" (reflected image "dropped onto", superimposed on direct image) or you can place the two Sun images in contact, limb to limb, one "above" the other, which has yet other subset of possibilities. Let's assume you're going with the first option...
Essentially, you're shooting the altitude of the Sun's center. So you want the average of the UL and LL values. You quoted corrections of +12.8 for LL and -19.5 for UL. The average of those is the sum (properly accounting for +/- signs) divided by two:
Ctr = (LL + UL)/2
= [12.8 + (-19.5)]/2
= (12.8 - 19.5)/2
= -3.35
Take your pick on rounding that, either 3.3 or 3.4 is fine. What you'll discover is that this is nearly identical to applying the "stars" altitude correction since you're only dealing with refraction in both cases (for the Sun, there is a negligibly small parallax correction that's formally included --but to emphasize, it's negligible for practical sextant navigation, only 0.15 minutes of arc). You can test this. Look up the altitude correction as if it's a star sight. Then look up the Sun UL/LL values. Average those and you should find the result matches the star sight altitude correction to within one or two tenths of a minute of arc.
Note that the so-called Sun Main correction, the UL/LL altitude correction table for the Sun, is a real oddity in the official Nautical Almanac. This table probably should have been replaced decades ago. Among the issues, why UL corrections? Very nearly no one shoots the Sun's UL --more than 99% of Sun sights are LL sights. By contrast, for Moon sights, it's 50:50 depending on the Moon's orientation. And of the small remainder, many navigators need the Sun's Center altitude --like you. Sun LL/Ctr tables would make more sense. Also, the idea that the corrections suddenly jump from one six-month approximation to the other is obviously a little strange. Alas, in the modern world (for several decades running...) these tables are mostly a means of beating up navigation students on exams. Sun UL sights are not real-world navigation problems, but they do tend to turn up in soul-crushing classroom exercises.
Frank Reed
PS: Admin topic: Peter, would you like to be named here in NavList messages with something closer to your real name? You listed yourself in your first post as just "Peter". I tagged you with an "X". We normally require last names or at least a surname initial that is close. Please let me know. If you like being "Peter X" that's fine, too.