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Moon altitude correction question
From: Stan K
Date: 2013 Aug 17, 12:37 -0400
From: Stan K
Date: 2013 Aug 17, 12:37 -0400
On the bottom of page 259 of the 2013 Nautical Almanac, it says "The correction table for the Moon includes the effect of semi-diameter, parallax, augmentation, and mean refraction." However, looking at the example on page 281, I do not see where augmentation is considered. The formula for semi-diameter used (SD = 0.2724HP) must be for geocentric semi-diameter, since it does not include altitude. The fact that the oblateness of the Earth is ignored in the example affects the correction by less than 0.1', but augmentation could affect it by almost 0.3' for high-altitude sights.
In the examples, the apparent altitudes are low enough that the difference between the corrections calculated in the examples and those using the tables are only about 0.1'. But what happens when the apparent altitudes are, say, 80º for both the upper and lower limb examples, and the HP is, say 60.3'?
By the method of the examples:
Lower Upper
Refraction - 0.175 - 0.175
Parallax (HPcosH)) +10.471 +10.471
Semi-diameter (0.2724HP) +16.426 -16.426
_____________________________________________
Corr (rounded) +26.7 -6.1
Lower Upper
Main (upper table) +20.5 +20.5
Add'l (lower table) + 6.0 +3.2
-30' for UL -30
___________________________________________
Corr +26.5' -6.3'
0.2' differences for an apparent altitude of 80º, which approaches 0.3' as the apparent altitude approaches 90º.
What's more, since augmentation makes the semi-diameter larger, whether it is added or subtracted, it would tend to make the calculated lower limb correction even further from the tabular correction, and the calculated upper limb correction closer to the tabular correction.
What am I doing wrong here? I must be overlooking something.
Stan
In the examples, the apparent altitudes are low enough that the difference between the corrections calculated in the examples and those using the tables are only about 0.1'. But what happens when the apparent altitudes are, say, 80º for both the upper and lower limb examples, and the HP is, say 60.3'?
By the method of the examples:
Lower Upper
Refraction - 0.175 - 0.175
Parallax (HPcosH)) +10.471 +10.471
Semi-diameter (0.2724HP) +16.426 -16.426
_____________________________________________
Corr (rounded) +26.7 -6.1
Lower Upper
Main (upper table) +20.5 +20.5
Add'l (lower table) + 6.0 +3.2
-30' for UL -30
___________________________________________
Corr +26.5' -6.3'
0.2' differences for an apparent altitude of 80º, which approaches 0.3' as the apparent altitude approaches 90º.
What's more, since augmentation makes the semi-diameter larger, whether it is added or subtracted, it would tend to make the calculated lower limb correction even further from the tabular correction, and the calculated upper limb correction closer to the tabular correction.
What am I doing wrong here? I must be overlooking something.
Stan
