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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Lars Bergman
Date: 2023 Dec 14, 06:11 -0800
Dough S asked how to proceed using the current NA.
Call the time of meridian passage of the star T1. The star's SHA is found in the NA.
Call the time of the moon's bright limb meridian passage T2. Now,
GHAAries(T1) + SHAstar + longitude = 0, also
GHAAries(T2) + SHAbl + longitude = 0, where SHAbl is the SHA of the moon's bright limb, at time T2.
Subtracting one equation from the other and rearranging, yields
SHAbl = SHAstar - [GHAAries(T2) - GHAAries(T1)], where the value inside the square brackets is known, becase T2 - T1 is known and GHAAries changes 15°2.46' per hour.
The tricky part comes next: reduce SHAbl to the SHA of the moon's (and the earth's ?) center. I don't know how to do that, but maybe enclosed pages from an old NA might give some hints.
Then calculate SHA of the moon's center for two or more integer UT-hours, SHAmoon = GHAmoon - GHAAries using the current NA. Find the UT corresponding to SHAmoon by inverse interpolation. With this UT find moon's GHA, which is equal to the observer's westerly longitude.
The maximum rate of change of the moon's SHA is around 40' per hour. With current NA, giving values to 0.1' precision, at the very best UT could be determined to 9 seconds of time and thus longitude to some 2', not bad at all. At minimum rate of change, UT could theoretically be determined to some 13s, but I am afraid the limited precision of SD and HP will deteriorate the actual achievable result. Another limitation is the difficulty, in current NA, to find a suitable star with declination and SHA close to those of the moon.
Lars
