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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,

GHA_Aries(T₁) + SHA_star + longitude = 0, also
GHA_Aries(T₂) + SHA_bl + longitude = 0, where SHA_bl is the SHA of the moon's bright limb, at time T₂.

Subtracting one equation from the other and rearranging, yields

SHA_bl = SHA_star - [GHA_Aries(T₂) - GHA_Aries(T₁)], where the value inside the square brackets is known, becase T₂ - T₁ is known and GHA_Aries changes 15°2.46' per hour.

The tricky part comes next: reduce SHA_bl 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, SHA_moon = GHA_moon - GHA_Aries using the current NA. Find the UT corresponding to SHA_moon 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 13^s, 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