A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Tibor Miseta
Date: 2022 Jan 6, 12:49 -0800
I've tried to estimate by the illuminated disk. I measured the diameter of the Moon (between the ends of the horn) 732 pixs, and the shadowed disk from the terminator to the dark limb 672 pixels. The illuminated size is than: (732-672)/672 = 8.2%
A rough estimate from the Air Almanac: the illuminated disk for 01.04 18:00Z is approx 6% and for 01.05 06:00Z is approx 9%, so 12 hours change is 3% (almost linear in the neighbouring halfdays), a quick interpolation gives 01.05 02:48Z. But this is very inaccurate, because the almanac data was given as whole integers only.
A better estimation if we try to calculate the illuminated disk from GHA differences. By one of Meeus' approximate formula the illuminated fraction is k = (1-cos i)/2, where cos i is approx - cos(delta Lat) * cos (delta Lon), so an estimate is k = (1 - cos(delta GHA))/2. (I neglected the latitude differences, because they are so close, that the cosine of small angles are nearly 1.) So I got the following results:
01.04 18:00Z = 6.7%
01.05 06:00Z = 10.0%
A quick interpolation for 8.2% is 7:38 from 01.04 18:00Z, that is 01.05 01:38Z
The watch correction is approx +25 minutes (1:38 - 1:13)
This is still just an estimate of course, more accurate measurement and calculation could be performed.