NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Antoine Couëtte
Date: 2023 Oct 4, 03:41 -0700
Hello to all,
Rather than handdrawing a paper and ruler solution, I have decided for a "more or less mathematical" solution this time.
All angles in decimal degres or in arc minutes as specified on the attachment.
To the accuracy stated on top of the Attachment and in reference to my previous post, from position N20°/W090° I have computed Sun and Moon UL's and LL's heights and azimuths for UT#1 = 17:00:00.0 and UT#2 = 18:30:00.0.
Numbers given include all effects of refraction and Augmented SD's. Height of Eye is irrelevant here since only differences in heights are of interest.
Ignoring differential refraction, we can state that the apparent Moon Center is exactly halfway between LL and UL. Same for the Sun. Hence Moon and Sun Centers heights given between brackets are the exact averages of respective LL and HL heights.
2 Change of variables to make computations easier:
2.1 - From heights and Azimuths in GC degrees, use Arc minutes instead.
2.2 - Use T = UT - 17:00:00.0, hence T varies between 0:00:00.0 and 1:30:00.0
Assuming that the respective differences in both Heights and Azimuths between Sun LL (/UL) as well as the Moon SD do vary as an exact Linear function of the elapsed time between UT#0 and UT#1, we can then compute in a plane the apparent distance between Sun LL (/UL) and Moon Center minus Moon SD. When this function becomes negative, the relevant Limb is obscured by Lady Moon.
End results :
- The Sun UL is not obscured by the Moon.
- The Sun LL is covered by Lady Moon between 17:10:13.5 UT and 18:17:32.0 UT
Last note : results here-above significantly different from Lars' solution (Between UT 17h11m11s and 18h01m41s the moon will cover the sun's lower limb) which I have not opened up yet.
Interesting difference between our results, can we learn something from it ? Any independent advice from a third party ?
By lack of time I have not investigated this difference yet. And do not take me wrong : I am just looking here for somebody to defeat my solution hereabove.
We can learn so much from our own mistakes.
Kermit
