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Jake,

Thank you for that comprehensive and detailed account. I do remember you (I believe) from that early workshop, which I think may have been twelve years ago. I agree with everything you wrote. You spotted more issues than I did!

I, too, noticed the puzzling errors in the semi-diameters. And I agree with you that it's not necessarily a big deal, but where did the error come from? It does, however, contribute to the peculiar problem of unjustified significant figures in the final result, even if there were no issues of principle (which there are).

You wrote:
"At this point, it's nothing but a straight traditional lunar distance sight that I can clear using standard corrections or using your website app, Frank. It doesn't matter what he's using the observation for. It can be cleared and checked as what it is. It's a lunar!"

You're right, and, yes, that does boil the analysis right down to its fundamental salts... He shot this lunar at the minute when the true geocentric LD was 90.000°, and that's what it should clear to, regardless of any musings about Greeks. The error in the cleared result is five minutes of arc if we assume no index error. And honestly, that would not be half bad for a Davis plastic sextant. But since he asserts that the index error is 45 minutes of arc, whether positive or negative, then the error in this observation is actually quite large.

If we go with your idea of creating a "demo" of the plan of Aristarchus, using the time of 90° 00.0' phase angle at the Moon (that's angle between the Sun and the observer on the Earth as seen from the Moon), then there might be an interesting backyard observation to experiment with here. It's not the time the original poster used, and it's not an independent determination of the distance to the Sun since any precomputed time like this has that distance "baked in", but it might be interesting regardless. It seems that would be highly dependent on the observer's location on the Earth which was something Aristarchus could ignore when he thought that the deficit angle would be several degrees instead of the several minutes or arc that should actually result/

That's probably the end of this topic, though if anyone has any new thoughts, please feel free. I chose to write about this video here rather than on mainstream social media (the original video is on youtube and he posted about it on facebook) so as not to mess with the poor guy's reputation with his followers. Jake, thank you again for addressing this video, and, yes, please do stop by my "Lunars" workshop at Mystic Seaport that first weekend in June, whether you decide to attend formally or not. :)

Frank Reed
Clockwork Mapping / ReedNavigation.com
Conanicut Island USA