NavList:

Hello Frank. I attended your "lunar distances" symposium ten years ago at Mystic Seaport. I got pretty good at shooting lunar distances and got pretty hardcore about the math. I think I can take a stab at finding the problems in this video.

ONE:
Like you said he's ignoring the principle of the method of Aristarchus. Through the early modern period in the history of astronomy, people experimented with this technique and always discovered that it didn't give a useful result. The idea was to OBSERVE the moon and pick the time when the moon was 50% illuminated visually ; by observation. Then at that time, an astronomer was supposed to measure the angular distance between the Moon and the Sun. This is identical to what has been called a lunar distance since the 1700's. But it doesn't work. Aristarchus reported numbers which are generally regarded as fake or at best "hpothetical", and his result was that the sun was only abou a dozen times further away than the moon instead of 400 times!! The angle when the linear distance (in km) to the sun is very great compared to the distance to the linear distance to the moon, is so close to 90 degrees that there is nothing to see. When the moon appears to be 50% illuminated, it can be anywhere from 89 to 91 degrees from the sun. This is no use determining the distance to the sun. IF WE LIVED IN ANOTHER SOLAR SYSTEM where the sun was only five times further away than the moon, then this would work. If we watch for the time when the moon is half full in that imaginary solar systen, it would happen when the elongation of the moon from the sun is about 78.5 degrees.

ONE with an EXCUSE:
Let's give him the benefit of the doubt and say that he's calculating the phase of the moon, or using a pre-calculated phase of the moon, just to set up an interesting pseudo-observation. It doesn't really determine the distance to the sun relative to the moon, but it's a demo of how this COULD work in a different universe. Now the problem is different. I agree that the time he has provided, 19:13 UTC on April 15, 2024, is the common almanac time for the event of the first quarter phase. That time by modern definition is not the time when the phase angle AT THE MOON is 90 degrees which would make the moon perfectly, exactly half full. That time, 19:13 UT, is when the angle AT THE EARTH between the moon and sun is exactly 90 degrees for a geocentric observer. This excuse doesn't help.

TWO:
What about history? Hipparchus and Ptolemy no longer suggested using the logic of Aristarchus to determine the relative distance of the sun. And why not Tycho or Kepler or Halley or Maskelyne for that matter? Why send James Cook and the Endeavour to Tahiti to observe the transit of Venus in 1769? The distance to the moon was known by then, and a measure of the distance to the sun as a multiple of that, which the method of Aristarchus promised, would have saved a long trip to the far side of the world. The method of Aristarchus didn't work then, and it doesn't work now. There's no way to estimate visually when the moon is half full. CANNOT BE DONE. Not to the requirements of Aristarchus.

THREE:
His values for the SD of the sun and the moon are just WRONG. For the sun he has 15.14'. It is NEVER that small. The minimum SD of the sun happens at the beginning of July. According to you lunar distances almanac website, Frank, the minimum sun SD is 15.74' (here's that data... https://clockwk.com/apps/predict/?OT=L&B=MS-L9&D=2_jul_2024&Z=UT&hri=3&df=.m&Lat=41_20&NS=N&Lon=73_12.5&EW=W). His 15.14' is no good. Same for his moon SD, but there are more possibilities there.

THREE with an EXCUSE:
The errors in his two SD values are in oppposite directions and less than a minute of arc. No problem then. No problem except that the values used are wrong. But not a major contribution to the errors in all of this.

FOUR:
After explaining earlier that it's imporatant to do a limb to limb observation of the lunar distance angle, he then describes placing the sun on top of itself to get the index error. That's inconsistent. The scale of the index error at 45 minutes of arc is very large. Does he use this sextant at all? Then he says that he's going to add the index correction. After which he subtracts it.

FOUR with an EXCUSE:
Maybe he mis-spoke. It's easy to get muddled when accounting for index error signs. We can work it up both additive and subtractive. SPOILER: neither works. This excuse does not help.

FIVE:
He says that his sextant angle, from averaging three observations in quick succession is 90d 05'. NOW I have something to work with. 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!

Data as follows: 19:13:00 UTC on April 15, 2024. Location central Michigan. Distance from moon to sun: 90d 05' plus or minus an index correction of 45 minutes of arc (try both). For Michigan locations, I tried A: 43 00 N, 85 40 W (near Grand Rapids), B: 42 45 N, 84 30 W (near Lansing), C: 42 15 N, 83 45 W (near Ann Arbor), D: 43 30 N, 84 15 W (near Midland), E: 42 00 N, 85 00 W (near Coldwater). At each of these locations, the errors in the sextant sight are as follows: +39' with +45 I.C. (one case is +40'), -5' with ZERO I.C., -50' with -45 I.C.

Repeating, an index correction of +45 implies that the sight is wrong by 39 minutes of arc. An index corrction of -45 implies that the sight is wrong by -50'. So no matter which way we go, the results are terrible. I checked this using your lunars clearing web app, Frank, and longhand, too. It's clear to me that the original poster didn't know about the Moon's parallax in this context. Even if Bob assumed ZERO index error, his sight was wrong by 5'.

FIVE with an EXCUSE:
There is no conceivable excuse. It's a bad observation, and misinterpreted.

SIX: Until this point he's been working to the nearest minute of arc which is fine since a plastic Davis sextant is only accurate to a few minutes of arc. But now he jumps more than an order of magnitude and continues at thousandths of a degree. That's weird. He's also working at the last step to four significant figures when the process doesn't deserve more than one significant figure. That's weird, too.

The quality of the calculation after here is unremarkable. He can add. But the inputs are wrong AS DESCRIBED ABOVE. The measured angle is clearly incorrect. The semi-diameters of the sun and moon are wrong. There's no correction for parallax (nor refraction but that's much smaller). And yet he gets a result that is awfully cloe to the answer that he wanted. How did that happen??? Sometimes getting lucky on numbers can be unlucky. Maybe that's all it is. I am outta here on further speculation on this "lucky" result.

Thanks for reading, and thanks again, Frank, for getting me into LUNARS so long ago. I see you have another Lunars workshop scheduled at Mystic Seaport in early June. I may just have to dive in for a refresher!

Jake