A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Sean C
Date: 2021 Jan 7, 06:23 -0800
"Since HermanD's Jan 6, 2021, 4:02 PM post, I suspect that you have fixed the problem!"
That's just it: I haven't changed anything. I'm still baffled as to why that is happening.
You also wrote:
"I did notice that small discrepancies appear progressively with past dates for the Moon."
I'm not sure what algorithms Astron uses (although I know I've used it before and found it to be very accurate), but this doesn't really surprise me. Apparently there are a lot of factors affecting the motion of the Moon, and Meeus simplified the algorithm he used by omitting many of the smaller order terms. He states in chapter 47 of Astronomical Algorithms 2nd Ed. that "In order to calculate accurately the position of the Moon for a given instant, it is necessary to take into account hundreds [emphasis in original] of periodic terms in the Moon's latitude, longitude and distance." Well, he pared that number down to about 160. IIRC, Frank uses SOFA. I would expect that to be much more accurate.
One thing I have noticed about my spreadsheet is that sometimes an error will begin to appear in the position of a planet, for example, as the time gets further from J2000. But, as I increment the time even further, the error disappears again. I suppose Meeus' trimming can have an effect somewhat similar to averaging. IDK.
"Even more trivial, you state a start date of 1900:1:1 00:00:00. In fact it gives errors before the 19 hours 12 minutes of that millennium!"
Yes, and I've been meaning to fix that. It would literally only take a couple of seconds, I just haven't prioritized it. In fact, I intend to extend the table of TAI-UT1 values in both directions. I just have to decide on a prediction algorithm. And I think it might be particularly difficult to choose a good one just now. Extending the table backwards is not really a problem at all.
"Your earlier post of Jul 28, 2020, 5:16 AM states "There are no macros in the workbook - only tables." My official version of Excel flags up 24 of them!"
Oops. Forgot to mention that I added those, sorry. They're just there to make the buttons do magic stuff. I'm pretty sure you could delete all of the macros and the spreadsheet would still basically work. You'd just have to do a lot more manual entry.
Anyway, I am glad to hear that my spreadsheet agreed with the other sources in most of the tests (for you, at least). And thank you very much for taking the time to put it through its paces. I look forward to learning anything else you may find ... good or bad.