Thork - you still haven’t addressed how you could predict the start of a new saros series using your tables, or an antikythera mechanism if you’d prefer.
The saros cycle isn't the only cycle eclipses use, that tables predict or indeed the antikythera machine can predict.
Below is an eclipse table.
The resulting Saros-Inex Panorama proved useful in organizing eclipses. For instance, one step down in the panorama is a change of one Saros period (6585.32 days) later, while one step to the right is a change of one Inex period (10571.95 days) later. The rows and columns were then numbered with the Saros and Inex numbers.
Very convenient in the classification of eclipse cycles. Inex series, after a sputtering beginning, go on for many thousands of years giving eclipses every 29 years or so. One inex after an eclipse, another eclipse takes place at almost the same longitude, but at the opposite latitude. So just because my saros cycle ran out, I can still move a column to the right and pick up a different cycle to see where this next eclipse is coming from and restart my saros cycles from there.
There are others too: the Tritos (11 years, 1 month), the Metonic Cycle (19 years), the Exeligmos (triple Saros).
all tables, all known for thousands of years, all helping us predict eclipses.
Now, with your round earth hokum ... demonstrate how YOU would predict a new saros cycle. You seem so adamant that NASA aren't using these tables that do it for them ... show the special maths they use referring to how round the earth must be, to predict this new cycle. And when you can't, don't change the subject. You're in check ... its mate in one.
Well, first of all, congratulations on learning some stuff - you've progressed from thinking that it was all just Saros periods and that the cycles went on for ever uninterrupted.
Now we're into Inex cycles. Again, great, you're learning stuff. But if you're going to quote websites, you need to read and understand everything that's going on, not just the first bit you find that matches your preconceptions. That Saros-Inex panorama is a brilliant piece of work, but as the website you yourself got it from (there's a pattern developing here, isn't there?) points out, whilst it has some useful predictive power, and it's helpful in understanding eclipse timings, it has many limitations. You can see just by looking at it that whilst there is a general pattern, the individual cycles are irregular, which limits their predictive power. Again, from your link:
No single Inex-Saros combination meets all three criteria, but there are periods that do a reasonably good job for any one of them.
And then a little later:
Modern digital computers using high precision solar and lunar ephemerides can directly predict the dates and circumstances of eclipses. Nevertheless, the Saros and Inex cycles remain useful tools in understanding the periodicity and frequency of eclipses.
An enormous Saros-Inex panorama has been produced by Luca Quaglia and John Tilley in the form of a Microsoft Excel file. It shows 61,775 solar eclipses over a 26,000-year period from -11,000 to +15,000 organized by Saros and Inex Series.
So I guess your contention is that every ephemeride is in fact secretly using tabular data built from cycle periods, and not the gravity/orbital mechanics models they claim to be. Aside from the fact that your own source points out inaccuracies and limitations of just using tables, let's drill into ephemerides and their use a little deeper.
So, you asked for how to make predictions...here's an example that compares two ephemerides, DE200 and DE405 for accuracy.
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwjzgdmftpbwAhULesAKHZd0BJMQFjABegQIBRAD&url=https%3A%2F%2Fjournal.walisongo.ac.id%2Findex.php%2Fahkam%2Farticle%2Fdownload%2F5036%2F2796&usg=AOvVaw3M8VLR1bh6BnuHOL3w492pThere's pretty good detail on how to analyse the data and extract eclipse instances from the raw position data.
So that's half the battle, but of course you could argue that the ephemeris itself is just cyclical tables and not actually an orbital mechanics model (although as a flat earther you should be wondering how the eclipses match so perfectly with a model that is based on spherical bodies in alignment...).
If you're interested, there's a lifetime's worth of reading on what goes into an ephemeris model. Here's a detailed description of some of the measurement data that went into one of them, DE405, for example:
https://web.archive.org/web/20120220062549/http://iau-comm4.jpl.nasa.gov/de405iom/de405iom.pdfThey are enormously complex. I suppose that the people who put that together are either in on the conspiracy, or they are genuine? The bizarre insistence that their usage of numerical methods to generate model data as evidence of fraud or invalidity that seems to pop up on this site from time to time is just plain weird - just because a set of PDEs can't be solved analytically doesn't mean they aren't correct. Indeed, having created a set of solutions it's possible to back-test the data against the original equations, and to run other tests such as energy conservation (poor solutions add or lose energy over time, which can't happen).
You're in check ... its mate in one.
I think this is the problem, neatly summed up in one short line. Good scientist shift their position on new evidence. I don't consider this to be a game of win or lose. I'm not trying to defeat you, whereas you appear to consider this to be a case of picking a side and defending it, regardless of all evidence. It's ok, in fact it's positively fantastic, to change your position. Go ahead, read some stuff, and learn.