Isn't it possible to model the positions of the planets relative to each other on a computer? Surely 'tis. And then run the model backwards and simply count and see if there is a 56 year eclipse cycle? I say "simply", though it would be impossible for me. Don't fight forces, use them R. Buckminster Fuller.
But: I now know I definitely do not believe him.
There is a 112-year eclipse cycle, that was known in Arabia about the time of Mohammed. (The dating is a bit vague. The archaeological artifact is a brass bowl and it might date from centuries earlier.) This is 118 Dragon rounds. In some ways it is not particularly good--but never mind that. It took me a while to remember this cycle (which I had read about several years ago and checked out myself).
The problem is that you cannot cut the cycle in half. You can cut 112 years to 56 years, and 118 Dragon rounds to 59 Dragon rounds, no problem, but it turns out this means cutting 1385 months to 692.5 months. That half of a month means you are swapping solar eclipses (new Moon) for lunar ones (full Moon) which is okay (if a bit weird) for the modern astronomer but not okay at all for the neolithic astronomer who is burdened with serious problems of observation. (Solar eclipses are complicated. Latitude, longitude, time of day, EVERYTHING matters. For a lunar eclipse--if it is nighttime, you're good.) It really doesn't work.
Oh yes. The Dragon. There's your eighth planet. Or eighth and ninth, if you are Hindu. The Head of the Dragon is known to modern astronomers as the Ascending Lunar Node; the Tail of the Dragon is the Descending Lunar Node. The Head and Tail are the places where the Moon's path against the sky crosses the ecliptic (the Sun's path against the sky), so the position of the Dragon and the phase of the Moon are the key elements in eclipse prediction--everything else is secondary or else irrelevant. Between the Head and the Tail the Moon is above the ecliptic; between the Tail and the Head the Moon is below.
E.
Throughout Britain there are neolithic stone tables which some archaeologists have argued mark (from a proper vantage point) the lowest position of the Moon in the sky. If one accepts this, then one accepts that knowledge of the Moon's position above and below the ecliptic was a matter of interest, for the Moon is lowest when it is near the winter solstice point AND is midway between the Dragon's Tail and Head. The concurrence of these two conditions depends upon the interaction of the season (year) and the Dragon. This interaction repeats every 56 years--which is very precisely 59 Dragon rounds.
Incidently, the first condition is satisfied for the full Moon at the height of summer, for last quarter at the spring equinox, for new Moon in the depth of winter, and for first quarter at the fall equinox.
Historically, the Dragon is one of the oldest and most important deities. Several creation myths start with the Dragon, and many religions describe how their deities overcame the Dragon. But their is a cultural dividing line running through Eurasia--on the western side the Dragon has been supplanted and is generally feared; on the eastern side the Dragon continues to be viewed positively. Tibet is on the eastern side of the line, India on the west. In Tibet eclipses are auspicious ("good deeds on the day of an eclipse are multiplied a hundredfold"); in India inauspicious barely begins to describe it--people literally hide under their beds.
About this last, I am not kidding. When I was there I spent a week killing conversations before I learned better. When I would answer queries by explaining I was in India to see the eclipse (the path of totality was going to pass nearby) people abruptly staggered away in stunned silence. There was no way to comprehend my words, nor imagine a response.
The Dragon is the guardian of doorways, and the bringer of sudden change. The Fates are kind.