This has gone way off the rails.
The N-body problem is a red herring.
The issue I raised in the opening post of this topic is the TFES Wiki's (Tom's) claim that eclipse predictions are based on patterns. That's wrong, and whether or not the N-Body problem eludes solution doesn't matter. Cycles are time-based. There is nothing about a Saros cycle that can provide the parameters needed to calculate Besselian elements of a solar eclipse.
You can't get this from a cycle:
![](http://oi67.tinypic.com/27y8k08.jpg)
You can't produce this based on a mere cycle:
![](http://oi65.tinypic.com/317cj6u.jpg)
This is the predicted solar eclipse for July 2, 2019. It's part of Saros cycle 127. But that's not the basis for predicting the detailed characteristics of the eclipse: the where, the how much, the duration, etc. For that, you need the Besselian elements, which are based on the relative position and motion of the earth/moon/sun and spherical geometry of the earth. It doesn't matter if the ephemeris providing earth/moon/sun location and motion are divinely granted or calculated based on a perfect solution to the 3-body problem of these 3 bodies, with or without perturbation by other solar system or galactic bodies. It doesn't matter. That's a distraction. Either intentional or misguided.
The ability to calculate where on earth the eclipse will be seen, the degree of totality, the coverage of the umbra and penumbra, precisely when it will begin and end, etc. doesn't hinge on solving the n-body problem. There is no flat earth model analog for how Fred Espenak performs his calculations by using an ephemeris of a rotating globe earth, orbited by a globe moon, orbiting a spherical sun. It's based on spherical geometry and absolutely requires input of position and motion of the 3-bodies. It's not "patterns" at all.
Tom has managed to derail this and get everyone debating aspects how the ephemerides are produced, under the illogical reasoning that if a million-year stable n-body solution can't be calculated using Newtonian mechanics, that the entire edifice collapses and all that remains is "patterns."
When eclipse #58 in Saros Cycle 127 begins, it will occur and have the characteristics predicted. That prediction won't be just a table look up of a pattern. It will be calculated based on the shape of the earth, the shape of the moon's shadow on the convex surface of the globe earth, based on position and motion of the 3-body earth-moon-sun system taken from an ephemeris, the utility or accuracy of which doesn't require a solution to the n-body problem.