peter wrote:
What interests me here is the degree of accuracy (<1%) this model was able to produce re the observed data and still be totally wrong at it's very center (excuse the weak pun

). I wonder how accurate our current calculations are re their fit. From an 'insrumentalists' point of view it matters little which of the models (heliocentric or geocentric) are correct - what matters to them is merely the predictive accuracy of the respective models. For him there is no requirement for a scientific model to correspond to 'the truth'. it is exactly that - a model for use in prediction,no more. (Hasten to add this is *not* leading to an argument in favor of geocentrism).
From last to first...IIRC, there were at least a couple peeps in the 200BCE era that knew the sun-center was correct [at least in more manageable sense], but they said basically [paraphrasing of course] "But that's just a fact, the truth is a matter for religion/philosophy."
I would think it matters more to the instrumentalist which is correct...because the instruments will tell you [when they're good enough] that the other planets literally do not do little reverse circles at various points in their orbits. The math is the part that is equally accurate for both models...one kind is just simpler to calculate...though if [as I now suspect you are] you're speaking of the philosophical school "instrumentalism", I concede the point.
On the accuracy, it's pretty amazing they could do it so well...and if they knew there were more planets and that orbits were ellipses not circles they'd have done even better. On our current fit of predictions...barring something like a planetary-mass or larger thing sneaking up on us, we're talking a time scale of
at least 10's of millions of years before the error is up to 1%, I suspect even much longer. For instance, in the late 1980's [the reason I know about this is a random long story itself, almost a surreal...but I won't digress further] a refinement of an earlier calculation method allowed for the prediction of everything from Mars inwards on a scale of 1 INCH of error total over the span of January 2000 Plus or minus 4thousand years. I'm betting there are much better methods and observations now.