> It seems rather obvious that local space-time curvature
> is definitely affected by the distribution of mass in the
> entire universe and that you cannot think of the solar
> system as an isolated system.
The effects of all the mass in the rest of the universe on the local curvature of space-time in our solar system is ridiculously small compared to the curvature caused by nearby bodies, most especially the sun.
Understanding, rather than assuming, would do you wonders in your arguments.
Try a thought experiment: suppose two observers were measuring the apparent motion of a star. Pick a star, any star. One observer is on the surface of the sun, the other on the surface of the earth. Thanks to a vast, magical power, let's call it "god", you have the ability to make either the sun or the earth wink out of existence briefly, so you do so, first with the sun, then with the earth. In which of these equivalent coordinate systems would there be a sudden, large change in the observed velocity of the distant star?
The observer on the sun would have to have very sensitive instruments indeed to note any change in the distant star's apparent velocity. Leaving aside that the observer on earth orobably would have died to the sudden acceleration when the sun winked out of existence, if his instruments survived they would record a large change in the apparent velocity of the distant star.
GR basically turned the "orbiting" problem into a geometry, albeit 4 dimensional, non-Euclidean geometry, problem rather than a force problem. That obsoleted the old, Newtonian and Copernican terminology, but you can't pretend it validates ancient Hebrew cosmology.
And the distance that the center of gravity must be moved to conform to a geocentric model is likewise 'ridiculously small'.
Your logic is invalid in that you consider the space-time curvature in local terms when I have explained more than once that you must consider the space-time curvature in universal terms.
But you merely go back to error that heliocentrists always make. That is the error of ignoring the rest of the universe while the geocentrists always properly include it. That is something that Einstein and Hoyle properly understood, but heliocentrists try to avoid at all costs.
"GR basically turned the "orbiting" problem into a geometry, albeit 4 dimensional, non-Euclidean geometry, problem rather than a force problem. That obsoleted the old, Newtonian and Copernican terminology, but you can't pretend it validates ancient Hebrew cosmology."
Oh, it didn't 'obsolete' anything. What GR did was reconcile the lack of evidence for earth's *assumed* orbital velocity with the lack of evidence thereof.
And you can't honestly pretend that GR invalidates geocentricity either, but you'll try your best...