Regner stated: But if all the stars, and with them, all the galaxies, are centered on the Sun, what then is centered on the Earth, justifying the label of "Geocentric Universe"??? I agree in principle with the essence of that question, that is exactly why I have never liked that idea ( although that does not mean it is not posible) ....however......If the stars are centered on the Earth, there would be no parallax. I believe we agree on that, correct? To know and or claim that parallax is proof for the proper motions when the proper motions of the stars themselves must be assumed to make any such deductions .....is the very question under consideration!?......that is not just presumptuous but So if the observations of sun planet and stars timing is not observed as perfectly consistent ..............ummmm............again you must demonstrate the observation that shows it is just an illusion first before you assume it is just an illusion that then can be used to interpret the observations from.....! It amazes me you cant see your own inconsistencies in both your methods used to frame your arguments as well as the substance of your arguments themselves.... .... ..well silly.... Your statment would only be true if and only if you first assume that the sun & or back ground stars have no other intrinsic or distinguishable proper motions external of a smooth consent velocities in orbit or in a rotating universe...and why would it?!....any given rotating mass has intrinsic vibrations and uncertainties to it no matter how "balanced" it is,......... in fact you can't have any motion without vibrations.......ummm.........worse assume that the sun has no other intrinsic orbital variations it is timing.......Now that it quite a presumption..because the sun and moon are erratic and never ever have perfectly identical circuit times....hence the use of atomic clocks rather then just timing the good olʼ sun& moon.........ummmm......