Geocentric and heliocentric models are interchangeable under GR coordinate systems. Einstein admitted as much and so did Hoyle. Ernst Mach proved that the laws of geometry would be violated if there were any essential defference. If you can't see that heliocentric and geocentric models are interchangeable, then you have the wrong understanding of the geocentric model, or both.
Michelson-Morley failed to detect the motion of the earth around the sun.
Michelson-Gale detected the relative rotational motion between the earth and the universe, so motion is detectable.
Airey's Failure failed to detect the motion of the earth around the sun.
Apparently it is your understanding of geocentrism that is flawed, not Ernst Mach, Einstein, Hoyle or me.
I'm sure you're right.
So let's just define terms, then.
"Geo-centric" is the word for the concept that the Earth does not move at all. That the rest of the universe is moving *around* the Earth.
"Helio-centric" is the word for the idea that the sun's mass is the center of gravity that holds this system we call the 'solar system' together.
So are you saying you don't believe the Earth moves . . . at all?
Umm, not exactly. They failed to detect the motion of the earth relative to the ether - and so the concept of an ether was discarded. Though, of course, there were those who said that the earth and the ether moved in - let's say - divine harmony.