We can easily explain the motions of the other heavenly objects if we assume a fixed earth and limit ourselves to their motion relative to us. But when you start trying to explain their motion relative to each other, if you asume a fixed earth it quickly becomes untenable. Copernicus debunked the earth-centric universe in the 16th century.
So the tail CAN wag the dog.
But it would have to wag everything else too.