Stellar parallax was the key to it; Brahe, in particular, insisted that if there was no stellar parallax, there was no reason to prefer Galileo's system over hi

Stellar parallax was the key to it; Brahe, in particular, insisted that if there was no stellar parallax, there was no reason to prefer Galileo's system over his. If memory serves, stellar parallax was only demonstrated in the 1800s -- whereupon the Church issued a statement that Galileo's model was right after all.