Let’s give Galileo a break. As a retired engineer/scientist who is an amateur astronomer and ex-high-power shooter, I’m puzzled.
Stellar parallax is observed, and would prove that the stars are not all at the same distance from earth. But doing so took optics designed by Fraunhofer in the 1820s. Credit for the first measurement is given to Friedrich Bessel for an 1839 measurement of 61 Cygni.
The parallax for the nearest star, Proxima Centauri, is ca 0.77 arc-seconds. Admittedly, this is a half-angle of the observed shift but an arc-second is darn small.
Ca. 1/60th of a marksman’ minute-of-angle, and equivalent to 1 part in nearly 1.3 million or a dime at 3.7 km.
Right. Stellar parallax does in fact exist, but it was so infinitessimal that Galileo could not observe it. And that’s the point: Nicholas di Cusa posited that the universe was unimaginably huge, and not at all organized into the spheres that Galileo’s and Aristotle’s science predicted it was.
Had di Cusa’s work been considered, Galileo and his successors would have realized that the absence of observable interstellar parallax suggested the enormity and complexity of the universe. Instead, following the reductionist principles he elucidated, he presumed falsely a small, simple universe, and ignored the (lack of) observations he could not explain.