# How Galileo could both possibly say that Earth is revolving around the Sun and develop the Galilean relativity?

I always have been curious about this part of the History of Science. To claim that Earth is orbiting the Sun instead of the opposite is equivalent to change one absolute referential (Earth) to another one (the Sun); something Galilean relativity forbids. So how come Galileo is credited for both the statement and the theory?

• Galilean relativity concerns inertial frames, i.e. those moving linearly and uniformly. Rotating frames are not inertial, so between the Earth and the Sun the real center of rotation is privileged: centrifugal and Coriolis forces are absent in its frame. Oct 6, 2022 at 17:48
• Galilean relativity is a group transformation that states, among other things, there is no absolute referential. Before Galileo, Earth was the center of the Universe, after him, it became the Sun. Both statements are false. In the Earth referential, the Sun is revolving around Earth, it is not an illusion, every year, the Sun comes back to the same position. In the Sun referential it is the opposite. Galileo is the father of the Galilean relativity and most likely understood that. Oct 7, 2022 at 0:18
• You are confusing Galilean relativity with Einstein's general principle of relativity. Galilean relativity easily combines with an absolute frame, which Newton explicitly did in Principia and showed that rotational motion is non-relative, see Newton's bucket. Galileo certainly did not use modern formulations with transformation groups either, even for his case. That is the work of 19th century. Oct 7, 2022 at 4:14
• I am not confusing anything. Classical mechanics is based on Galilean relativity. There is no mechanical experiment that can distinguished two referentials in mutual translation and therefore there is no absolute referential. When Maxwell's equations were developed, Lorentz found out it was incompatible with the Galilean group and derived its transformation. tau.ac.il/education/muse/museum/galileo/… Oct 7, 2022 at 14:09
• If you do not know the answer, that's fine, but please do not try to answer. aapt.scitation.org/doi/10.1119/10.0000303 Oct 7, 2022 at 14:18