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?
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3$\begingroup$ 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. $\endgroup$– ConifoldOct 6, 2022 at 17:48
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1$\begingroup$ 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. $\endgroup$– ShaktyaiOct 7, 2022 at 0:18
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3$\begingroup$ 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. $\endgroup$– ConifoldOct 7, 2022 at 4:14
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$\begingroup$ 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/… $\endgroup$– ShaktyaiOct 7, 2022 at 14:09
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$\begingroup$ 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 $\endgroup$– ShaktyaiOct 7, 2022 at 14:18
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For Galileo, the relativity principle was an observational principle. When he writes about the thought experiment on a moving ship where the observer cannot recognize that there is movement, it is clear to the reader that it is indeed a moving ship. So for Galileo, there can be an absolute reference system, where the Sun is at the center, and then there are all these empirically equivalent systems, such as two moving ships, whose movements cannot ever be observed. There is no contradiction between those.
This duality persisted until the early twentieth century. We find this for example in Newton, who believed in absolute space and empirically equivalent inertial systems; in Maxwell, who believed in the ether but whose equations are equivalent for moving systems; and in Lorentz, who assumed an absolute ether system but had it as a principle that the ether contracted in such a way that each inertial system was by principle empirically equivalent. It was only with Poincaré and Einstein that someone thought this duality was particularly problematic.
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$\begingroup$ So basically Galileo was as wrong as the Church by claiming that Earth and the other planets were orbiting the Sun and thus making the Sun an absolute referential. It may be easier to use the heliocentric system for studying the motion of planets but for the 99.9999% of the the population who does not care about that, the Geocentric referential is as good and a more practical choice. $\endgroup$– ShaktyaiNov 2, 2022 at 0:31
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1$\begingroup$ Please note that I have never claimed that Galileo said that the Sun was at the center of the universe. I have noted that claimed that the Earth revolved around the Sun and that this is not necessarily in contradiction to his claim that an observer does not notice the difference between these reference systems. In fact, I was hard pressed to find any statement from Galileo about the Sun in the Universe. You must be careful not to conflate Galileo's ideas with those who followed him. $\endgroup$– cktaiNov 2, 2022 at 7:46