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As far as I know, while Galileo's hypothesis about the tides was wrong, his discovery of the phases of Venus while passing the sun should have been sufficient to leave the geocentric crystal spheres shattered - figuratively and literally.

But in the context of an answer to another question (https://philosophy.stackexchange.com/a/50328), comments claim the reasons Galileo gave for the heliocentric model were no good science at all.

That seems suspicious to me but I thought I'd better get an expert's view on how valid Galileo's arguments were.

I don't know the exact reasons for the criticism, maybe someone who shares it wants to elaborate here; otherwise I'd be happy with a short summary of the scientific "canon" view on the topic.

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I assume the doubts refer to the commentary on Dialogue Concerning the Two Chief World Systems in The Galileo affair: who was on the side of rationality? on Less Wrong. I do not believe that Galileo's case was as weak as the post suggests.

The main objections to heliocentrism and rotating Earth were known since antiquity: the absence of stellar parallax or of fly-off (to which more subtle "Coriolis effect" was added later). There was little that either Copernicus or Galileo could say about the former, other than to speculate that the stars are too distant for the effect to be measurable. The parallax was only measured in 1838 by Bessel. As for the fly-off argument, Galileo's experiments illustrating the relativity of motion, such as descriptions of events on a moving ship, were directly meant to disarm it.

Galileo's arguments were also aimed at undermining geocentric Aristotelian physics generally, e.g. it explanation of falling bodies by their movement to their "natural place", the center of the Earth, mentioned in the post. According to Aristotle, the "degree" of attraction depends on the body's weight, heavier bodies fall faster. This idea was mocked by Philoponus already in antiquity, and Galileo's famous thought experiment with tying two bodies together to show that their weights are moot was also plausible if not logically airtight, see Is Galileo's argument about falling bodies logically flawed?. So, contrary to the psot's author, this was not a particularly strong argument for geocentrism at the time. It is true, however, that Galileo did not have an alternative comprehensive dynamical theory to replace Aristotle's, that would only come later, with Descartes, Huygens and ultimately Newton.

Judging the tidal argument "silly" is anachronistic. Yes, Galileo thought that the tides are due to the rotating Earth rather than Moon's gravity, and that would not work under Newtonian dynamics. But there was no Newtonian dynamics at the time, and the implied effect is real, it explains Earth's bulged shape if not the tides. And the geocentric allusion to "Moon's influence" had no basis in Aristotelian physics of natural places. The connection was based on observed correlations, not on any geocentric insight, and so provides no support either way.

The main contemporary arguments for heliocentrism are not even discussed there. We are not talking about the time a century earlier when Copernicus still had to use epicyclets and excenters to match his system to observations. After Kepler replaced circles with ellipses the match heliocentric system provided was unparalleled. One would need towers of epicycles to get the same precision geocentrically. And trying to incorporate ellipses into something like Tycho Brahe's hybrid system would upend Aristotelian physics anyway. In fairness, Galileo himself mentions neither Tychic system nor elliptic orbits in the Dialogue.

But Galileo's own discoveries of the moons of Jupiter and of the phases of Venus did appear, and suggested that the Earth was no special "natural place". Kepler already speculated about gravity like effects, see Who was first to explain intuitively the inverse square law of gravity?, his speculations were based on Gilbert's theory of magnetism, which Galileo explicitly invokes in the Dialogue.

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  • $\begingroup$ Since comments to the other answer question the relevance of the phases of Venus, could you maybe extend your answer to discuss that point, giving sources if possible? I guess that will have to be the deciding factor which answer I accept. $\endgroup$ – elias_d Apr 6 '18 at 4:55
  • $\begingroup$ @elias_d Both heliocentric and epicyclic orbits produce phases of Venus, but the heliocentric ones that Galileo observed are more pronounced. The idea was proposed as a deciding experiment by Castelli in 1610. He thought they would also rule out a Tychic system, but Riccioli pointed out in 1651 that they do not. See a nice discussion on Renaissance Mathematicus. Heliocentric and Tychic systems rule out Aristotelian physics, crystal spheres were not taken literally already at the time of Copernicus. $\endgroup$ – Conifold Apr 6 '18 at 16:21
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Galileo had no proof of heliocentrism, and no proof of the diurnal rotation of the Earth. His main argument was about tides, and this argument is incorrect. Moreover, it contradicts Galileo's own mechanics, namely the relativity principle. (Contrary to what Conifold writes, the foundations of mechanics are due to Galileo, not to Newton. But when he became engaged in this Earth rotation polemics, he somehow forgot his earlier discoveries). Of course, heliocentrism was an attractive hypothesis since Copernicus, but certainly there was no proof of it.

In fact this question does not deserve the attention which it attracts: it is a question of the choice of a coordinate system, and the choice of a coordinate system is actually a question of convenience. Geocentric co-ordinates are still widely used in many problems, whenever convenient. So "heliocentrism" belongs more to philosophy than to science.

Earth diurnal rotation is another matter. This is something which can be proved or disproved by experiment and various experiments were proposed. But as far as I know the first decisive and successful experiment was Foucalut pendulum, and this was much later than the time of Galileo. By the way, the main subject of "discussion" between Galileo and Catholic church was diurnal rotation, not heliocentrism. And both sides used wrong arguments in this discussion.

Kepler's great discovery that the orbits are actually ellipses, not circles, or combinations of circles was truly revolutionary, and it led to replacement of Ptolemy's system by the new one. But this has nothing to do with Galileo: Galileo never even mentioned Kepler's laws in his writings!

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  • $\begingroup$ How do you judge the argument about the phases of Venus? $\endgroup$ – elias_d Apr 5 '18 at 5:32
  • $\begingroup$ The argument on the phases of Venus only shows that Venus is illuminated by the Sun (does not shine with its own light). $\endgroup$ – Alexandre Eremenko Apr 5 '18 at 14:47
  • $\begingroup$ Are you sure we're talking about the same thing? As far as I know, what Galileo discovered was that when Venus passes the sun (i.e. disappears as evening star and reappears several days later as morning star, or vice versa), it is sometimes nearly in "full-moon"-phase (i.e. behind the sun), but at other times instead nearly in "new-moon"-phase (in front of the sun). I don't know if the prevailing view at that time still was that the planets are attached to crystal spheres - those spheres would be left shattered. (...) $\endgroup$ – elias_d Apr 5 '18 at 17:43
  • $\begingroup$ (...) Even without spheres, the distance of sun and Venus to earth could not be constant anymore, so they could not move in geocentric circles. $\endgroup$ – elias_d Apr 5 '18 at 17:43
  • $\begingroup$ @elias_d: In geocentric systems (of Ptolemy and Brahe) the planets do not move on circles centered on Earth. They move on more complicated curves obtained by combinations of circles. $\endgroup$ – Alexandre Eremenko Apr 5 '18 at 19:07

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