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This might be more a question for historians, but it's a question I've given some thought to.

By using what was essentially Euclidean geometry, Aristarchus was able to calculate, with some measure of accuracy, the distance and the size of both the Moon and the Sun. His calculations were off, mostly due to the difficulty in perceiving the variation of shadow on the Moon to Earth, but his method was both sound and reproducible. I've also read that Archimedes knew about and agreed with Aristarchus' theory.

Here's my question, in 2 parts.

Firstly, since the theory was sound and the results reproducible, why didn't it catch on? I know that Aristotle was perhaps more respected and he believed in the geocentric model. Aristarchus followed Aristotle, and science usually moves forward. I would think that good scientists who followed would have known about and recognized the validity of Aristarchus' work, especially since Archimedes agreed with him.

Logically, there's a few possibilities. One, a number of the scientists of the time, 1st and 2nd century BC might have agreed with Aristarchus and it wasn't until later that the Geocentric model became the "accepted truth", or two is that Aristotle was held above reproach, or three, word simply didn't get around very well. I hope anyone can shed some light on why this sound and simple theory didn't catch on.

Secondly, I read that Ptolemy, a couple century's later, found the idea of Earth spinning at $1,000\ \frac{\text{miles}}{\text{hour}}$ too improbable, so he became the champion of geocentrism, even had the model named after him, but in the 300 or so years between Aristarchus and Ptolemy, why didn't Aristarchus' theory stick?

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    $\begingroup$ Because there were not compelling evidence regarding the truth of the heliocentric hypotheses. The right level of discussion and rejection of Aristarchus' theory by his contemporaries is still debated; see Aristarchus. The fact that A's works has not survided can be due to the overwhelming influence of Arsitotle, with his support of geocentric theory. Aristotle physical theories was hardly compatible with the idea of Earth moving around the Sun, but the hsitorical issues realted to this debate are multiple and interesting. $\endgroup$ – Mauro ALLEGRANZA Feb 16 '15 at 10:34
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    $\begingroup$ First, Archimedes did not agree with Aristarchus, he just mentioned his view along with the geocentric one. Second, Hipparchus followed Aristarchus and his geocentric models made much better predictions, so the science did move forward. And third, if we measure "soundness" by what we know today then Democritus, who advocated infinite universe with multiple worlds, was way "sounder", and he lived two centuries before Aristarchus. $\endgroup$ – Conifold Feb 16 '15 at 20:00
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    $\begingroup$ The first long paragraph describes measurements of distance and size. The last three paragraphs discuss heliocentrism versus geocentrism. I don't see any connection here...? $\endgroup$ – Ben Crowell Feb 16 '15 at 21:28
  • $\begingroup$ @Ben, that occurred to me as well, but I would think the measurement that the sun was significantly larger than the earth might logically lead to the earth going around the sun. But, you and others are right, it's not a sound proof that the earth goes around the sun, but his estimates of the Sun's size do appear sound and hard to argue with, if not perfectly measured. But you're right, I hadn't really thought the connection between those 2 ideas through. $\endgroup$ – userLTK Feb 17 '15 at 10:12
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    $\begingroup$ On a similar note, incorrect estimates of the apparent sizes of the stars were used as an argument against heliocentrism in the era of Galileo: arxiv.org/abs/1211.4244 $\endgroup$ – Ben Crowell Feb 18 '15 at 6:13
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I agree with the answer of David, but I would like to add few points to it:

  1. It is a common misconception that Aristarchus found (or attempted to find) the sizes of Sun and Moon or distances to them. What his surviving book contains is a method of finding the RATIO of the distance to the Sun to the distance to to the Moon. He estimated this ratio (with a gross error) and it is likely that he made no actual observations.

The only way to find the distance to the Moon available to the ancients was measuring its parallax and finding the radius of the Earth. The early attempts to estimate the distance led only to the statements that "Moon is probably bigger than Peloponnese".

Archimedes (in Psammites) briefly mentions various opinions on the sizes of Sun and Moon, and says that "according to majority of astronomers Sun is bigger than the Earth". Ptolemy, who wrote much later computed that Sun is 5 1/2 bigger than Earth (diameter).

  1. I am sure that astronomers of antiquity as well as later ones understood that kinematically the heliocentric system is EQUIVALENT to the geocentric one, and the choice between them is a question of mathematical convenience.

To decide what "really rotates about what" one needs physics (dynamics). And all reasons which Ptolemy gives against rotation of the Earth (I mean rotation about its axis) are based on physics. And his physics was wrong. Galileo's physics which he used to justify heliocentric system was also wrong by the way.

To refute that Earth has any other motion, Ptolemy refers to the absence of parallax. And he is right. More than 1000 years had to pass before parallax could be observed.

The correct physics was discovered by Newton, and the acceleration of the Earth was confirmed experimentally only in 18-th century.

The argument that Sun is bigger than the Earth does not prove anything: who knows what the Sun is made of? Perhaps it is bigger but the Earth is heavier? Comet tails are much bigger in size than the Sun, btw.

To conclude, there was no real reason in antiquity to prefer the heliocentric system in comparison with geocentric one. Physics was not sufficiently developed.

And without physics the question is meaningless.

EDIT. Let me use this opportunity to explain one general misunderstanding which is very common (see the comments of David Hammen). All scientific theories are APPROXIMATIONS to reality. Every scientific theory explains certain class of phenomena. We do not have and probably will never have a "theory of everything" which will explain everything, with absolute precision. So it is WRONG to say that Newton mechanics is "incorrect". It is correct. It is one of the MOST SUCCESSFULL scientific theories ever found. It explains the motion of planets perfectly (except ONE very small correction related to Mercury). It explains a lot of other things, and a lot of technology is based on it. But it was never supposed to explain such things as light or electricity.

This is why it is CORRECT, and this is why it is taught in all physics courses.

Electromagnetism and the workings inside the atom are simply out of the scope of classical mechanics. And we have different theories which explain these things.

The question was about motion of planets. Motion of planets is COMPLETELY explained by Newtonian mechanics (except one little correction that I already mentioned).

Similarly, Ptolemy's theory is CORRECT. It explains and permits to predict the motion of the planets. Look at the modern Astronomical Almanac. It describes the motion of the planets in Ptolemy's terms! And to compute this almanac, trigonometric series are used (which is the same as epicycles). It is another matter that we have different theories about planets which are better for other purposes. But Ptolemy's theory does what it is supposed to do.

On the other hand, Aristotle's physics is INCORRECT. It cannot be used to predict anything quantitatively. It contradicts the experiments.

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    $\begingroup$ No!!! Newton's physics is correct! It is a complete misunderstanding of science and its history to say that it is wrong. Newton physics is taught in all universities nowadays. Why would they teach a wrong thing?!! $\endgroup$ – Alexandre Eremenko Feb 17 '15 at 2:52
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    $\begingroup$ Newtonian mechanics is demonstrably wrong with regard to many aspects of electromagnetism. Late 19th century physics was all about reconciling the mismatch between Maxwell's electrodynamics and Newton's mechanics. Newtonian mechanics is also demonstrably wrong in the regimes of the very, very small (quantum mechanics), the very, very large (cosmology), the very, very fast (special relativity), and the very, very massive (general relativity). $\endgroup$ – David Hammen Feb 17 '15 at 6:04
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    $\begingroup$ Newtonian mechanics is still taught for two primary reasons. One is that it is approximately correct in a narrow but very important regime, the regime of ordinary life. The other is that it is an important stepping stone to understanding quantum theory, relativity theory, and cosmology. $\endgroup$ – David Hammen Feb 17 '15 at 6:06
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    $\begingroup$ @Javier: The Greeks did measure Moon's parallax, and you do not have to travel to do this. But they could not measure it accurately because they did not have good measuring devices. $\endgroup$ – Alexandre Eremenko Feb 19 '15 at 12:53
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    $\begingroup$ @Javier: Newton mechanics is used not only to launch missiles, but also to build houses and automobiles, bridges and roads, and most other object that surround you. But many modern people d not notice these objects, and see only their iPhones. $\endgroup$ – Alexandre Eremenko Feb 19 '15 at 12:57
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Firstly, since the theory was sound and the results reproducible, why didn't it catch on?

Aristarchus' heliocentric model was not sound and the results were not reproducible. Not only was there an utter lack of compelling evidence for Aristarchus' heliocentric point of view, there was an immense amount of compelling evidence against that point of view given the theoretical and observational science of the time. Evidence for? None. Evidence against? No parallax (it wasn't until 1838 that astronomers (Bessel) finally did see parallax) and nonsensical physics given the physics everyone at the time "knew" was right.

The modern view naively presents Aristotle and Ptolemy as incredibly dumb. They were not. They rank amongst the most brilliant people of all time. Their science withstood the test of time for two millennia. Newton? His science withstood the test of time for a mere 300 years. Einstein? His special relativity withstood the test of time for just a decade, when Einstein himself introduced general relativity. Everyone knows that general relativity too is somehow wrong, they just don't know how.

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  • $\begingroup$ Derision of Aristotle and Ptolemy hasn't been the modern view for a while now as even Wikipedia articles on them show for example. $\endgroup$ – Conifold Feb 16 '15 at 20:03
  • $\begingroup$ Well, I certainly didn't mean to present Aristotle as dumb since his views made sense and he came first. I have considered questioning Ptolomy's judgement on choosing Aristotle's model when he had both theories available to him. But, that was part of why I asked the question, to see what else might have happened in that time in between. $\endgroup$ – userLTK Feb 17 '15 at 10:19
  • $\begingroup$ @userLTK In Hellenistic times Aristotle was not the authority he became during middle ages. Apollonius and Hipparchus rejected his astronomy based on homocentric spheres of Eudoxus, replacing it with epicyclic models that were computationally simpler and more precise (more precise than Aristarchus's too). After that Hellenistic science fell on hard times for two centuries due to Roman conquests, but Ptolemy inherited epicyclic astronomy from Hipparchus, not Aristotle, and made it more precise with equants, that were incompatible with Aristotle's physics, even as he paid lip service to it. $\endgroup$ – Conifold Feb 17 '15 at 18:56
  • $\begingroup$ Your last paragraph only implies that humanity's knowledge increases faster as time goes by, not that Aristotle or Ptolemy were smarter than Newton, Einstein, or anyone for that matter. $\endgroup$ – hjhjhj57 Feb 19 '15 at 4:47
  • $\begingroup$ We don't know that general relativity is wrong, we know that it's incompatible with quantum mechanics. It's still an open question as to which one is wrong. $\endgroup$ – Mark Jul 19 at 22:50
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Alexandre has given a very good answer to this question, but I have some remarks about his conclusion:

“To conclude, there was no real reason in antiquity to prefer the heliocentric system in comparison with geocentric one. Physics was not sufficiently developed.”

This is true not only “in antiquity”, but also for Copernicus, and even for Kepler, don’t you think? For Copernicus the attraction of the heliocentric model was that it is more economical with regard to perceived motions, not that it was better physics.

Aristotle’s development of the Eudoxian model makes sense within the framework of Aristotle’s own physics (the element aether has an inherent circular motion around the centre of the cosmos), but it was soon rejected in favour of Ptolemy’s cycle/epicycle theory, which is a purely mathematical model that makes no pretence of offering a physical explanation of the movements.

The reason the heliocentric model was rejected is that it is counterintuitive. It says that the earth is spinning around its own axis, but our sensory perception is that we are standing still. Why don’t we feel the earth rotating?

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  • $\begingroup$ Actually, Ptolemy makes every pretense of adhering to Aristotelian cosmology. He describes it at the opening of Almagest and in greater detail in Planetary Hypotheses (epicycles are smaller spheres embedded into homocentric ones). He never explains how equant fits into it though, or even acknowledges the issue, which later led many Arabic astronomers to treat his models as pure mathematics, and even to look for epicyclic replacements for the equant. $\endgroup$ – Conifold Feb 17 '15 at 18:41
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    $\begingroup$ You are right. Physics was not "sufficiently developed" neither at the time of Copernicus nor at the time of Galileo/Kepler. As I said, Galileo's physical arguments in defense of heliocentrism were wrong. Which is amazing: Galileo contributed so much to the development of physics:-) $\endgroup$ – Alexandre Eremenko Feb 18 '15 at 0:11

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