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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?

userLTK
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    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. – Mauro ALLEGRANZA Feb 16 '15 at 10:34
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    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. – Conifold Feb 16 '15 at 20:00
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    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...? –  Feb 16 '15 at 21:28
  • @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. – userLTK Feb 17 '15 at 10:12
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    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: http://arxiv.org/abs/1211.4244 –  Feb 18 '15 at 06:13

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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.

Alexandre Eremenko
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  • Newton's physics was wrong, too. Relativity theory and quantum mechanics are better models of reality than is Newtonian mechanics. Even these aren't perfect; a good chunk of the money in theoretical physics goes toward replacing GR and QM with an even better model (and thereby showing GR and QM to be wrong). This however brings up the issue of wronger than wrong. – David Hammen Feb 16 '15 at 21:48
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    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?!! – Alexandre Eremenko Feb 17 '15 at 02:52
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    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). – David Hammen Feb 17 '15 at 06:04
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    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. – David Hammen Feb 17 '15 at 06:06
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    @David Hammen: as I said, your comments show that you do not understand what science is. Unfortunately the space allowed for comments does not permit me to explain. (Otherwise I would be glad to). – Alexandre Eremenko Feb 17 '15 at 21:03
  • @AAlexandre Eremenko - Get a mirror, look in your reflection. Scientists from Newton's age thought they were uncovering the true nature of the universe. It turned out they weren't. Scientists of today aren't quite so bold or arrogant. They have seen multiple theories, including Newtonian mechanics, proven to be false. Modern science is an attempt to build ever improving models. Very few are so arrogant to claim that the models they create are "true". – David Hammen Feb 17 '15 at 22:52
  • @David Hammen: Scientists from the age of Archimedes and Ptolemy understood what they are doing. If you want to learn what science is about, better read and listen to them, rather than to people who do not understand what they are talking about. – Alexandre Eremenko Feb 17 '15 at 23:27
  • Your update is completely wrong, wrong enough that I have to downvote. Newtonian mechanics is a falsified theory. Moreover, unless by modern you mean pre-Keplerian, there is nothing remotely resembling Ptolemy's theory in the modern Astronomical Almanac. The modern Astronomical Almanac is based on the JPL Development Ephemerides (DE 405, which is a bit out of date now). The JPL Development Ephemerides account for relativistic effects, and not just for Mercury, but for every body in the solar system. – David Hammen Feb 17 '15 at 23:46
  • @David Hammen: I am not going to argue with you. I only can give you an advise: do not tell this to your physics teacher (that Newton's mechanics is "wrong"). Concerning your downvote: I do not care, of course. My goal in this site is not to maximize my "reputation" :-) – Alexandre Eremenko Feb 18 '15 at 00:07
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    I wanted to just put this out there. One, I liked Alexandre's answer very much and I appreciate it. I also, personally, find it offensive to an extent that somebody would go on about how Newton was wrong. Whether he was wrong or not is largely a matter of semantics and on that point, I don't care, but his equations were correct in the sense that they explained not only what was observed, but could predict what would happen in given circumstances. That's very different than Kepler not recognizing the inverse square which I didn't know, as that would generate very wrong calculations. – userLTK Feb 18 '15 at 02:43
  • @David, Whatever terminology you want to use, I had no idea that Galileo's model was wrong (point made above), so to me, that's very cool. I'll have to look that up. The simple truth is that Newton's models could be built upon without correction, and that's an important difference. incorrect models, not necessarily dumb, are harder to build on. So, If you must say Newton was incorrect, which I don't personally like, at least recognize that there are different levels of incorrect and Newton's "incorrect" was the foundation of science for 200 years and it's still used today. – userLTK Feb 18 '15 at 02:54
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  • Well, I believe Newton's mechanics are still used to launch rockets into space.

    • $$ $$ 2)Was the lack of measurable parallax in the Moon because ancient greeks wouldn't travel far enough?

    – hjhjhj57 Feb 19 '15 at 04:57
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    @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. – Alexandre Eremenko Feb 19 '15 at 12:53
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    @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. – Alexandre Eremenko Feb 19 '15 at 12:57
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    @hjhjhj57 The parallax of the Moon is very hard to see and measure because it's only about 1 degree in the best circumstances. Greater distance might have helped, but it had more to do with the telescope and better measuring devises. Lunar parallax wasn't accurately measured until the 18th century. – userLTK Jul 19 '17 at 17:27
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    @userLTK: This is not true. Lunar parallax was known to Ptolemy, even if he did not measure it accurately, and one degree is a substantial angle, even with the ancient observation techniques. After all, the visible diameter of Sun and Moon is about 1/2 degree. This is a big angle! – Alexandre Eremenko Jul 19 '17 at 20:50
  • @AlexandreEremenko it was known but it was hard to measure. I think the answer to hjh's question is better equipment. – userLTK Jul 19 '17 at 20:55
  • @userLTK: I disagree. There was no progress in equipment between Ptolemy and Copernicus. In fact Copernicus had to make his instruments himself, and judging from descriptions they were more primitive than what Ptolemy describes. – Alexandre Eremenko Jul 19 '17 at 21:00