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Many factors in history have contributed to society's taking a long time to accept the heliocentric (= the Earth orbits the Sun) model: the first that come to mind immediately are religion and, more generally, people's instinctive resistance to drastic changes in ideology.

While the sphericity of the Earth was widely recognized in Greco-Roman astronomy from at least the 3rd century BC, the Earth's daily rotation and yearly orbit around the Sun was never universally accepted until the Copernican Revolution.

Moreover, the Copernican model was devised in 1543, but was accepted by no more than a few astronomers until the 17th century, when - among other things - the use of telescopes provided a lot of proof which favored the heliocentric model over the Ptolemaic model.

So considering religion, generic resistance to change, and technology, what would need to have been different in our history in order to lead to an earlier (let's say 1200s, but the earlier the better) wide acceptance of the modern heliocentric model?

Andreas Cellarius's illustration of the Copernican system, from the Harmonia Macrocosmica

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    $\begingroup$ The major show stopper was that in the Antiquity and the Middle Ages astronomers were searching for a model using only circular and uniform motions. The major breakthrough in favor of the heliocentric model was Kepler's discovery of the laws of planetary motion, based on Tycho Brahe's lifelong observations. These provided a better predictive power with a much simpler model. Until that time there was no compelling reason to change the model. $\endgroup$ – AlexP Feb 2 '18 at 15:23
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    $\begingroup$ There is some interesting stuff at the end of section en.wikipedia.org/wiki/… on how the helocentric view prevailed in the 17th century. It might give some clues as to how to proceed. $\endgroup$ – P Chapman Feb 2 '18 at 17:15
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    $\begingroup$ Doesn't really answer the question, since it doesn't apply to OUR solar system, but in an alternate universe where Venus has a large moon similar to Luna, which early astronomers would be able to see much easier than the moons of Saturn, they'd know that things orbit other planets than ours, and so heliocentric makes more sense than geocentric. Credit for original idea goes to Terry Pratchett. $\endgroup$ – AndyD273 Feb 2 '18 at 18:15
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    $\begingroup$ I think you're leaving out the fact that a totally naive observer on the surface of the Earth would be initially inclined to interpret what they see and feel as standing on a flat, fairly level surface with a sky above them that changes and whirls around them. The ground doesn't look curved away from them and they don't feel like they are moving at all. I'd say that "first impression" is a bigger factor than religion. Look at modern flat-earthers; there doesn't seem to be any religious aspect to their... viewpoint. $\endgroup$ – Todd Wilcox Feb 2 '18 at 20:11
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    $\begingroup$ Teach everyone to value the Scientific Method and science. The rest follows. You'd have semiconductors by 1450, Shakespeare would have a mobile, Liza Bennett would have a teleporter. $\endgroup$ – Harper Feb 3 '18 at 19:04

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First of all, we have to recognize that before Newton's laws of motion and law of universal gravitation, and before the advent of telescopic astronomy, the only two criteria which an astronomical model had to satisfy were elegance (how simple it was) and accuracy (how well it could predict the positions of the planets). There was nothing else to judge.

To understand why the ancients didn't fall for a heliocentric model, we must understand what Ptolemy’s, Copernicus’s and Kepler’s model were.

  • Ptolemy's model works like this:

    • Earth is a sphere, fixed and imobile.

    • Everything else rotates around the center of the Earth in a uniform circular motion, completing a rotation in 23 hours, 56 minutes, and 4 seconds (a sidereal day); this is called the first or diurnal motion.

    • For the fixed stars, that’s all there is.

    • Each of the seven classical planets (the Moon, Mercury, Venus, the Sun, Mars, Jupiter, and Saturn) executes two supplementary circular motions:

      • A circular motion along a path called the deferent, the center of which is not the center of the Earth, but a point called the eccentric; this second motion is uniform with respect to a point called the equant, which is placed on the line from the center of the Earth to the eccentric, at a distance from the eccentric equal to the distance between the eccentric and the center of the earth — that is, the eccentric is exactly midway between the equant and the center of the Earth. This motion describes the movement of the center of the third motion. The duration of one complete revolution of the second motion is what we call orbital period.

      • A uniform and circular third motion on a path called the epicycle around the point executing the second motion.

  • Copernicus’s model is almost the same, just considering the Sun fixed. Earth rotates around its axis (replacing Ptolemy’s first motion) and moves on an epicycle which moves on a deferent which revolves around an eccentric with uniform angular speed with respect to an equant (thus mimicking Ptolemy’s second and third motions) etc. There is nothing to choose between Ptolemy’s and Copernicus’s models, they are almost equivalent from a kinematic point of view; they describe very similar motions, differing only in the frame of reference.

  • Kepler’s model is radically different:

    • The sun is a fixed and immobile sphere with respect to the fixed stars.

    • Earth, Mercury, Venus, Mars, Jupiter, and Saturn move along elliptic paths, with the Sun in one of the foci; their motion is such that the line from the Sun to the planet sweeps equal areas in equal times (areal uniformity).

    • The cube semi-major axis of each ellipse is proportional to the square of the orbital period.

    • The Moon executes a similar motion around the Earth.

    • The Earth rotates around its axis, completing one rotation in a sidereal day (23 hours, 56 minutes, and 4 seconds).

Kepler’s model is kinematically different from Ptolemy’s or Copernic’s models, which are equivalent. That is, when computing the future position of the Sun, the Moon, Mercury, Venus, Mars, Jupiter, or Saturn at a future date, Ptolemy’s and Copernicus’s models give very similar results, while Kepler’s gives a different result.

Johannes Kepler was stimulated to develop a new model because he had access to the fantastically accurate observations made by Tycho Brache at his fantastically expensive Uraniborg observatory. These observations did not match the predictions of the Ptolemaic model. They matched the predictions of the Keplerian model. Game over.

As history is prone to irony, within Kepler’s lifetime the arguments in favor of his model accumulated: Galileo Galilei discovered the Galilean satellites of Jupiter, the phases of Venus (which were simply impossible to explain in a Ptolemaic framework, but were explainable in the kinematically equivalent Copernican model), and the rotation of the Sun around its axis. Nevertheless, the only decisive advantages the Keplerian model had were its simplicity (only eight motions instead of 15) and its better accuracy.

Then came Newton, and the Keplerian model was shown to be a direct consequence of three simple laws of motion and one simple law of universal gravitation.

So, how could a heliocentric model be favored in earlier times?

  • First of all, the rotation of the Earth could have been proven using an experiment similar to Foucault’s pendulum. There is nothing in Léon Foucault’s 1851 experiment which could not have been done in 1581 ,or 1081, or 581 or even 81 CE. They just didn’t think of it — and they did not study pendulums very carefully before Galileo. They could have, but they didn’t.

  • Then there was nothing revolutionary in Tycho Brache’s Uraniborg. It was the most advanced naked-eye observatory ever built simply because it was the biggest and by far the most expensive: to build it, king Frederick III of Denmark allocated 1% of the state’s budget per year for five years. No astronomer before or after Tycho Brache ever had such budget.

  • Kepler was very good at numerical calculations and very dedicated. When Tycho asked him to recalculate the orbit of Mars in accordance with the new precise observations, Kepler first set to compute it using Ptolemy's model. After many months of calculation he achieved an accuracy of 2 to 8 arc-minutes, but he wasn't satisfied; he then began trying to replace circular motions with various ovoid shapes; at the 40th attempt he tried an ellipse and his law of uniform areal motion: and it worked to better than 1 arc-minute. In the antiquity, only Archimedes was as good and dedicated at numerical calculations, and Archimedes was not interested in astronomy.

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    $\begingroup$ “before Newton's laws ... the only two criteria which a ... model had to satisfy were ... how simple it was ... and accuracy” these are arguably still the criteria for a modern model of anything. $\endgroup$ – leftaroundabout Feb 3 '18 at 17:44
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    $\begingroup$ @leftaroundabout: We generally like to make the model work in a way analogous to the way the modeled system works. It's only when we have no idea how the system actually works, or when the actual physics is too complicated, that we use empirically determined models. For example, the perceived lightness of a light source is related to its physical intensity by a relationship approximating a power law; we cannot derive it from first principles, so we use one of several empirical models, such as sRGB. $\endgroup$ – AlexP Feb 3 '18 at 18:51
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The heliocentric model already had support long before the time period you are after (1200s). In fact, some of the Greeks tried to prove the heliocentric model thousands of years ago. There was also religious support for the heliocentric model even before that.

Technology: Greeks

There were some bright Greek astronomers who were on the right track and viewed the cosmos similarly to how we do now. They realized that if Earth is orbiting around the sun, then there should be a calculable parallax for the stars. That is, if you make astronomical observations at one point in the year, then you make the same observations precisely 6 months later - when we would be on the opposite side of the sun - we should have moved enough to see some of the stars in the sky change location relative to each other.

The calculations are simple trigonometry. The Greeks tried it, and calculating the trigonometry would have provided difficult to dispute proof of the heliocentric model.

Interesting side-note: According to the Wikipedia page on trigonometry, "The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies". The study of triangles started long before that; this is referring to trig much more as we know it today. So it was the astronomical observations and debates much like the one that we are discussing in this Q&A that actually established current trigonometry.

The problem, which the Greeks were unaware of, was that even the closest stars are so unreasonably far away that the parallax is so small that you need a descent telescope just to measure it. The Greeks were so close to proving the heliocentric model, but their astronomical observations just did not provide enough precision to discern the parallax. And so the geocentric model had a victory instead of the heliocentric model.

So the answer to your question here is to provide the Greeks with better astronomy equipment. That shouldn't be too difficult. Just shift the timeline of the telescope forward by giving them an improved control over optics.

Citation for the stellar parallax, including the Greek use of it.

According to the above source, from Penn State, the stellar parallax observation was not successfully done until the 1800s. So you might need to shift the development of telescopes forward a lot. Though usually developments take many generations, it is not unheard of to make drastic leaps and bounds in 1 generation if you get a dedicated individual who devotes their life to it, such as was done for clocks when moving from weighted systems to springs. You could have a history where a Greek person obsessed with optics spends his life pushing the telescope hard shortly before the heliocentric debate happens.

Religion: The Diplomacy

(Edit: See new note at bottom of this section)

Religion itself was not a barrier to the heliocentric model. At least, the predominant Abrahamic religions (Judaism, Islam, Christianity) were not; I cannot say with confidence about other religions.

If you are thinking about the catholic church's blocking of the heliocentric model, considering it heresy, that was not a religious issue. That was purely a diplomatic issue. The catholic church was a governing structure which relied on its word being unquestioningly accepted. If the catholic leadership allowed their word to be questioned, they lost their power. The catholic church's actions should be viewed as the actions of a government, not a result of religion.

In fact, ancient texts used by the Jews, Christians, and I think the Muslims too actually support the heliocentric model. Despite the catholic church's own proclamations otherwise (which was essentially heresy by the church government), their bible actually states that the Earth is what moves through space. Earth is said by the bible to be a sphere that travels through space, and yet many of the governing leaders who abused the faith of their followers tried for centuries to tell us that the Earth was flat or that it was the stationary center of the universe, despite that bible.

So religion itself actually supports the heliocentric model, but the people did not accept that.

So the answer to your question as far as religion is concerned is to change the people somehow so that they are not arrogant jerks (not the words I want to use, but I'm keeping it G-rated). Let religious people actually practice their religion and develop it instead of having dictators pervert religion to their whims. Wouldn't that be grand? In theory, this is actually a smaller and easier change than the one above about changing the history of optics, but in practice changing people to be better is very difficult.

Please note: I am trying to find sources for my claims in this section. It is easy to find the claims in the bible that Earth is round and suspended in space, but I am having difficulty finding the one I recall about it actually moving through space. Also, some people are pointing out in comment the supposed biblical evidence for flat earth and geocentric models: to that, I suggest people take notice of the fact that the sections that sound geocentric are often in symbolic, metaphoric sections (ex: Psalms is literally a collection of songs and poems), and I find such biblical geocentric claims to be weak personally - but yes, there are hints of geocentric ideas as well. I would also point out that the biblical heliocentric support is generally in the more literal sections. Overall, feel free to take the biblical claims with a grain of salt until such time as I update this section; however, the claim still stands that the catholic blockade of the heliocentric model was, as many catholic actions through history, a diplomatic power play rather than a religious requirement. This is evident in that many supporters of the heliocentric model were themselves very religious Christians as well.

Resistance to Change

Your other issue was the generic resistance to change that many people have.

There is not a lot you can do about this. However, given one or both of the above changes, I don't think you would actually need to do anything else special here.

If the religious texts were actually taken at face value, instead of having governmental perverts keeping people from reading their own religious texts, then the religious groups would have been on board with the heliocentric model.

If the Greeks had made better observations, they would have been on board with the heliocentric model.

The Greeks and the Abrahamic religions were, arguably, the two most influential things in history to much of science and art that would follow, even to this day. If the people in both those camps supported the heliocentric model, I don't think there even would have been a change necessary, as it would have been the default.

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    $\begingroup$ Citations needed $\endgroup$ – tar Feb 2 '18 at 17:54
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    $\begingroup$ @tar I'm looking for one for the biblical Earth moving through space part. I know I remember it being there somewhere. As for the stuff about the Greeks, I did that from memory when learning about the history of astronomical ranging from an upper-level astronomy class in college; but I will try to find sources for that too. $\endgroup$ – Loduwijk Feb 2 '18 at 18:14
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    $\begingroup$ @tar I found a great one for the stellar parallax and Greek use of it. It covers everything I said about it in one academic place. Still looking for the biblical citations: I can easily find ones where the Earth is said to be round and suspended in space, but I need the specific one where it is said to be moving through space to fully support that section, and that is eluding me at the moment. $\endgroup$ – Loduwijk Feb 2 '18 at 18:28
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    $\begingroup$ @Aaron I'm quite certain you're wrong about the Bible saying the Earth moves through space. Though even should you find a verse which suggests so the Bible also contains Psalms 104:5 "He set the Earth on its foundations; it can never be moved." $\endgroup$ – EldritchWarlord Feb 2 '18 at 19:15
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    $\begingroup$ Job 26:10. "He drew a circular horizon on the face of the waters, At the boundary of light and darkness." The horizon only looks circular from space; from the ground it's a straight line. Implies knowledge that the Earth is a sphere. $\endgroup$ – Jay Feb 3 '18 at 21:53
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Resistance to change is only a factor if people start out with a geocentric model. If you posit a heliocentric model coming first, then resistance to change would favor that. In any case, while it is certainly true that there are people who reject new ideas because, "the old way was good enough for my grandfather and it's good enough for me", there are also plenty of people who embrace new ideas out of a love of novelty. Teenagers routinely question their parents' beliefs and chase after new ideas. (The Bible mentions that Paul of Tarus took advantage of how the Greek intellectuals loved to discuss new ideas as a way for him to introduce Christianity. "For all the Athenians and the foreigners who were there spent their time in nothing else but either to tell or to hear some new thing." -- Acts 17:91) So it's not at all clear that resistance to new ideas would be a major barrier.

It's not clear how religion supports the geocentric view. Nothing in the Bible supports a geocentric view, and the Greek and Roman pagans didn't have a clear body of authoritative writings. I haven't studied what the Koran says on the subject.

Yes, yes, the Catholic Church opposed Galileo, but that wasn't for any religious reason. The Catholic Church at the time also ran the colleges, and the college professors were committed to the geocentric view because of their faith in Aristotle. The pope found Galileo unconvincing but was willing to let him spread his ideas ... right up until Galileo wrote a book with a character named "Simplico", which means "simpleton", i.e. idiot, who was clearly modeled after the pope. Insulting powerful people in print is not a recipe for success in any society. Also, while we remember Galileo as being right, most of his arguments were flawed. For example, he said that tides were caused by the motion of the Earth: as the Earth moved in its orbit, the oceans tended to lag behind because of inertia, causing tides. Opponents blew holes in that argument.

Heliocentric ideas have been around for a long time. I don't know who first proposed a heliocentric theory, or if anyone today can say for sure. Archimedes assumed a heliocentric model in his paper that is now called "The Sand Reckoner", circa 250 BC, which discusses the size of the universe and large numbers. (He assumes that the universe might be as much as 2 light years across.) Others have mentioned Aristarchus of Samos, same era.

I think the real problem is this: What experiment can you perform to distinguish a geocentric universe from a heliocentric universe? Of course everyone today knows that the Earth goes around the Sun and that those ancient people who thought otherwise were incredibly stupid to think such nonsense. But ask them how they KNOW that the Earth goes around the Sun and not vice versa, and few could give an answer beyond "I read it in a book" or "they said so in that science show on TV".

The geocentric model actually worked pretty well for predicting things people could observe: the rising and setting of the Sun, seasons, eclipses, even the observed motions of the planets. What I think really did it in was as telescopes improved and people were able to make better observations of the motions of the planets, the geocentric model had to get more and more complicated to explain them. They had to introduce "epicycles" and all sorts of contorted sub-theories to fit the experimental observation. Ultimately people realized that with a heliocentric model and elliptical orbits, everything worked out quite nicely. Then Occam's Razor, pick the simplest theory that fits the facts, and the heliocentric theory won.

As @Aaron notes, people eventually figured out that there in fact IS a measurable parallax in observation of the stars. But it is minuscule: the difference at opposite ends of the Earth's orbit is 1/3600 of a degree for a star 3.26 light years away -- a "parallax second". No one was able to measure that finely until 1838.

So all of that said ... I think the way to get a heliocentric theory sooner is for astronomers (or astrologers) to make sufficiently detailed observations of the planets earlier and realize the awkwardness and unlikeliness of epicycles.

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    $\begingroup$ Voted up for relating the issues to whether, at the time, the heliocentric arguments were demonstrably an improvement on the existing theories. And for placing Galileo's problems in the correct context. $\endgroup$ – StephenG Feb 3 '18 at 8:31
  • $\begingroup$ -1 for lack of explicit Biblical citation for Heliocentrism. Job 26:7 only refers to the Earth being suspended in space; nothing about it moving. $\endgroup$ – RonJohn Feb 4 '18 at 4:51
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    $\begingroup$ @RonJohn Nowhere did I say that the Bible explicitly teaches a heliocentric universe. See my comments on Aaron's answer, where I explicitly said that I was not aware of anything in the Bible that says heliocentric vs geocentric. Which, immediately after my post saying that I don't know of anything in the Bible that specifically says heliocentric, you then proceeded to fault me for not giving a Bible reference saying heliocentric. Hmm. $\endgroup$ – Jay Feb 4 '18 at 6:09
  • $\begingroup$ I might have confused your comments with someone else's. $\endgroup$ – RonJohn Feb 4 '18 at 6:53
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The heliocentric model existed as early as the second century BC.

Unfortunately it was based on circles, and as such, it did not work too well because, well, ellipses (and it's not so likely that Hypatia really did intuit that as in the film Agora).

So, until Copernicus, the geocentric model was all the rage because it worked better (until even more advanced observations) and was anyway good enough to explain mostly everything. Religious arguments were found to support it - one of the most famous being Joshua's request for God to stop the Sun over Gibeon (Book of Joshua 10,12-13):

And the Sun stood still, and the Moon stayed, until the people had avenged themselves upon their enemies. Is not this written in the book of Jasher? So the Sun stood still in the midst of heaven, and hasted not to go down about a whole day.

(The obvious counter-argument being that, as in the passage where the Bible states that the Earth is flat and square as a table, the descriptions are from the point of view of the people of the time).

In fact, even after the observations started supporting Copernicus, the weight of tradition and religious arguments still made opinion tilt in favour of geocentrism.

And that's your answer.

Have Aristotle become convinced that Aristarchus' heliocentric model is more sensible. Have the early religion not be so hung-up on not resembling Mithraism and discard any associations between the Sun and God Almighty; actually have it do the contrary. Have the Sun associated with God's grace and have it maybe stem from a revised interpretation of the Jewish Qabbalah - with some handwaving you could have them posit even the Big Bang theory; then, of course, let there be Light.

Ellipses could be said to have to be ellipses because circles are perfect and only God may be perfect - the original theistic argument, as most irrational arguments, can run both ways.

Once the elliptical orbits are a God-given Truth, the fact that geocentric predictions initially fit just as well will simply be discarded and (correctly!) attributed to errors in measurements and rudimental instruments; also, supporting geocentrism will now be seen as a teleological faux pas - what, you want planets to revolve around the Earth? Whom do you serve - God, or Mammon?

From an astronomer's standpoint, this scenario is also better. For centuries, astronomers had to have noticed that the better they observed, the worse were the results. To make things fit, the "geocentric" model had to deny itself and introduce eccentrics, then epicycles and deferents, and by 1500 it was clear that a further level of deference was needed to make calculations fit the observations.

But starting with a belief in the heliocentric system, they would get large errors in the beginning, but the better the observation, the better the results. This would have been a way stronger incentive to both observe and publish.

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Have Ptolemy (AD 100 - c.170) be convinced by the heliocentric model of Aristarchus of Samos (310 - 230BC), and use it in his writings. That puts him in conflict with Aristotle (384 - 322BC), who was firmly geocentric, but it makes geocentrism vs. heliocentrism a live issue.

From that point, the weight of opinion can come down in favour of heliocentrism at any time you choose.

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    $\begingroup$ The model of Aristarchus made worse predictions that the model of Ptolemy. In the Antiquity there was no knowledge of gravitation or dynamics, so they considered the models from a purely cinematic point of view, and obviously the model which made better predictions was preferred. $\endgroup$ – AlexP Feb 2 '18 at 15:22
  • $\begingroup$ @AlexP are you saying that better model would be all it takes? Or at least would make it easier? If so, could you write that as an answer? I'd upvote it. $\endgroup$ – Mołot Feb 2 '18 at 15:34
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    $\begingroup$ People will accept the model which gives then the answers they need. Astronomical predictions were especially important in agriculture i.e. when to plant and harvest, and sailors were able to calculate latitude with a fair degree of accuracy using bare eye observations. A model which gave less accurate answers could have disastrous consequences. $\endgroup$ – Thucydides Feb 2 '18 at 16:42
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    $\begingroup$ Well, you have to also account for what people were using this stuff. Only Sun and Moon have practical impact and the model makes no major difference for those. Geocentric might even be better. Stars are potentially useful for navigation but do not care about the model. Planets were mostly used for astrology and direct observation would actually work better than a demystifying model for that. You need to be able to predict conjunctions and such for religious events and ceremonies but prediction based on observed patters is probably sufficient. $\endgroup$ – Ville Niemi Feb 2 '18 at 16:43
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Discovery of the Earth's axial procession is attributed to Hipparchus in the 2nd Century BC, by comparing astronomy records written in the 3rd Century BC. But Hipparchus wasn't confirmed until Ptolemy in the 2nd Century AD. It took a half-millenia of relatively consistent data and a common written language to confirm it. https://en.wikipedia.org/wiki/Axial_precession#History

Hipparchus even confirmed the old observations in secondary sources, but the data he could match up was limited to a certain star on a certain date. He knew the stars around the ecliptic were moving, but didn't assume it was the whole sky (ie: the Earth moving, not parts of the sky). He didn't have the full picture, and didn't even have the exact years, so he made a rough estimate and dropped it, but if he'd had more data from the past he might have been able to calculate the axial procession more accurately.

In an alternate history, the recorded data might have been preserved better over the centuries, and as he solved that rotation it might have occurred to him that everything processing means the Earth is wobbling. For a Worldbuild-y twist, our axial procession could be a little more obvious, or perhaps our orbit a little more elliptical, and it wouldn't have taken five centuries of written records to see long-term issues that the accepted epicycles didn't solve.

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  • $\begingroup$ Did the Mayan calendar 'predict' events due to the axial procession about 12.000 years ago? Of course that was not known in Europe around 300-200 BC. $\endgroup$ – BentNielsen Feb 3 '18 at 18:34
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Perhaps it would have helped if the Moon had a moon. Such setup is theoretically possible, even though perhaps not stable in long term - the orbit of sub-satellite would sooner or later be destabilized by tides.

However, having explanatory model of planetary system available for education and study on nightly basis might have changed the world view of past civilizations.

Note that this changes the "current model" of Solar System as defined by OP - it would not be the real Solar System any more.

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  • $\begingroup$ ...and now I noticed earlier comment from @AndyD273 above about the Venus with a moon. Which is basically same idea. $\endgroup$ – Congenital Optimist Feb 2 '18 at 20:31
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Just as a child first learns about their own house and later about their own community as they grow older and explore farther, so an ancient society learned more and more about the world and its size as it explored farther and farther.

It may be noted that the Sun and the Moon have the same apparent size as seen from Earth. And as someone travels farther and farther from home, and sees the apparent size of the sun and the moon stay about the same no matter where he goes, he can estimate how far away they could have to be to look the same size every where he went, and thus how big they would have to be to look that big at such a distance.

Anaxagoras (c. 510-c. 428 BC) proposed that the Sun was even bigger than the Peloponnesus. Thus the Sun should have been at least 180 miles wide and thus at least 20,626.498 miles away to have its apparent angular diameter.

Aristarchus of Samos (c.310-230 BC) claimed that the Earth and the planets revolved around the sun, that the earth rotated, and that the stars were distant suns. Aristarchus calculated that the Sun should be 18 to 20 times as far away as the Moon and thus 18 to 20 times as wide. He also calculated that the distance of the Moon was 20 times the radius of the Earth. So the diameter of he Moon would be 0.0872 the diameter of the Earth, and thus the diameter of the sun would be 1.570 to 1.744 times the diameter of Earth. Calculating that the Sun should be significantly larger than the Earth might have persuaded Aristarchus that the Sun was the center of the solar system.

Eratosthenes of Cyrene (c. 276-195/194 BC) calculated the circumference of the Earth to an accuracy of 10 or 15 percent. Eratosthenes is also said to have calculated the Sun's diameter at 27 times that of the Earth, a vast understatement. Eratosthenes is said to have calculated the distance to the sun as either 4,080,000 stadia (about 399,799.2 miles) or 804,000,000 stadia (about 78,783,960 miles), the latter being approximately the correct figure.

Clautius Ptolemy (c. AD 100-AD 170) calculated the distance to the Moon to be about 60 times Earth's radius, thus making the distance to the Sun using Aristarchus's calculation - 18 to 20 times the distance to the Moon - about 1,080 to 1,200 times Earth's radius and making the Sun's diameter about 4.5 to 5 times the Earth's diameter.

So in the late Hellenistic era and Roman era people educated in philosophy knew that some astronomers had evidence that the Sun and the moon were vast balls of rock similar to the Earth. Lucian of Samosata (c.AD 125-after 180) wrote A True History that included a trip to the moon and war between the natives of the Sun, the Moon, and various planets and stars, which were thus depicted as places. That's right the first Space opera was written in the 2nd century AD!

Ancient Greek and Romans made many types of glass, including glass clear enough for eyeglasses, telescopes, and microscopes. Lenses may have been used for some purposes in ancient times. So inventing telescopes would not have been totally impossible in Hellenistic and Roman times.

Since philosophers had more or less proven that the Sun was much bigger than the Earth, and since Aristarchus, Seleucus of Seleucia (b. 190 BC), Martinus capella (5th century AD), mentioned by Copernicus, and others supported the heliocentric system, telescopic observations that supported the heliocentric system might eventually convince philosophers that the Earth revolved around the sun.

The Galilean moons of Jupiter showed that celestial bodies could revolve around bodies other than the Earth. The phases of the planets, showed the geometrical relation between a planet, the Sun, and the Earth at the moment of observation. Repeated observations were a strong argument for the heliocentric model of the solar system.

Tycho Brahe (1546-1601) developed a "geo-heliocentric" system in which the Sun and the Moon revolved around the Earth and all the other planets revolved around the Sun. Once the phases of Venus were discovered, only the heliocentric and Tycho's "geo-heliocentric" system could explain them, the plain and millennia old geocentric system could not. Thus observing the phases of Venus would be enough to eventually disprove the geocentric system.

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There are a lot of factors that played into the geocentric and heliocentric beliefs, but these are just a few of the biggest influences that would change a lot of things related to them.

Ptolemy is the main reason why the geocentric system dominated stargazing for more than 1,000 years. Ptolemy was actually unsure whether he was right about the geocentric system and that currently there was no way to figure out for sure whether it was true. But he still was very influential was many people treated his word as law. If you want an earlier heliocentric system, then the easiest way would be if Ptolemy had been convinced of the earlier heliocentric theories. But even if that had changed, then the geocentric theory still might have survived.

The Church was another big reason why the geocentric system was so popular. They at the time had a philosophy that as people were the most important parts of the universe, they should also be the center. The center meant the center of attention, the universe, and the solar system. At the time, it just made sense that it would work like this. The Church just took Ptolemy's writings as a scientific backup for their ideas. If the church had been more open to astronomy and not threatened to kill anyone who disagreed with them, then there would be more open thinkers and people would have come to the conclusion of a heliocentric solar system much quicker.

Aristotle had a lot of influence, and he personally believed in a geocentric solar system. He has definitely influenced the important believers in the geocentric theory, and Ptolemy might not have come up with some of his theories without hearing about some of Aristotle's works. So changing Aristotle's views would definitely change some things. But do not remove him altogether, as that would also change countless modern-day concepts such as classifications of animals, other correct theories in astronomy, and many other things.

If Aristarchus of Samos had been more vocal about his beliefs, then the public might have been convinced of the heliocentric theory and there would have been more of an open debate in this field, as the other answer suggested.

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It would seem to take a number of events to make a helocentric model better than the alternative as expressed in

https://en.wikipedia.org/wiki/Copernican_heliocentrism#Copernican_Revolution

from that entry:

During the 17th century, several further discoveries eventually led to the wider acceptance of heliocentrism:

Using the newly invented telescope, Galileo discovered the four large moons of Jupiter (evidence that the solar system contained bodies that did not orbit Earth), the phases of Venus (the first observational evidence not properly explained by the Ptolemaic theory) and the rotation of the Sun about a fixed axis[43] as indicated by the apparent annual variation in the motion of sunspots;

So one thing would be an asteroid large enough to be seen without a telescope orbiting the moon. Even if this object was eventually ejected from orbit it would be evidence that some solar system bodies did not orbit earth.

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