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As I was reading about the heliocentric model, a question came up: How was Nicolaus Copernicus able to figure out that the sun is at the center of the solar system, and that all planets orbit around it, even though the telescope had not been invented yet? During his time the geocentric model was the standard.

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  • $\begingroup$ I'm voting to close this question as off-topic because this is better suited to hsm.stackexchange (history of science and math) $\endgroup$ Commented Jul 24, 2019 at 18:06
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    $\begingroup$ The on-topicness of this History of Astronomy question can also be gauged by the other 102 questions tagged history as well as explicitly in the help center. $\endgroup$
    – uhoh
    Commented Jul 25, 2019 at 0:16
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    $\begingroup$ @CarlWitthoft "better suited" is never a close reason. One has to demonstrate that it is off-topic here, which it is not! Right in What topics can I ask about here? it lists "History of Astronomy" as on-topic. Consider retracting the close vote and possibly avoiding further "better suited" close votes? As a stand-alone comment it would have been helpful, but as a close reason it is invalid. Thanks! $\endgroup$
    – uhoh
    Commented Jul 25, 2019 at 0:21

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Copernicus did not figure out that the Sun was at the centre of the solar system. He merely proposed that a heliocentric model simplified the calculation of planetary orbits. Epicycles (circles within circles) were still needed in the Copernican model, for instance for the orbit of Mars, but there were fewer of them than in the Ptolemaic model.

The Copernican model received a boost when Kepler, discovering that planetary orbits were elliptical, removed the need for epicycles completely, thus increasing Copernicus' advantage over Ptolemy.

The first evidence that the Copernican model was a true representation of actual reality came with the observation of stellar parallax in 1806. Until then, it was preferred only because it was a simpler description - a much simpler one, after Kepler.

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  • $\begingroup$ Apart from being heliocentric, a key feature of the Copernican system is that it eliminated equants, although it retained epicycles. $\endgroup$
    – PM 2Ring
    Commented Jul 25, 2019 at 5:50
  • $\begingroup$ While the Copernican system eliminated equants, it did so at the cost of accuracy. The Copernican system was less accurate than the Ptolemaic model. $\endgroup$ Commented Jul 25, 2019 at 20:42
  • $\begingroup$ Kepler's ellipses made considerably more accurate predictions than Ptolemy's or Copernicus's model, not just a "simpler" explanation. Also, the observation of the aberration of starlight predated the observation of stellar parallax by a century. $\endgroup$ Commented Jan 31, 2021 at 23:34
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    $\begingroup$ There were actually more epicycles (48) in the Copernican model than in the Ptolemaic model (40); there were needed to reproduce the non-uniform motion of the planets. (He didn't need equants, which was an improvement over Ptolemy.) astronomy.ohio-state.edu/~pogge/Ast161/Unit3/copernicus.html $\endgroup$ Commented Jan 31, 2021 at 23:39
  • $\begingroup$ As Peter Erwin pointed out, Copernicus’s model had more epicycles than Ptolemy’s. This did not make calculations simpler; quite the contrary! His model was thus slow to adopt because it was more complex and gave basically the same results as Ptolemy’s; also, it did not introduce anything new or explain anything that wasn’t explained by earlier models. $\endgroup$ Commented Jul 27, 2023 at 3:13
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Basically, because it was a more elegant solution to describe the motion of the planets. This could be see easily without any telescopes. The big difference was that it needed way less so called epicycles (he still needed those as all his orbits were circular not elliptic):

One of the glaring mathematical problems with this model was that the planets, on occasion, would travel backward across the sky over several nights of observation. Astronomers called this retrograde motion. To account for it, the current model, based on the Greek astronomer and mathematician Ptolemy's view, incorporated a number of circles within circles — epicycles — inside of a planet's path. Some planets required as many as seven circles, creating a cumbersome model many felt was too complicated to have naturally occurred.

-Space.com

Besides that, the idea wasn't entirely new. Aristarchus proposed the idea of a moving earth in 250 BC and Copernicus was probably familiar with that. (Source)

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As noted in @SpaceBread's answer, Copernicus did not 'discover' heliocentricity (there were no observations to support his theory) nor did he invent it (that was done two thousand years earlier). Nor was his his model better -- because he insisted on circular orbits it was contradicted by observations and a worse fit even than Ptolemy's model.

What he did was popularize the heliocentric model and argue that its simplicity made it preferable even though it was clearly wrong.

The real breakthrough was Kepler's who showed that a heliocentric model with elliptical orbits gave an excellent fit to observations. And then Newton showed why Kepler's model worked.

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The main point, emphasized by Copernicus himself, is that his theory described solar system. In other words, the theory was able to predict distances of all planets from the Sun and between each other (including the Earth). In geocentric system you can expand or shrink orbit of a given planet without affecting others. This is impossible in Copernicus system - it essence, he created 3D model of the solar system.

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