It's easy to find resources stating that the heliocentric model is right and geocentric is wrong.

But how wrong was it? Was it correct in any way?

It was built on incorrect assumptions, but despite that - was it of any use to describe the apparent motion of celestial bodies? Was it more accurate for some things, but less accurate for others? Or was it altogether a flop and astronomers couldn't get anything out of it either way?

I can only find multiple articles proving the heliocentric model, explaining the geocentric one or claiming that it was simply wrong - but I can't find anything about its accuracy and usefulness.

(1) (2) (3)

Edit 1:

I incorrectly used geocentric model when it seems I wanted to say Ptolemaic model - the one with deferents and epicycles, with Earth as its origin.

ptolemaic model
Ptolemaic model (click for full size)

Thank you for clarifying, and sorry for the confusion. The answers provided regarding any other geocentric models are still valid and useful, so this is just a minor errata.

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    $\begingroup$ Well, they got the relationship between the Earth and the Moon basically right. Other than that... $\endgroup$ – Darrel Hoffman Sep 16 at 19:01
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    $\begingroup$ I highly recommend the nine-part series of blog posts by Michael Flynn (not that one) titled The Great Ptolemaic Smackdown. It presents a lot more of the arguments that were made for the geocentric model and against the heliocentric model than most other popular-level histories do. $\endgroup$ – Michael Seifert Sep 17 at 11:45
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    $\begingroup$ Related, but not a duplicate, at the physics.SE: Are all reference frames equally valid? $\endgroup$ – David Hammen Sep 17 at 11:46
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    $\begingroup$ It's all about Occam's Razor. Both models are usable, but the geocentric model requires many extra complications such as epicycles. $\endgroup$ – Barmar Sep 17 at 17:54
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    $\begingroup$ I would also recommend The Coperncian Revolution from the Inside; it helped me to get a good understanding of the reasons behind some of what was going on. $\endgroup$ – wizzwizz4 Sep 18 at 19:57

Ptolemy's epicyclic, geocentric model, in use until the Renaissance, was very accurate in terms of predicting the positions of planets and the times of eclipses. What it couldn't account for were things like the correlations between apparent size and phase of Venus, or to properly account for the variation in brightness of the planets.

Thus the reason for discarding the geocentric model was not really because it lacked precision, but that it failed to explain various other observational facts, especially after the development of telescopes.

No doubt you could tune the Ptolemaic system even further (more epicycles?) to iron out some of the small errors that were revealed by Tycho's positional measurements at the turn of the 16th century, which had a precision unavailable to Ptolemy. However, the advent of Kepler's laws and subsequent explanation by Newton, rendered the geocentric model obsolete.

As you can judge from (well written) articles like this one, geocentrism is actually quite hard to kill-off observationally, if you are prepared to accept that the universe is arranged "just so".

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    $\begingroup$ And with the theory of relativity, all we can say is that we find the heliocentric frame of frame more useful. The geocentric frame of reference is valid, just unnecessarily complicated. $\endgroup$ – Acccumulation Sep 16 at 22:08
  • $\begingroup$ Would you have some sources to support the first paragraph? Excellent answer Rob - speaking about accuracy precisely is exactly what I needed - thank you! $\endgroup$ – Voy Sep 17 at 0:22
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    $\begingroup$ @Accumulation - I don't think that you need either of SR or GR for the basic insight that there are multiple possible frames of reference. It would have been equally obvious to Newton. Perhaps Earth tended to be the sole considered frame of reference before it became obvious that humans and/or their instruments could in principle travel all the way to celestial bodies? $\endgroup$ – Jirka Hanika Sep 17 at 8:53
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    $\begingroup$ From the perspective of accuracy and simplicity, even a heliocentric model doesn't quite cut it. Developers of modern ephemerides use a barycentric model because third body effects vanish in such a frame. Those third body effects result in an implicit second order ODE. Using Newtonian gravity, the equations of motion are fully explicit from a barycentric perspective. Relativistic effects do make the equations of motion implicit, even from a barycentric perspective, but the relativistic effects are small enough that the Newtonian acceleration form a very good approximation. $\endgroup$ – David Hammen Sep 17 at 12:27
  • $\begingroup$ @Acccumulation Is that so? Is an object in orbit not in an accelerated frame? $\endgroup$ – kutschkem Sep 18 at 6:56

None other than Galileo himself pointed out that there is no real right or wrong with this.

In fact, you can choose any arbitrary point you want, and calculate the movements of the sun, planets, the moon, and so on, all relative to that point.

Now, it is true that the movements of most objects are pretty simple relative to the center of mass of the solar system. It's also true that the sun is close enough to the center of mass that treating it as the center works out close enough for most purposes--that is, it also keeps the movements relatively simple.

Nonetheless, there's ultimately no "right" or "wrong" involved. And other possible points don't need to be entirely arbitrary either. For example, you could make a case for computing all the orbits relative to the center of the Milky Way. Computing intra-solar system movement that way would be painful to put it mildly. This is compounded by the fact that we have considerable difficultly even observing the center of the Milky Way, and doing so (at least at our present level of technology) seems to provide no advantage. Nonetheless, if we wanted to call that the center we could do so, and it would be no more "right" or "wrong" than calling the sun the center.

If you do some searching for terms like "Galileo relativity", you should be able to find a fair amount about the basic ideas involved (though at least the last time I looked, finding translations of his original paper was much more difficult).

I would add that at the time, much of the "right" or "wrong" involved stemmed from something rather different that really was wrong. At the time, it was fairly common among astronomers (including Galileo, and initially Kepler as well) to believe that when they looked up toward the stars they were literally looking at "heaven" as it was described in the Bible. Following directly from that, they concluded that everything up there was required to be "perfect"--and they thought of ellipses as imperfect imitations of circles.

As such, many of them resisted (or even outright refused) to accept orbits as being elliptical, and instead treated them as circular. This (of course) led to inaccurate computations and predictions. Kepler (eventually, when he saw no other choice) accepted orbits as being elliptical--but he initially believed they not only were, but needed to be circular. For a while, he seems to have convinced himself that they really were circular, but treating them as if they were elliptical happened to be a convenient way to produce answers that ended up being more accurate.

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  • $\begingroup$ Well, there is a wrong. It is wrong to suggest that Venus goes around the Earth. $\endgroup$ – Rob Jeffries Sep 16 at 21:14
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    $\begingroup$ @RobJeffries Venus going around the Earth can be easily observed at night. The average orbital period is exactly one day, with long periodic liberations from side to side. $\endgroup$ – SE - stop firing the good guys Sep 16 at 21:33
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    $\begingroup$ @SE-stopfiringthegoodguys No you need Venus to be orbiting the Sun, otherwise the relationship between phase and apparent size remains unexplained. $\endgroup$ – Rob Jeffries Sep 17 at 6:08
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    $\begingroup$ @RobJeffries It's just harder to explain. Venus could be "breathing," changing size over time. Of course, the heliocentric model is far simpler and has fewer independent variables, but you can model just about anything if you remove the assumptions which lead us to the heliocentric model in the first place. $\endgroup$ – Cort Ammon Sep 18 at 8:54
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    $\begingroup$ The best professor I ever had used to say, "All models are equally wrong." The utility of Occam's Razor is not in determining which model is "right" (which is a question of pure applied metaphysics), but in which is determining which is easiest to use; that is, which requires the least effort to produce the greatest predictive power. With sufficient effort, all models can be induced to converge on physical reality, but it's a lot easier to do this with e.g. the standard model than with epicycles. $\endgroup$ – Vector Gorgoth Sep 18 at 19:18

There is more than one heliocentric model.

Copernicus modelled orbits with circles and this article suggests that Tycho found that the predictions of Copernicus agreed better with observations of the superior planets and solar eclipses, while Ptolemy's (geocentric) predictions were more accurate for lunar eclipses and the positions of the inferior planets.

One of the main uses of these models was to produce an ephemeris of the position of the stars and planets for purposes such as navigation at sea. By 1627, the standard method of producing ephemerides was the Rudolphine tables of Johannes Kepler. These were based on Kepler's three laws (including eliptical planetary orbits) better than anything the Ptolemaic tables could produce. I think it would be difficult to find direct comparisons between Ptolemy and Kepler after that because the relative simplicity and utility of Kepler's methods meant that Ptolemy was no longer used.

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  • $\begingroup$ Are you essentially saying that it's impossible to know the accuracy of the geocentric model, given that it was deprecated with tables made using Kepler's laws? In fact, I'm not even looking for comparisons between the two, just whether geocentric model was of any use at all, and how precise it was when used. Either way an interesting read, so thank you for writing it Dave. $\endgroup$ – Voy Sep 17 at 0:38
  • $\begingroup$ @Voy I think it's impossible to know from the current historical records how the Keplerian and Ptolemaic models compared. The Rudolphine tables were there and produced adequate results that could be efficiently calculated. I'd guess the adoption wasn't instant and the Ptolemaic model took some time to fully fall out of use, but I haven't found any records of it's later use, or what it may have been used for. It would be an interesting exercise to run both models together and see how they compare for various phenomena but that wouldn't tell us what happened in history. $\endgroup$ – Dave Gremlin Sep 17 at 9:25

The thing is, there is more than one Geocentric system, there's the Ptolemaic system, with the sun and planets revolving around the Earth and then there's the Tychonian system (named after the famous astronomer Tycho Brahe, who invented it in the mid 16th century), with the Sun and stars going around the Earth and the planets going around the Sun, it looked like this (blue orbits go around the earth, orange ones around the sun): Tychonian system

While it may seem hilariously stupid to us now, it was actually more scientifically valid for a century.

In terms of accuracy, it's literally identical to the Copernican system in terms of what you see from the Earth. And until Newton published his theory of gravity (a century after Tycho published his), neither system had an explanation for why the celestial bodies move the way they do, except for "God willed it".

However, the Copernican system had one glaring flaw, that Tycho noticed: If the Earth moves around the sun, then the angles of the stars at opposite ends of it's orbit should be different (this phenomena is called stellar parallax). We now know that stellar parallax exists, but instruments precise enough to measure it didn't exist until the 19th century. However, even the smallest visible star has some apparent width. We now know that it's an optical illusion, but the knowledge of optics required to discover that didn't exist until the 19th century (again). Given the calculated orbit of the Earth, Tycho determined that at the smallest possible distance with no visible parallax (for the measurement precision of the day), the dimmest visible star would have to be bigger than the Solar System and the biggest way bigger than that, which he considered preposterous.

So basically, it took Newton, the discovery of Stellar Aberration in the 18th century and the invention of the Foucault pendulum in the 19th (yet again) to prove the Earth rotates, to finally bury the Tychonian system.

I think that the popular perception of the Heliocentrism vs Geocentrism is that of Galileo muttering "And yet it moves" before the stupid Inquisition(Apocryphal btw, there's no contemporary evidence of it happening). But Galilleo was like Columbus(1), right, but for the wrong reasons and has an extremely in-accurate mythos(2) due to what amounts to propaganda(3).

(1) This is an aside, but demonstrates a similar popular misconception. Columbus was basically a fool who got extremely lucky. Contrary to popular opinion (3), he didn't discover the Earth was round against the opposition of church troglodytes who thought it was flat. Eratosthenes had correctly calculated the circumference of the Earth in the 2nd century BC and his writings were widely known and accepted in the church and Europe in general at the time. Knowledgeable people derided the idea of sailing west to reach India, because they knew approximately how far east India was and given how far west you'd have to sail (the width of the Atlantic + America + the Pacific), they knew no ship could possibly make it. Instead, he thought he could do better and incorrectly re-calculated the circumference of the Earth, showing it to be significantly smaller than it actually is and thus the voyage was possible. He used his considerable powers of persuasion to convince Queen Isabella (who was clueless in these matters) to fund his voyage. If the Americas didn't have the good luck to exist, he and his entire crew would have died of thirst and disappeared without a trace. To his dying day, he thought he had discovered India.

(2) Galilleo had the kind of personality that could best be summarized as "contrarian douche-bag". If he thought he was right, anyone who dis-agreed with him was an idiot and he did not hesitate to insult them. He wasn't imprisoned for saying Copernicus was right, he was imprisoned because in his famous book, "Dialogue Concerning the Two Chief World Systems" (which was written in the form of a dialog between philosophers), the opposing view-point is espoused by a foolish character called Simplicio (overtly named after the philosopher Simplicius, but an Italian double-entendre for Simpleton/Moron), who had characteristics identifying him (for everyone who knew him personally) as Pope Urban VIII, Galileo's former friend and patron, who opposed the Copernican system (he also pulled the straw-man trick by opposing the Aristotelian system to the Copernican one and pretending that the Tychonian system did not exist, although it was the most popular theory at the time). So basically, as far as all the important people in Europe were concerned, had publicly called the Pope a moron with the barest fig-leaf of plausible deniability. At the time, the Pope was also functionally a head of state, with lands and an army and that kind of insult would have have been ample grounds for any nobleman from Baron upwards to kill Galileo on the spot, given the mores of the day, but all he got was house arrest in a mansion for the rest of his life. P.S. Galileo actually spent way more ink arguing for his (incorrect) theory of the tides being caused by the Earth going around the Sun.

(3) This all happened during the Reformation and the wars of religion, so Protestant intellectuals jumped on any chance to portray the Catholic church as venal idiots, holding back scientific progress, so any nuance was (very probably deliberately) omitted from their literature.

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  • $\begingroup$ Today, we can't explain why gravity behaves like it does either. We can't explain scientifically why massive objects curve spacetime. God willed it. $\endgroup$ – Giovanni Sep 17 at 12:49
  • $\begingroup$ Explaining something is never in conflict with "God willed it". It is just good to make God wills more consistent and even predictable. In that sense, gravity is in pretty good state. $\endgroup$ – fraxinus Sep 17 at 18:43
  • $\begingroup$ Re: (1) Which is why native Americans have been called "indians" (or "injuns", or similar bastardisations) to this day. Columbus' folly has stayed with us for 5 centuries. $\endgroup$ – Arthur Sep 18 at 10:32

To add to Jerry Coffin's very good answer, there've been experiments that disproved geokinetism and proved geocentricity. They're called the Michelson Morley experiment and Airy's failure and made clear whether absolute gocentrism is correct or not. Since then, it was made effort to disprove the results of these experiments because absolute geocentrism would be proof of God and Scripture, the evil wanted to avoid that.

This proven geocentricity is called the Neo-Tychonic model, after Tycho Brahe who lived in about the same time as Copernicus. The difference to the original Tychonic model is that in the neo-Tychonic model the stars are focused on the Sun, not on the Earth. This explains parallaxes, and this geocentricity has the very same effects like an Earth spinning on its axis, such as the Foucault pendulum, geostationary satellites staying up, and a lower gravity at the equator.

If you don't trust these experiments nor Scripture, the only way to find out which model is true (Copernican or neo-Tychonic) would be to stand outside the universe and look onto it.

For more information see The Principle documentary by Robert Sungenis with various scientists.

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    $\begingroup$ Wasn't Michelson–Morley explicitly about the luminiferous aether theories of the time, i.e. whether aether drag was a thing? Unless you postulate that Lorentz and Einstein were fundamentally mistaken, I fail to see the connection to geocentricity. $\endgroup$ – Ruther Rendommeleigh Sep 16 at 20:04
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    $\begingroup$ @RutherRendommeleigh For Lorentz and Einstein to be proven, one ought to repeat the Michelson-Morley experiment on another celestial body. I think Mars would be best because its rotation period is similar to that of Earth (respectively to that of the universe around the Earth). If M-M and Airy's Failure have the same results, Lorentz and Einstein may have been correct, but if they prove a rotating/moving Mars, it will be clear that the Earth is immovable (Psalm 93:1 Psalm 96:10 a.o.) while the other planets aren't. $\endgroup$ – Giovanni Sep 17 at 5:51
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    $\begingroup$ AFAIK the speed of light to/from Mars does not change according to its velocity wrt Earth. Such changes would have been noted by satellite tracking systems, which are capable of locating satellites in orbit around Mars to less than a metre. $\endgroup$ – Rob Jeffries Sep 17 at 6:32
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    $\begingroup$ @RobJeffries I mean performing the experiments on the surface of Mars, once astronauts might land there. If they have the same results, Lorentz and Einstein were right, and geocentricity won't be proven experimentally, but if not, they prove e.g. the Lorentz contraction wrong and geocentricity to be true. $\endgroup$ – Giovanni Sep 17 at 7:53
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    $\begingroup$ What is special about the surface of Mars compared with being in orbit around Mars or communicating across the solar system? Special (and General) Relativity is in common use between the Earth and things flying around all over the solar system and between objects flying around in the solar system. If the claim is that the aether is stationary wrt Earth, then it is not stationary wrt Mars, so the light speed measured between Earth and Mars will depend on Mars' relative motion and position wrt Earth (which it doesn't). $\endgroup$ – Rob Jeffries Sep 17 at 8:13

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