This article was the subject of a Wiki Education Foundation-supported course assignment, between 23 August 2021 and 25 December 2021. Further details are available on the course page. Student editor(s): Besmeraldo.
Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 19:55, 17 January 2022 (UTC)
This article was the subject of a Wiki Education Foundation-supported course assignment, between 24 August 2020 and 16 December 2020. Further details are available on the course page. Student editor(s): BoomerSooner1101.
Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 19:13, 16 January 2022 (UTC)
I ran across someone elsewhere (slashdot) mentioning that the notion of epicycles upon epicycles being added in the middle ages is bad history, and that this is one that Britannica had some very bad articles on at one point. So someone (unlike me) who does know this well may want to double-check this entry and maybe comment on other mis-information floating around...
Yeah, I have mentioned that on slashdot a couple of times. And indeed, I think this article is still inaccurate. In fact, I think we have some good ammunitation against Britannica here, because Britannica carries a lot of the responsibility for the exaggarations :-) . I haven't worked on this subject for the last few years, and some of my books are packed down somewhere, but let me take something from memory.
The most fundamental thing here is that Owen Gingerich recomputed the Alfonsine Tables, which was computed in the 13th century, and found that they were based on a purely Aristotelian model. Still, Alfonse lamented the complexity of the calculations, and that has often been interpreted as complexity had been added. I think we can safely say that if epicycles were added, they had no practical influence whatsoever.
So, to the question of whether it is correct to say that epicycles were added upon epicycles. There is a short discussion in a book by J. L. E. Dreyer where there is also a figure of a world system with circles within circles. I guess you could point to that and say "see, they did", but there is very little record of this having any substantial influence on astronomy, and so, I still think that this article needs a good rewriting. I'd like to do it one day, I just need the time... :-) Kjetil Kjernsmo 00:10, 5 November 2005 (UTC)
You have added far too many (disputed - see talk page) comments - surely one would be enough?? I think that this should be changed. I will modify it a little.
Regarding the last part:
"The switch to the Sun-centered model removed epicycles for a while, but the original versions insisted on circular orbits for the planets. (disputed — see talk page) Better observational data from improved telescopes once again showed data counter to the model, and epicycles were brought back to plug the holes. (disputed — see talk page) It wasn't until Kepler developed the elliptical orbital model that epicycles were finally eliminated."
I have some disagreements here too. Who is disputing that Copernicus gave the planets circular orbits? Also, I have Never heard of epicycles being added to his system - where is the evidence for this? There is some discussion on the Copernicus site but is there a translation of his book availiable to firm up what he did or didnt say? Copernicus' model was disputed by the Church, but one of their objections was that his system gave predictions for planetary positions that was as bad as, or worse, than Ptolemy's system.
Kepler realised that the planets had elliptical orbits and this straight away removed the errors with the Copernican system. I'll modify some of the text and come back at another date to discuss some more.Adrian Baker 15:10, 10 December 2005 (UTC)
Thanks for the source by Gingeriich. I'll try and get a copy and read it. This would help clarify some of the points above. Regarding your comment about "Kepler 'straight away'.... ...is absurd", you have misread what I have written. I did NOT say that Kepler straight away hit the right solution, I said that "Kepler realised that the planets had elliptical orbits and this straight away removed the errors..." - two very different things. Adrian Baker 23:16, 15 January 2006 (UTC)
With regard to "epicycles upon epicycles": it has been pointed out in Ptolemaic System (referred from Equant) that "The eccentric in the figure below (the figure of eccentric) is fixed; it could also be made movable. In this case the center of the large circle was a point that rotated around the Earth in a small circle centered on the Earth. In some constructions this little circle was not centered in the Earth."
It seems to me that the cited statement is mathematically equivalent to the following: we add one epicycle on another one. However, it's not usually called that way. Besides, due to the difference in size of these circles, the whole system looks quite different. --Fir-tree 17:47, 22 February 2006 (UTC)
Is it correct to speak of planetary "orbits" in Ptolemaic astronomy? As I understand it (someone correct me if I'm wrong), before astronomers began to seriously attack that idea of the heavens being eternal (e.g., Tycho Brahe's calculations that comets move through different planetary spheres and are not sub-lunar, widespread observation of novae, etc.), the basic cosmology involved planets embedded within rotating spheres and not actually orbiting anything.--ragesoss 18:52, 19 May 2006 (UTC)
I realise that it's important not to confuse the two issues, but it should be pointed out that the epicycle approximation is a useful approximation made by people studying stellar dynamics to this day. I don't know whether it should get a mention here, or in separate page which gets linked from here?
I find this sentence: "The popular total of about 80 circles for the Ptolemaic system seems to have appeared in 1898" rather strange. Could it be a mistake or a typo? Or maybe it suggests that this large number was added in posterior sources (modern encyclopedias)? Hugo Dufort 02:04, 16 November 2006 (UTC)
The last paragraph starts "The difficulty with this account" and corrects some errors in the previous several paragraphs. As it is, the "Epicycles on epicycles" section is confusing and contradictory. I hope someone fixes this. Roger 06:00, 28 December 2006 (UTC)
(1) Looking at the java applet (external link to University of Nantes) I'm getting confused by geometry. Epicycles are usually presented as a bad attempt to explain the solar system with the earth at the middle instead of the sun. But surely if this were the only problem, the simplest epicycle model would have been to give all planets exactly the same deferent, with the earth at its middle, and the sun at the point where all the planets have their epicycle. Then each planet would have an epicycle corresponding to its orbit, and everything would be fine. Heliocentricity or Earth-centricity is merely a matter of viewpoint! The Java applet makes this clear, as both diagrams trace out the same relative positions of Earth/Planet/Sun, but one diagram moves around on the screen, the other doesn't.
So surely epicycles should be presented rather as a bad solution to eliptical orbits.
(2) And this brings me to point 2. Is it worth a mention that even after heliocentricity caught on, epicycles were still in practical use. A glance at the page on the "Orrery" will show a mechanism where the moon is on a cranked arm, which presumably rotated once per orbit, in a clockwise direction, to simulate the eliptical part of the moon's orbit, and is obviously a mechanical epicycle in action. I'm no mathematician: is this truly an elipse?
Should there, in any case, be a link from some part of the solar system set of Wiki pages to the Orrery page?
195.92.194.11 (talk) 19:58, 9 February 2008 (UTC)
I propose that Equant be merged into this article and the article be renamed as to have a more general name (such as Elements of Ptolemaean astronomy or something) as if deferents and epicycles are covered in one article, so should equants be, presumably. I am basing the assumption that all the aforementioned items are elements of Ptolemaean astronomy on pp. 30-31 of ISBN 0 00 715252 3. It Is Me Here (talk) 18:41, 7 July 2008 (UTC)
Characterizing use of epicycles as "Bad Science" is nonsense. Observers of the time of Ptolemy were trying to find ways to derive mathematical descriptions of the planetary motion they saw against the (apparently) invariant star field. They didn't know orbits. They didn't know geocentric. They didn't know science. They may not have been aware that the Earth rotated about its own axis. They saw the star field moving cyclically on a daily basis so naturally they assumed that the Earth was fixed at the center of the universe. This fit in with religious dogma (particularly Christian) that asserted that the universe was miraculously created and the Earth was the center of that creation.
They used epicycles to trace out planetary motions because that's what worked. The problem was made more complicated by the retrograde motion that the planets displayed from time to time. The solution was to superimpose more epicycles and bring in the equant idea to make the math work. The cost was inordinate complexity in the model. They did the best they could with what they had at the time.
Copernicus' great contribution was in discovering that moving the center of the universe to the Sun greatly simplified Ptolemy's model. The motion of the planets as seen from the Sun is much simpler than that seen from the Earth. He also introduced the notion that the Earth rotated on its axis and presented the trigonometric transformations needed to resolve observations made on Earth to Heliocentric coordinates. Again, he used epicycles because that's what worked. They worked because the orbits of the then-known planets are nearly circular. Copernicus probably didn't know orbits, however. The idea of the Earth moving about the Sun was not well received particularly by the Catholic Church but also by many astronomers of the time.
The notion of orbital motion came with Galileo's discovery of the moons of Jupiter. Kepler refined the idea with his discovery that planetary orbits were elliptical rather than circular.
Characterizing use of epicycles as bad science implies that people like Ptolemy were cranks or quacks who didn't know what they were doing. They were honest people trying to make sense of the universe they saw around them. Virgil H. Soule (talk) 19:31, 19 October 2008 (UTC)
Given that the current best models of the planetary motion (VSOP) use thousands of terms, surely it is enormous modernistic hypocrisy to denigrate epicycles that did work with "only" 80 terms?Old_Wombat (talk) 07:53, 30 July 2011 (UTC)
I just read the article and viewed the Java applet it links to, and it really doesn't adequately describe the subject. From the article I get the impression that if you approximate all the orbits in this system, then you'd get a model that is heavily centered on the angle between the earth and the sun. And that in turn should have triggered the question of what made the sun so special much sooner, especially for the inner planets. Then furthermore I can't square the Java applets with the text. The Ptolemy version clearly shows deferents and epicycles, but no hint of equants. Also for the outer planets the epicycles are somewhat unexpected, although I can kind of see the behaviour it tries to model, I can't say it's really understandable. What is the Ptolemaic location versus the real location of the planets in these cases? Then there's Brahe's version, which is what you'd expect to find, but with no equant again. I can't make sense of these mismatches and the article is not sufficiently referenced or illustrated to really tell what's going on... what was the motivation for example for the equant, and the motion of the epicycles with respect to these? Why this and not something else? What did it really look like? The illustration in the article doesn't show this at all, and the applets appear inconsistent with the article. What was the modelled location and the now known real location of the planets in various situation in the various models? Also, part of the article needs to be rewritten for accessibility to laypeople. 82.139.86.37 (talk) 01:48, 21 March 2009 (UTC)
The ancients worked from a geocentric perspective because the Earth was the platform on which they stood. Some Greek astronomers (e.g., Aristarchus of Samos) had speculated that the planets (Earth included) orbited the Sun but the mathematics needed to transform geocentric observations to a heliocentric perspective didn’t exist in Ptolemy’s time.
The latter claim is highly dubious. Indeed, considering this property of the Ptolemaic system:
Despite the fact that the Ptolemaic system is considered geocentric, the planets' motion was not thought to be actually centered on the Earth. Instead, the deferent was centered around a point halfway between the Earth and another point called the equant. The epicycle, meanwhile, rotated and revolved along the deferent with uniform motion. The rate at which the planet moved on the epicycle was fixed such that the angle between the center of the epicycle and the planet was the same as the angle between the earth and the sun.
the claim can be seen to be nonsense, since a heliocentric system requires less complication in the math than a deferent-centric system of the kind described. It would be a mistake to assume that anything as general as a modern understanding of coordinate transformations would have been required.
Also, according to Bartel Leendert van der Waerden's "The Heliocentric System in Greek, Persian and Hindu Astronomy", there is evidence that the math needed was available to and used by Seleucus of Seleucia, well before Ptolemy's time.
There is some discussion of more plausible reasons why heliocentric theories might not have been accepted earlier in the Heliocentrism article. --David-Sarah Hopwood ⚥ (talk) 00:14, 6 January 2010 (UTC)
Both Deferent and epicycle and Phlogiston theory were theories that fit the data but were abandoned due to other reasons. 96.26.97.207 (talk) 00:54, 27 February 2012 (UTC)
I'm no expert on complex valued Fourier series, but comparing the Mathematical Formalism subsection of this article with the Exponential Fourier Series subsection of the Fourier Series article suggests the terms are under specified (they are in fact left undefined). Comparing the mathematics in the Mathematical Formalism subsection with Hanson's paper, for the Fourier expansion in the latter there are two epicycles for each value of j, one for and one for . Hanson sums from -N to N, whereas the series in the subsection sums from 0 to N. Furthermore, I think the must be defined using integer multiples of the fundamental frequency, e.g., .
Perhaps it is possible to fix things up so the sum goes from 0 to N, but I think there are advantages to summing from -N to N. Specifically, for j = 0, there would be only one term, which can be used to center the deferent on a point other than the origin of the coordinate system. This seems to fall out naturally, since , which is a constant.
One other point. It probably is prudent to indicate in this section that the Mathematical Formalism provided is an extension of the Deferent and Epicycle system used in the Ptolemaic model. I believe the latter only used one epicycle per deferent. Dnessett (talk) 16:50, 17 April 2013 (UTC)
It seems to me that there is a lot more information in this article than there needs to be. It's about "deferents and epicycles", but it gets into eccentrics, equants, Ptolemy, Copernicus and Brahe, stuff related to but way beyond the named subjects, all of which should be moved to articles on geocentrism and the planetary theories of the afore-mentioned worthies. Compare, for example, to the article on the equant. I have myself lately been guilty of gilding the lily on this article, before I pulled back somewhat for a larger picture.
I propose to rewrite it to that standard, and while I'm waiting for comment, I'll wander on over to geocentrism and see what needs to happen there.SkoreKeep (talk) 20:01, 5 August 2014 (UTC)
All the topics you list as ‘too much’ are for me necessary context to make sense of the rest of the article. In fact, I think that Brahe, who currently is but a footnote in this article, should get a bit more coverage here. Wikipedia aims to be an encyclopaedia, not a dictionary. It isn't sufficient to provide a one-paragraph definition. Rather, a topic should be fully covered, including common details, history, competing theories or related topics, people involved and so on and so forth. — Preceding unsigned comment added by 80.114.146.117 (talk) 21:42, 9 May 2016 (UTC)
Babylonian observations are mentioned in the article. I think earlier Sumerian observations were made, also.
I'm not much of a mathematician, but I don't believe this statement is true. Certainly many complex paths can. But a straight line cannot, and does not have a Fourier transform valid for all time. Neither does a non-periodic trivial predator-prey model. If there is no analytical expression possible, then while an infinite set of points could be said to represent such curves, one cannot represent such points exactly without the original "open-form" expressions which are not based on epicycles nor a fourier basis.Dpleibovitz (talk) 16:46, 9 February 2016 (UTC)
I question whether Hanson is in this section a reliable source in general, and for the quote in particular.
Having read the reference I cannot help but feel that Hanson is out of his depth on this matter. The relevant section is outside of his regular area and he clearly lacks the required historical knowledge to accurately present what he discusses.
Further, the quote in this article is pulled out of context. As it is quoted, it is subtly wrong. It would be correct if it said ‘infinite’ instead of ‘finite’, but that would go against what the reference is trying to say, namely that a wide variety of curves can be approximated by stacking a few epicycles on top of each other. But due to the quote being pulled out of context it appears to say that any curve in use can be exactly reproduced and that isn't true.
Considering that the quote is wrong, needs a lot of context to become right, isn't necessary nor particularly relevant to this article, doesn't really add anything to this article and comes from a relatively shaky source, I propose to remove it altogether. — Preceding unsigned comment added by 80.114.146.117 (talk) 22:31, 9 May 2016 (UTC)
Hello fellow Wikipedians,
I have just modified 2 external links on Deferent and epicycle. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
This message was posted before February 2018. After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than regular verification using the archive tool instructions below. Editors have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the RfC before doing mass systematic removals. This message is updated dynamically through the template {{source check}}
(last update: 5 June 2024).
Cheers.—InternetArchiveBot (Report bug) 02:13, 8 September 2017 (UTC)
Dear Wikipedians, I've just created an animated javscript program that draws any given close curve with a number of epicycles (gianmarco-todesco.github.io/epicycles).
The animation is similar to other animations currently linked in the article but it has its own specificity and value. The program is open-source and released with an MIT license. The content is - IMHO - good visual support to the article. I want to contribute to Wikipedia (that I use daily) and so I added the external link. The link has been removed and I've received a warning.
I understand that I can not use Wikipedia to publish my own websites. On the other side, Wikipedia uses very many images that have been created and donated by contributors. I created the JavaScript program with the same spirit: I want to contribute to Wikipedia with a specific medium.
Is there a specific procedure that I can follow to submit an animation that I've created?
best regards, gmt Gianmarco-todesco (talk) 10:08, 21 January 2020 (UTC)
Update: User:NonsensicalSystem allowed me to restore the link. Gianmarco-todesco (talk) 10:30, 21 January 2020 (UTC)
In the first line of the article, Galileo is not mentioned, although he seems to have used epicycles. Galileo never accepted Kepler's ellipses, which were brought to his notice in 1609 and 1612. — Preceding unsigned comment added by 213.48.238.18 (talk) 16:27, 10 October 2021 (UTC)
On the latter sections, more than the first ones, there is an increase in the number of quotations, which partially goes against the wiki's guidelines on article writing, and I will paraphrase them to fit the guidelines better if any believe that this is incorrect, please feel free to undo my changes or reach out to me.Besmeraldo (talk) 03:14, 9 November 2021 (UTC)