Editing Geocentric model (section)

==Ptolemaic model==<!-- This section is linked from [[Giordano Bruno]] -->
[[File:Ptolemaic elements.svg|thumb|The basic elements of Ptolemaic astronomy, showing a planet on an [[epicycle]] with an eccentric deferent and an [[equant]] point. The Green shaded area is the celestial sphere which the planet occupies.]]

[[File:Ptolemaic Model.png|thumb|The Ptolemaic geocentric planetary model showing the epicycles of the planets and the Moon]]
Although the basic tenets of Greek geocentrism were established by the time of Aristotle, the details of his system did not become standard. The Ptolemaic system, developed by the [[Hellenization|Hellenistic]] astronomer [[Ptolemy|Claudius Ptolemaeus]] in the 2nd century AD, finally standardised geocentrism. His main astronomical work, the ''[[Almagest]]'', was the culmination of centuries of work by [[Ancient Greece|Hellenic]], [[Hellenistic civilization|Hellenistic]] and [[Babylonian astronomy|Babylonian]] astronomers. For over a millennium, European and [[Islamic astronomy|Islamic astronomers]] assumed it was the correct cosmological model. Because of its influence, people sometimes wrongly think the Ptolemaic system is identical with the '''geocentric model'''.

Ptolemy argued that the Earth was a sphere in the center of the universe, from the simple observation that half the stars were above the horizon and half were below the horizon at any time (stars on rotating stellar sphere), and the assumption that the stars were all at some modest distance from the center of the universe. If the Earth were substantially displaced from the center, this division into visible and invisible stars would not be equal.{{refn|group=n|This argument is given in Book I, Chapter 5, of the ''Almagest''.{{sfn|Crowe|1990|pp=60–62}}}}

===Ptolemaic system===
[[File:1550 SACROBOSCO Tractatus de Sphaera - (16) Ex Libris rare - Mario Taddei.JPG|left|thumb|Pages from 1550 ''Annotazione'' on Sacrobosco's ''[[De sphaera mundi]]'', showing the Ptolemaic system.]]
In the Ptolemaic system, each planet is moved by a system of two spheres: [[Deferent and epicycle|one called its deferent; the other, its epicycle]]. The deferent is a circle whose center point, called the eccentric and marked in the diagram with an X, is distant from the Earth. The original purpose of the eccentric was to account for the difference in length of the seasons (northern autumn was about five days shorter than spring during this time period) by placing the Earth away from the center of rotation of the rest of the universe. Another sphere, the epicycle, is embedded inside the deferent sphere and is represented by the smaller dotted line to the right. A given planet then moves around the epicycle at the same time the epicycle moves along the path marked by the deferent. These combined movements cause the given planet to move closer to and further away from the Earth at different points in its orbit, and explained the observation that planets slowed down, stopped, and moved backward in [[apparent retrograde motion|retrograde motion]], and then again reversed to resume normal, or prograde, motion.

The deferent-and-epicycle model had been used by Greek astronomers for centuries along with the idea of the eccentric (a deferent whose center is slightly away from the Earth), which was even older. In the illustration, the center of the deferent is not the Earth but the spot marked X, making it eccentric (from the [[Greek language|Greek]] ἐκ ''ec-'' meaning "from" and κέντρον ''kentron'' meaning "center"), from which the spot takes its name. Unfortunately, the system that was available in Ptolemy's time did not quite match [[observation]]s, even though it was an improvement over Hipparchus' system. Most noticeably the size of a planet's retrograde loop (especially that of Mars) would be smaller, or sometimes larger, than expected, resulting in positional errors of as much as 30 degrees. To alleviate the problem, Ptolemy developed the [[equant]]. The equant was a point near the center of a planet's orbit where, if you were to stand there and watch, the center of the planet's epicycle would always appear to move at uniform speed; all other locations would see non-uniform speed, as on the Earth. By using an equant, Ptolemy claimed to keep motion which was uniform and circular, although it departed from the Platonic ideal of [[uniform circular motion]]. The resultant system, which eventually came to be widely accepted in the west, seems unwieldy to modern astronomers; each planet required an epicycle revolving on a deferent, offset by an equant which was different for each planet. It predicted various celestial motions, including the beginning and end of retrograde motion, to within a maximum error of 10 degrees, considerably better than without the equant.

The model with epicycles is in fact a very good model of an elliptical orbit with low eccentricity. The well-known ellipse shape does not appear to a noticeable extent when the eccentricity is less than 5%, but the offset distance of the "center" (in fact the focus occupied by the Sun) is very noticeable even with low eccentricities as possessed by the planets.

To summarize, Ptolemy conceived a system that was compatible with Aristotelian philosophy and succeeded in tracking actual observations and predicting future movement mostly to within the limits of the next 1000 years of observations. The observed motions and his mechanisms for explaining them include:

{| class="wikitable"
 |+ The Ptolemaic system
 ! Object(s)
 ! Observation
 ! Modeling mechanism
 |-
 | Stars
 | Westward motion of entire sky in ~24 hrs ("first motion")
 | Stars: [[diurnal motion|Daily westward motion]] of [[celestial sphere|sphere of stars]], carrying all [[celestial spheres|other spheres]] with it; normally ignored; other spheres have additional motions
 |-
 | Sun
 | Eastward motion yearly along [[ecliptic]]
 | Eastward motion of Sun's sphere in one year
 |-
 | Sun
 | Non-uniform rate along ecliptic (uneven seasons)
 | Eccentric orbit (Sun's deferent center off Earth)
 |-
 | Moon
 | Monthly eastward motion compared to stars
 | Monthly eastward motion of Moon's sphere
 |-
 | The 5 planets
 | General eastward motion through [[zodiac]]
 | Eastward motion of deferents; period set by observation of planet going around the ecliptic
 |-
 | Planets
 | [[apparent retrograde motion|Retrograde motion]]
 | Motion of epicycle in same direction as deferent. Period of epicycle is time between retrograde motions ([[synodic period]]).
 |-
 | Planets
 | Variations in speed through the zodiac
 | Eccentric per planet
 |-
 | Planets
 | Variations in retrograde timing
 | Equants per planet (Copernicus used a pair of epicycles instead)
 |-
 | Planets
 | Size of deferents, epicycles
 | Only ratio between radius of deferent and associated epicycle determined; absolute distances not determined in theory
 |-
 | [[inferior planet|Interior planets]]
 | Average greatest [[Elongation (astronomy)|elongation]]s of 23° (Mercury) and 46° (Venus)
 | Size of epicycles set by these angles, proportional to distances
 |-
 | Interior planets
 | Limited to movement near the Sun
 | Center their deferent centers along the [[syzygy (astronomy)|Sun–Earth line]]
 |-
 | [[superior planet|Exterior planets]]
 | Retrograde only at [[opposition (astronomy)|opposition]], when brightest
 | Radii of epicycles aligned to the Sun–Earth line
 |}

The geocentric model was eventually replaced by the [[heliocentric model]]. [[Copernican heliocentrism]] could remove Ptolemy's epicycles because the retrograde motion could be seen to be the result of the combination of the movements and speeds of Earth and planets. Copernicus felt strongly that equants were a violation of Aristotelian purity, and proved that replacement of the equant with a pair of new epicycles was entirely equivalent. Astronomers often continued using the equants instead of the epicycles because the former was easier to calculate, and gave the same result.

It has been determined{{By whom|date=October 2019}} that the Copernican, Ptolemaic and even the [[Tychonic system|Tychonic]] models provide identical results to identical inputs: they are computationally equivalent. It was not until Kepler demonstrated a physical observation that could show that the physical Sun is directly involved in determining an orbit that a new model was required.

[[File:Ptolemaic system.svg|thumb|500px|[[Ptolemy]] thought the solar system looked like this]]
The Ptolemaic order of spheres from Earth outward is:<ref name= "Goldstein1967"/>
# [[Moon]]
# [[Mercury (planet)|Mercury]]
# [[Venus]]
# [[Sun]]
# [[Mars]]
# [[Jupiter]]
# [[Saturn]]
# [[Fixed Stars]]
# ''[[Primum Mobile]]'' ("First Moved")

Ptolemy did not invent or work out this order, which aligns with the ancient [[Seven Heavens|Seven Heavens religious cosmology]] common to the major Eurasian religious traditions. It also follows the decreasing orbital periods of the Moon, Sun, planets and stars.

===Persian and Arab astronomy and geocentrism===
{{Main|Maragheh observatory|Astronomy in medieval Islam|Islamic cosmology}}
After the [[Graeco-Arabic translation movement|translation movement]] that included the translation of [[Almagest]] from Latin to Arabic, Muslims adopted and refined the geocentric model of [[Ptolemy]], which they believed correlated with the teachings of Islam.<ref name="princeton.edu">{{Cite web|url=https://www.princeton.edu/~hos/mike/texts/ptolemy/ptolemy.html|title = Ptolemaic Astronomy in the Middle Ages}}</ref><ref name="link.springer.com">{{Cite book|chapter-url=https://link.springer.com/referenceworkentry/10.1007%2F978-1-4020-4425-0_8988|doi=10.1007/978-1-4020-4425-0_8988|chapter=Almagest: Its Reception and Transmission in the Islamic World|title=Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures|year=2008|last1=Kunitzsch|first1=Paul|pages=140–141|isbn=978-1-4020-4559-2}}</ref><ref name="astronomy.com">{{Cite web|url=https://astronomy.com/news/2017/02/muslim-contributions-to-astronomy|title = How Islamic scholarship birthed modern astronomy| date=14 February 2017 }}</ref> [[List of Muslim astronomers|Muslim astronomers]] generally accepted the Ptolemaic system and the geocentric model,<ref>{{cite journal | last1 = Sabra | first1 = A. I. | year = 1998 | title = Configuring the Universe: Aporetic, Problem Solving, and Kinematic Modeling as Themes of Arabic Astronomy | journal = [[Perspectives on Science]] | volume = 6 | issue = 3| pages = 288–330 [317–18] | doi = 10.1162/posc_a_00552 | s2cid = 117426616 }} {{blockquote|All Islamic astronomers from Thabit ibn Qurra in the ninth century to Ibn al-Shatir in the fourteenth, and all natural philosophers from al-Kindi to Averroes and later, are known to have accepted ... the Greek picture of the world as consisting of two spheres of which one, the celestial sphere ... concentrically envelops the other.}}</ref> but by the 10th century, texts appeared regularly whose subject matter expressed doubts concerning Ptolemy (''shukūk'').<ref>{{Cite book| publisher = Cambridge University Press| isbn = 9780521576000| last = Hoskin| first = Michael| title = The Cambridge Concise History of Astronomy| date = 1999-03-18|page=60}}</ref> Several Muslim scholars questioned Earth's apparent immobility<ref name= "Ragep2001a"/><ref name= "Ragep2001b"/> and centrality within the universe.<ref name=Setia2004 /> Some Muslim astronomers believed that [[Earth's rotation|Earth rotates around its axis]], such as [[Abu Sa'id al-Sijzi]] (d. circa 1020).<ref>{{Cite journal| volume = 108| issue = 67| pages = 762| last = Alessandro Bausani| title = Cosmology and Religion in Islam| journal = Scientia/Rivista di Scienza| date = 1973}}</ref><ref name=young /> According to [[al-Biruni]], Sijzi invented an [[astrolabe]] called ''al-zūraqī'', based upon a belief held by some of his contemporaries "that the motion we see is due to the Earth's movement and not to that of the sky".<ref name=young /><ref>{{Cite book| publisher = SUNY Press| isbn = 9781438414195| last = Nasr| first = Seyyed Hossein| title = An Introduction to Islamic Cosmological Doctrines| date = 1993-01-01|page=135}}</ref> The prevalence of this belief is further confirmed by a reference from the 13th century that states: <blockquote>According to the geometers [or engineers] (''muhandisīn''), the Earth is in constant circular motion, and what appears to be the motion of the heavens is actually due to the motion of the Earth and not the stars.<ref name=young>{{Cite book| publisher = Cambridge University Press| isbn = 9780521028875| editor-last1 = Young| editor-first1 = M. J. L.| title = Religion, Learning and Science in the 'Abbasid Period| date = 2006-11-02|page=413}}</ref></blockquote> Early in the 11th century, [[Alhazen]] wrote a scathing critique of [[Ptolemy]]'s model in his ''Doubts on Ptolemy'' ({{circa|1028}}), which some have interpreted to imply he was criticizing Ptolemy's geocentrism,{{sfn|Qadir|1989|p=5–10}} but most agree that he was actually criticizing the details of Ptolemy's model rather than his geocentrism.<ref>[http://setis.library.usyd.edu.au/stanford/entries/copernicus/index.html Nicolaus Copernicus], [[Stanford Encyclopedia of Philosophy]] (2004).</ref>
In the 12th century, [[Abū Ishāq Ibrāhīm al-Zarqālī|Arzachel]] departed from the ancient Greek idea of [[uniform circular motion]]s by hypothesizing that the planet [[Mercury (planet)|Mercury]] moves in an [[elliptic orbit]],<ref name= "Rufus1939"/><ref name= "Hartner1955"/> while [[Nur ad-Din al-Bitruji|Alpetragius]] proposed a planetary model that abandoned the [[equant]], [[Deferent and epicycle|epicycle and eccentric]] mechanisms,<ref name= "Goldstein1972"/> though this resulted in a system that was mathematically less accurate.<ref name= "Gale"/> His alternative system spread through most of Europe during the 13th century.<ref name=DSB>{{cite encyclopedia | last = Samsó | first = Julio | title =Al-Bitruji Al-Ishbili, Abu Ishaq| encyclopedia = [[Dictionary of Scientific Biography]] | publisher = Charles Scribner's Sons | location = New York | year=1970–80 | isbn = 0-684-10114-9 | url = http://www.encyclopedia.com/doc/1G2-2830904829.html}}</ref>

[[Fakhr al-Din al-Razi]] (1149–1209), in dealing with his [[Physics in medieval Islam|conception of physics]] and the physical world in his ''Matalib'', rejects the [[Aristotelianism|Aristotelian]] and [[Avicennism|Avicennian]] notion of the Earth's centrality within the universe, but instead argues that there are "a thousand thousand worlds (''alfa alfi 'awalim'') beyond this world, such that each one of those worlds be bigger and more massive than this world, as well as having the like of what this world has." To support his [[Islamic theology|theological argument]], he cites the [[Qur'an]]ic verse, "All praise belongs to God, Lord of the Worlds", emphasizing the term "Worlds".<ref name= "Setia2004"/>

The "Maragha Revolution" refers to the Maragha school's revolution against Ptolemaic astronomy. The "Maragha school" was an astronomical tradition beginning in the [[Maragheh observatory|Maragha observatory]] and continuing with astronomers from the [[Umayyad Mosque|Damascus mosque]] and [[Ulugh Beg Observatory|Samarkand observatory]]. Like their [[Al-Andalus|Andalusian]] predecessors, the Maragha astronomers attempted to solve the [[equant]] problem (the circle around whose circumference a planet or the center of an [[epicycle]] was conceived to move uniformly) and produce alternative configurations to the Ptolemaic model without abandoning geocentrism. They were more successful than their Andalusian predecessors in producing non-Ptolemaic configurations which eliminated the equant and eccentrics, were more accurate than the Ptolemaic model in numerically predicting planetary positions, and were in better agreement with empirical observations.<ref name= "Saliba1994"/> The most important of the Maragha astronomers included [[Mo'ayyeduddin Urdi]] (died 1266), [[Nasīr al-Dīn al-Tūsī]] (1201–1274), [[Qutb al-Din al-Shirazi]] (1236–1311), [[Ibn al-Shatir]] (1304–1375), [[Ali Qushji]] ({{circa|1474}}), [[Al-Birjandi]] (died 1525), and Shams al-Din al-Khafri (died 1550).<ref name= "Dallal1999"/>

However, the Maragha school never made the [[paradigm shift]] to heliocentrism.<ref name="Huff2003"/> The influence of the Maragha school on [[Copernicus]] remains speculative, since there is no documentary evidence to prove it. The possibility that Copernicus independently developed the Tusi couple remains open, since no researcher has yet demonstrated that he knew about Tusi's work or that of the Maragha school.<ref name="Huff2003" /><ref name="KirmaniSingh2005"/>