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0003, 9519, 11336, 72174, hdl, s00407, 017, 0198, exact, pre, ramasubramanian, srinivas, sriram, 790, 0011, 3891, 784, modification, hetherington, norriss, 9780313332418, 226, 48205, fraser, craig, 9780313332180, terminology, rising
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es or circles arranged in the order outwards from the center moon sun venus mercury mars jupiter saturn fixed stars with the fixed stars located on the celestial sphere in his myth of er a section of the republic plato describes the cosmos as the spindle of necessity attended by the sirens and turned by the three fates eudoxus of cnidus who worked with plato developed a less mythical more mathematical explanation of the planets motion based on plato s dictum stating that all phenomena in the heavens can be explained with uniform circular motion aristotle elaborated on eudoxus system in the fully developed aristotelian system the spherical earth is at the center of the universe and all other heavenly bodies are attached to 47 55 transparent rotating spheres surrounding the earth all concentric with it the number is so high because several spheres are needed for each planet these spheres known as crystalline spheres all moved at different uniform speeds to create the revolution of bodies around the earth they were composed of an incorruptible substance called aether aristotle believed that the moon was in the innermost sphere and therefore touches the realm of earth causing the dark spots maculae and the ability to go through lunar phases he further described his system by explaining the natural tendencies of the terrestrial elements earth water fire air as well as celestial aether his system held that earth was the heaviest element with the strongest movement towards the center thus water formed a layer surrounding the sphere of earth the tendency of air and fire on the other hand was to move upwards away from the center with fire being lighter than air beyond the layer of fire were the solid spheres of aether in which the celestial bodies were embedded they were also entirely composed of aether adherence to the geocentric model stemmed largely from several important observations if the earth moved then the apparent angular separations between stars would be expected to change due to a shifted viewpoint the shapes of the constellations should then change over the course of a year since the constellations appeared constant in shape throughout the year ancient astronomers concluded that either the stars were extremely distant or the earth was stationary the greeks chose the simpler of the two explanations citation needed stellar parallax was not detected until the 19th century citation needed another observation used in favor of the geocentric model at the time was the apparent consistency of venus luminosity which implies that it is usually about the same distance from earth which in turn is more consistent with geocentrism than heliocentrism in fact venus luminous consistency is due to any loss of light caused by its phases being compensated for by an increase in apparent size caused by its varying distance from earth objectors to heliocentrism noted that terrestrial bodies naturally tend to come to rest as near as possible to the center of the earth further barring the opportunity to fall closer the center terrestrial bodies tend not to move unless forced by an outside object or transformed to a different element by heat or moisture atmospheric explanations for many phenomena were preferred because the eudoxan aristotelian model based on perfectly concentric spheres was not intended to explain changes in the brightness of the planets due to a change in distance 5 eventually perfectly concentric spheres were abandoned as it was impossible to develop a sufficiently accurate model under that ideal with the mathematical methods then available however while providing for similar explanations the later deferent and epicycle model was already flexible enough to accommodate observations ancient indian edit before the kerala astronomers around 1500 indian astronomy was focused on predicting solar and planetary motions rather than as a model of the cosmos the earlier astronomers developed two different approaches one for the sun and inner planets mercury and venus and one for the outer planets mars jupiter and saturn the systems was broadly similar to the ptolemaic system but more accurate in calculating the planet s latitude by 1500 nilakantha somayaji developed a single approach for all of the planets 6 among the ancient indian astronomers aryabhata argued for rotation of the earth but his system was otherwise geocentric 7 ptolemaic model edit 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 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 written down by the hellenistic astronomer claudius ptolemaeus in the 2nd century ad finally standardized geocentrism the key work describing the system only survives via an arabic translation of a book named planetary hypothesis 8 for over a millennium european and 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 n 1 in the ptolemaic system each planet is moved by a system of two spheres 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 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 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 observations even though it was an improvement over hipparchus system pages from 1550 annotazione on sacrobosco s de sphaera mundi showing the ptolemaic 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 relatively accurate model of an elliptical orbit with low eccentricity the ellipse shape does not appear to a noticeable extent when the eccentricity is less than 5 but the offset distance of the center or the focus occupied by the sun is very noticeable even with low eccentricities as possessed by the planets persian and arab astronomy and geocentrism edit main articles maragheh observatory astronomy in medieval islam and islamic cosmology after the graeco arabic translation movement that included the translation of the almagest from greek to arabic muslims adopted and refined the geocentric model of ptolemy which they believed correlated with the teachings of islam 10 11 12 muslim astronomers generally accepted the ptolemaic system and the geocentric model 13 but by the 10th century texts appeared regularly whose subject matter expressed doubts concerning ptolemy shukūk 14 several muslim scholars questioned earth s apparent immobility 15 16 and centrality within the universe 17 some muslim astronomers believed that earth rotates around its axis such as abu sa id al sijzi d c 1020 18 19 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 19 20 the prevalence of this belief is further confirmed by a reference from the 13th century that states 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 19 early in the 11th century alhazen wrote a scathing critique of ptolemy s model in his doubts on ptolemy c 1028 which some have interpreted to imply he was criticizing ptolemy s geocentrism 21 but most agree that he was actually criticizing the details of ptolemy s model rather than his geocentrism 22 in the 12th century arzachel departed from the ancient greek idea of uniform circular motions by hypothesizing that the planet mercury moves in an elliptic orbit 23 24 while alpetragius proposed a planetary model that abandoned the equant epicycle and eccentric mechanisms 25 though this resulted in a system that was mathematically less accurate 26 his alternative system spread through most of europe during the 13th century 27 fakhr al din al razi 1149 1209 in dealing with his conception of physics and the physical world in his matalib rejects the aristotelian and 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 theological argument he cites the qur anic verse all praise belongs to god lord of the worlds emphasizing the term worlds 17 the maragha revolution refers to the maragha school s revolution against ptolemaic astronomy the maragha school was an astronomical tradition beginning in the maragha observatory and continuing with astronomers from the damascus mosque and samarkand observatory like their 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 28 the most important of the maragha astronomers included mo ayyeduddin urdi d 1266 nasīr al dīn al tūsī 1201 1274 qutb al din al shirazi 1236 1311 ibn al shatir 1304 1375 ali qushji c 1474 al birjandi d 1525 and shams al din al khafri d 1550 29 however the maragha school never made the paradigm shift to heliocentrism 30 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 30 31 ptolemaic and rival systems edit not all greeks agreed with the geocentric model the pythagorean system has already been mentioned some pythagoreans believed the earth to be one of several planets going around a central fire 32 hicetas and ecphantus two pythagoreans of the 5th century bc and heraclides ponticus in the 4th century bc believed that the earth rotated on its axis but remained at the center of the universe 33 such a system still qualifies as geocentric it was revived in the middle ages by jean buridan heraclides ponticus was once thought to have proposed that both venus and mercury went around the sun rather than the earth but it is now known that he did not 34 martianus capella definitely put mercury and venus in orbit around the sun 35 aristarchus of samos wrote a work which has not survived on heliocentrism saying that the sun was at the center of the universe while the earth and other planets revolved around it 36 his theory was not popular and he had one named follower seleucus of seleucia 37 epicurus was the most radical he correctly realized in the 4th century bc that the universe does not have any single center this theory was widely accepted by the later epicureans and was notably defended by lucretius in his poem de rerum natura 38 copernican system edit main article copernican heliocentrism in 1543 the geocentric system met its first serious challenge with the publication of copernicus de revolutionibus orbium coelestium on the revolutions of the heavenly spheres which posited that the earth and the other planets instead revolved around the sun the geocentric system was still held for many years afterwards as at the time the copernican system did not offer better predictions than the geocentric system and it posed problems for both natural philosophy and scripture the copernican system was no more accurate than ptolemy s system because it still used circular orbits this was not altered until johannes kepler postulated that they were elliptical kepler s first law of planetary motion tychonic system ed...
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