Geocentric model

From PhysicsWiki
Jump to: navigation, search
    This is about the historical term. For modern geocentrism, see Modern geocentrism.
    "Geocentric" redirects here. For orbits around the Earth, see Geocentric orbit.
    Figure of the heavenly bodies — An illustration of the Ptolemaic geocentric system by Portuguese cosmographer and cartographer Bartolomeu Velho, 1568 (Bibliothèque Nationale, Paris)

    In astronomy, the geocentric model (also known as geocentrism, or the Ptolemaic system), is the superseded theory that the Earth is the center of the universe, and that all other objects orbit around it. This geocentric model served as the predominant cosmological system in many ancient civilizations such as ancient Greece. As such, most Ancient Greek philosophers assumed that the Sun, Moon, stars, and naked eye planets circled the Earth, including the noteworthy systems of Aristotle (see Aristotelian physics) and Ptolemy.[1]

    Two commonly made observations supported the idea that the Earth was the center of the Universe. The first observation was that the stars, sun, and planets appear to revolve around the Earth each day, making the Earth the center of that system. Further, every star was on a "stellar" or "celestial" sphere, of which the earth was the center, that rotated each day, using a line through the north and south pole as an axis. The stars closest to the equator appeared to rise and fall the greatest distance, but each star circled back to its rising point each day.[2] The second common notion supporting the geocentric model was that the Earth does not seem to move from the perspective of an Earth bound observer, and that it is solid, stable, and unmoving. In other words, it is completely at rest.

    The geocentric model was usually combined with a spherical Earth by ancient Greek and medieval philosophers. It is not the same as the older flat Earth model implied in some mythology. However, the ancient Greeks believed that the motions of the planets were circular and not elliptical, a view that was not challenged in Western culture until the 17th century through the synthesis of theories by Copernicus and Kepler.

    The astronomical predictions of Ptolemy's geocentric model were used to prepare astrological charts for over 1500 years. The geocentric model held sway into the early modern age, but was gradually replaced from the late 16th century onward by the heliocentric model of Copernicus, Galileo and Kepler. However, the transition between these two theories met much resistance, not only from the Catholic Church, which was reluctant to accept a theory not placing God's creation at the center of the universe, but also from those who saw geocentrism as a fact that could not be subverted by a new, weakly justified theory.

    Ancient Greece[edit]

    Illustration of Anaximander's models of the universe. On the left, daytime in summer; on the right, nighttime in winter.

    The geocentric model entered Greek astronomy and philosophy at an early point; it can be found in Pre-Socratic philosophy. In the 6th century BC, Anaximander proposed a cosmology with the Earth shaped like a section of a pillar (a cylinder), held aloft at the center of everything. The Sun, Moon, and planets were holes in invisible wheels surrounding the Earth; through the holes, humans could see concealed fire. About the same time, the Pythagoreans thought that the Earth was a sphere (in accordance with observations of eclipses), but not at the center; they believed that it was in motion around an unseen fire. Later these views were combined, so most educated Greeks from the 4th century BC on thought that the Earth was a sphere at the center of the universe.[3]

    In the 4th century BC, two influential Greek philosophers, Plato and his student Aristotle, wrote works based on the geocentric model. According to Plato, the Earth was a sphere, stationary at the center of the universe. The stars and planets were carried around the Earth on spheres 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 47–56 transparent concentric spheres which rotate around the Earth. (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 rotation 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 (macula) 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, where the solid spheres of aether in which the celestial bodies were embedded. They, themselves, were also entirely composed of aether.

    Adherence to the geocentric model stemmed largely from several important observations. First of all, if the Earth did move, then one ought to be able to observe the shifting of the fixed stars due to stellar parallax. In short, if the earth was moving, the shapes of the constellations should change considerably over the course of a year. If they did not appear to move, the stars are either much further away than the Sun and the planets than previously conceived, making their motion undetectable, or in reality they are not moving at all. Because the stars were actually much further away than Greek astronomers postulated (making movement extremely subtle), stellar parallax was not detected until the 19th century. Therefore, the Greeks chose the simpler of the two explanations. The lack of any observable parallax was considered a fatal flaw in any non-geocentric theory. 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 reality, that is because the loss of light caused by Venus' phases compensates for the increase in apparent size caused by its varying distance from Earth. Objections to heliocentrism utilized the natural tendency of terrestrial bodies to come to rest as near as possible to the center of the earth, and barring the opportunity to fall closer the center, 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.[4] Eventually, perfectly concentric spheres were abandoned as it wasn't possible to develop a sufficiently accurate model under that ideal. However, while providing for similar explanations, The later deferent and epicycle model proved to be flexible enough to accommodate observations for many centuries.

    Ptolemaic Model[edit]

    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, espoused by the Hellenistic astronomer Claudius Ptolemaeus in the 2nd century AD finally accomplished this process. His main astronomical work, the Almagest, was the culmination of centuries of work by Hellenic, Hellenistic and Babylonian astronomers; it was accepted for over a millennium as the correct cosmological model by European and Islamic astronomers. Because of its influence, the Ptolemaic system is sometimes considered identical with the geocentric model.

    Ptolemy argued that the Earth was 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 was substantially displaced from the center, this division into visible and invisible stars would not be equal.[5]

    Ptolemaic system[edit]

    The basic elements of Ptolemaic astronomy, showing a planet on an epicycle with an eccentric deferent and an equant point.
    Pages from 1550 SACROBOSCO "Tractatus de Sphaera" with the Ptolemaic system.

    In the Ptolemaic system, each planet is moved by a system of two or more spheres: one called its deferent, the others, its epicycles. The deferent is a circle whose center point exists halfway between the equant and the earth, marked by the X in the picture to the right where the equant is the solid point opposite the earth. Another sphere, the epicycle, is embedded inside of the deferent and is represented by the smaller dotted line to the right. A given planet then moves along 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 caused observers to believe that the planet even slowed down, stopped, and moved backward (in retrograde motion). This apparent retrograde motion was one of the largest inconsistencies in Greek cosmological systems, and was one of Ptolemy's main reasons for creating the deferent, epicycle model. The apparent retrograde motion was eventually replaced by the heliocentric model, and dispelled as an observation that is made only from earthbound observers. However, this model of deferents and epicycles made observations and predictions much more accurate than all preceding systems. The epicycles of Venus and Mercury are always centered on a line between Earth and the Sun (Mercury being closer to Earth), which explained why they were always near it in the sky.

    The Ptolemaic order of spheres from Earth outward is:

    1. Moon
    2. Mercury
    3. Venus
    4. Sun
    5. Mars
    6. Jupiter
    7. Saturn
    8. Fixed Stars
    9. Sphere of Prime Mover

    The deferent-and-epicycle model had been used by Greek astronomers for centuries, as had the idea of the eccentric (a deferent which is slightly off-center from the Earth). In the illustration, the center of the deferent is not the Earth but X, making it eccentric (from the Greek ἐκ ec- meaning "from," and κέντρον centrum meaning "center"). Unfortunately, the system that was available in Ptolemy's time did not quite match observations, even though it was considerably improved over Aristotle's system. Sometimes the size of a planet's retrograde loop (most notably that of Mars) would be smaller, and sometimes larger. This mismatch prompted Ptolemy to come up with the idea of an equant. The equant was a point near the center of a planet's orbit which, if you were to stand there and watch, the center of the planet's epicycle would always appear to move at the same speed. Therefore, the planet actually moved at different speeds when the epicycle was at different points on its deferent. By using an equant, Ptolemy claimed to keep motion which was uniform and circular, although it departed from the Plato 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. But it predicted various celestial motions, including the beginnings and ends of retrograde motion, fairly well at the time it was developed.

    Geocentrism and Islamic astronomy[edit]

    Due to the scientific dominance of the Ptolemaic system in Islamic astronomy, the Muslim astronomers accepted unanimously the geocentric model.[6]

    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,[7][8] while Alpetragius proposed a planetary model that abandoned the equant, epicycle and eccentric mechanisms,[9] though this resulted in a system that was mathematically less accurate.[10] 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."[11]

    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.[12] 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).[13] Ibn al-Shatir, the Damascene astronomer (1304–1375 AD) working at the Umayyad Mosque, wrote a major book entitled Kitab Nihayat al-Sul fi Tashih al-Usul (A Final Inquiry Concerning the Rectification of Planetary Theory) on a theory which departs largely from the Ptolemaic system known at that time. In his book, "Ibn al-Shatir, an Arab astronomer of the fourteenth century," E.S.Kennedy wrote "what is of most interest, however, is that Ibn al-Shatir's lunar theory, except for trivial differences in parameters, is identical with that of Copernicus (1473–1543 AD)." The discovery that the models of Ibn al-Shatir are mathematically identical to those of Copernicus suggests the possible transmission of these models to Europe.[14] At the Maragha and Samarkand observatories, the Earth's rotation was discussed by al-Tusi and Ali Qushji (b. 1403); the arguments and evidence they used resemble those used by Copernicus to support the Earth's motion.[15][16]

    However, the Maragha school never made the paradigm shift to heliocentrism.[17] 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.[17][18]

    Geocentrism and rival systems[edit]

    This drawing from an Icelandic manuscript dated around 1750 illustrates the geocentric model.

    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.[19] 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.[20] 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 this is no longer accepted.[21] Martianus Capella definitely put Mercury and Venus in orbit around the Sun.[22] Aristarchus of Samos was the most radical. He 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.[23] His theory was not popular, and he had one named follower, Seleucus of Seleucia.[24]

    Copernican system[edit]

    In 1543, the geocentric system met its first serious challenge with the publication of Copernicus' De revolutionibus orbium coelestium, 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).

    With the invention of the telescope in 1609, observations made by Galileo Galilei (such as that Jupiter has moons) called into question some of the tenets of geocentrism but did not seriously threaten it. Because he observed dark "spots" on the moon, craters, he was able to remark that the moon was not a perfect celestial body as had been previously conceived. This was the first time someone was able to see imperfections on a celestial body that was supposed to be composed of perfect aether. As such, because the moon's imperfections could now be related to those seen on Earth, one could argue that neither was unique: rather, they were both just celestial bodies made from earthlike material. Galileo was also able to see the moons of Jupiter, which he dedicated to Cosimo II de' Medici, and stated that they orbited around Jupiter, not Earth.[25] This was a significant claim because if true, it would mean that not everything revolved around Earth, shattering previously held theological and scientific belief. As such, Galileo's theories challenging the geocentrism of our universe were silenced by the Church and general skepticism towards any system that did not place Earth at its center, preserving the thoughts and systems of Ptolemy and Aristotle.

    Phases of Venus

    In December 1610, Galileo Galilei used his telescope to observe that Venus showed all phases, just like the Moon. He thought that while this observation was incompatible with the Ptolemaic system, it was a natural consequence of the heliocentric system.

    However, Ptolemy placed Venus' deferent and epicycle entirely inside the sphere of the Sun (between the Sun and Mercury), but this was arbitrary; he could just as easily have swapped Venus and Mercury and put them on the other side of the Sun, or made any other arrangement of Venus and Mercury, as long as they were always near a line running from the Earth through the Sun, such as placing the center of the Venus epicycle near the Sun. In this case, if the Sun is the source of all the light, under the Ptolemaic system:

    If Venus is between Earth and the Sun, the phase of Venus must always be crescent or all dark.

    If Venus is beyond the Sun, the phase of Venus must always be gibbous or full.

    But Galileo saw Venus at first small and full, and later large and crescent.

    This showed that with a Ptolemaic cosmology, the Venus epicycle can be neither completely inside nor completely outside of the orbit of the Sun. As a result, Ptolemaics abandoned the idea that the epicycle of Venus was completely inside the Sun, and later 17th century competition between astronomical cosmologies focused on variations of Tycho Brahe's Tychonic system (in which the Earth was still at the center of the universe, and around it revolved the Sun, but all other planets revolved around the Sun in one massive set of epicycles), or variations on the Copernican system.

    Gravitation[edit]

    Johannes Kepler, after analysing Tycho Brahe's famously accurate observations, constructed his three laws in 1609 and 1619, based on a heliocentric view where the planets move in elliptical paths. Using these laws, he was the first astronomer to successfully predict a transit of Venus (for the year 1631). The transition from circular orbits to elliptical planetary paths dramatically changed the accuracy of celestial observations and predictions. Because the heliocentric model by Copernicus was no more accurate than Ptolemy's system, new mathematical observations were needed to persuade those who still held on to the geocentric model. However, the observations made by Kepler, using Brahe's data, became a problem not easily overturned for geocentrists.

    In 1687, Isaac Newton devised his law of universal gravitation, which introduced gravitation as the force that both kept the Earth and planets moving through the heavens and also kept the air from flying away, allowing scientists to quickly construct a plausible heliocentric model for the solar system. In his Principia, Newton explained his system of how gravity, previously considered to be an occult force, conducted the movements of celestial bodies, and kept our solar system in its working order. His descriptions of centripetal force[26] were a breakthrough in scientific thought, and finally replaced the previous schools of scientific thought, i.e. those of Aristotle and Ptolemy. However, the process was gradual.

    In 1838, astronomer Friedrich Wilhelm Bessel successfully measured the parallax of the star 61 Cygni, disproving Ptolemy's assertion that parallax motion did not exist. This finally substantiated the suppositions made by Copernicus with accurate, dependable scientific observations, and displayed truly how far away stars were from Earth.

    A geocentric frame is useful for many everyday activities and most laboratory experiments, but is a less appropriate choice for solar-system mechanics and space travel. While a heliocentric frame is most useful in those cases, galactic and extra-galactic astronomy is easier if the sun is treated as neither stationary nor the center of the universe, but rotating around the center of our galaxy, and in turn our galaxy is also not at rest in the cosmic background.

    Modern geocentrism[edit]

    Main article: Modern geocentrism

    The contemporary Association for Biblical Astronomy, led by physicist Dr. Gerardus Bouw, holds to a modified version of the model of Tycho Brahe, which they call geocentricity.[27]

    Polls conducted by Gallup in the 1990s found that 16% of Germans, 18% of Americans and 19% of Britons hold that the Sun revolves around the Earth.[28] A study done in 2005 by Dr. Jon D. Miller of Northwestern University, an expert in the public understanding of science and technology,[29] found that one adult American in five (about 20%) thinks the Sun revolves around the Earth.[30]

    Planetariums[edit]

    The geocentric (Ptolemaic) model of the solar system is still of interest to planetarium makers, as, for technical reasons, a Ptolemaic-type motion for the planet light apparatus has some advantages over a Copernican-type motion.[31] The celestial sphere, still used for teaching purposes and sometimes for navigation, is also based on a geocentric system.[32]

    Geocentric models in science fiction[edit]

    Alternate history science fiction has produced some literature of interest on the proposition that some alternate universes and Earths might indeed have laws of physics and cosmologies that are Ptolemaic and Aristotelian in design. This subcategory began with Philip Jose Farmer's short story, Sail On! Sail On! (1952), where Columbus has access to radio technology, and where his Spanish-financed exploratory and trade fleet sail off the edge of the (flat) world in his geocentric alternate universe in 1492, instead of discovering North America and South America.

    Richard Garfinkle's Celestial Matters (1996) is set in a more elaborated geocentric cosmos, where Earth is divided by two contending factions, the Classical Greece-dominated Delian League and the Chinese Middle Kingdom, both of which are capable of flight within an alternate universe based on Ptolemaic astronomy, Aristotle's physics and Taoist thought. Unfortunately, both superpowers have been fighting a thousand-year war since the time of Alexander the Great.

    See also[edit]

    Notes[edit]

    1. Lawson, Russell M. (2004). Science in the ancient world: an encyclopedia. ABC-CLIO. pp. 29–30. ISBN 1851095349. Retrieved 2 October 2009. 
    2. Thomas S. Kuhn, The Copernican Revolution, pp. 5–20
    3. Fraser, Craig G. – The Cosmos: A Historical Perspective (2006) – p.14
    4. Hetherington, Norriss S. – Planetary Motions: A Historical Perspective (2006) – p.28
    5. This argument is given in Book I, Chapter 5, of the Almagest (Crowe, 1990, pp.60–62).
    6. A. I. Sabra, "Configuring the Universe: Aporetic, Problem Solving, and Kinematic Modeling as Themes of Arabic Astronomy," Perspectives on Science 6.3 (1998): 288–330, at pp. 317–18:
      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.
    7. Rufus, W. C. (May 1939). "The Influence of Islamic Astronomy in Europe and the Far East". Popular Astronomy 47 (5): 233–238. Bibcode:1939PA.....47..233R. 
    8. Willy Hartner, "The Mercury Horoscope of Marcantonio Michiel of Venice", Vistas in Astronomy, 1 (1955): 84–138, at pp. 118–122.
    9. Bernard R. Goldstein (March 1972). "Theory and Observation in Medieval Astronomy", Isis 63 (1): 39–47 [41].
    10. "Science and Its Times". Thomson Gale. 2005–2006. Retrieved 2008-01-22.  |chapter= ignored (help)
    11. Adi Setia (2004). "Fakhr Al-Din Al-Razi on Physics and the Nature of the Physical World: A Preliminary Survey". Islam & Science 2. Retrieved 2010-03-02. 
    12. George Saliba (1994), A History of Arabic Astronomy: Planetary Theories During the Golden Age of Islam, p. 233–234, 240. New York University Press, ISBN 0-8147-8023-7.
    13. Ahmad Dallal (1999), "Science, Medicine and Technology", in The Oxford History of Islam, p. 171, ed. John Esposito, New York: Oxford University Press
    14. Guessoum, N. (June 2008). "Copernicus and Ibn Al-Shatir: does the Copernican revolution have Islamic roots?". The Observatory 128: 231–239. Bibcode:2008Obs...128..231G. 
    15. Ragep, F. Jamil (2001a). "Tusi and Copernicus: The Earth's Motion in Context". Science in Context (Cambridge University Press) 14 (1-2): 145–163. 
    16. Ragep, F. Jamil (2001b). "Freeing Astronomy from Philosophy: An Aspect of Islamic Influence on Science". Osiris, 2nd Series 16 (Science in Theistic Contexts: Cognitive Dimensions): 49–64 & 66–71. Bibcode:2001Osir...16...49R. doi:10.1086/649338. 
    17. 17.0 17.1 Toby E.Huff(1993):The rise of early modern science: Islam, China, and the West[1]
    18. N.K. Singh, M. Zaki Kirmani,Encyclopaedia of Islamic science and scientists[2]
    19. K. F. Johansen, H. Rosenmeier, A History of Ancient Philosophy: From the Beginnings to Augustine (1998), p.43
    20. George Sarton, Ancient Science Through the Golden Age of Greece (1953), p.290
    21. Eastwood, B. S. (1992-11-01). "Heraclides and Heliocentrism – Texts Diagrams and Interpretations". Journal for the History of Astronomy 23: 233. Bibcode:1992JHA....23..233E. 
    22. Lindberg, David C. — The Beginnings of Western Science – p.197
    23. Lawson, Russell M. — Science in the ancient world (2004) – p.19
    24. Russell, Bertrand — History of Western Philosophy (2004) – p.215
    25. Finocchiaro, Maurice A. The Essential Galileo. Indianapolis: Hackett Publishing Company, 2008. pg 49.
    26. Selections from Newton's Principia. ed. Dana Densmore. Green Lion Press, 2004. pg. 12.
    27. Geocentricity.com
    28. Steve Crabtree (July 6, 1999). "New Poll Gauges Americans' General Knowledge Levels". Gallup. 
    29. "Jon D. Miller". Northwestern University. Retrieved 2007-07-19. 
    30. Cornelia Dean (30 August 2005). "Scientific Savvy? In U.S., Not Much". New York Times. Retrieved 2007-07-19. 
    31. William Jillard Hort, A General View of the Sciences and Arts, (1822), Page 182
    32. Kaler, James B. – The Ever-changing Sky: A Guide to the Celestial Sphere (2002) – p.25

    References[edit]

    External links[edit]

    Script error