Geocentric model

This article 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model (also known as "geocentrism, "geocentricism," or the Ptolemaic view of the universe), is the theory, now superseded, that the Earth is the center of the universe and other objects go around it. Belief in this system was common in ancient Greece. It was embraced by both Aristotle (see Aristotelian physics) and Ptolemy, and most, but not all, Ancient Greek philosophers assumed that the Sun, Moon, stars, and naked eye planets circle the Earth. Similar ideas were held in ancient China.

Two common observations were believed to support the idea that the Earth is in the center of the Universe: The first observation is that the stars, sun, and planets appear to revolve around the Earth each day, with the stars circling around the pole and those stars nearer the equator rising and setting each day and circling back to their rising point; the second is the perception that as the Earth is solid and stable it is not moving—but is 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. The ancient Greeks believed that the motions of the planets were circular and not elliptical, a view that was not challenged in Western culture before the 17th century.

The predictions of Ptolemy's geocentric model were used for astrology for over 1500 years. The geocentric model held sway into the early modern age; from the late 16th century onward it was gradually replaced by the heliocentric model of Copernicus, Galileo and Kepler.

Classical Greece

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.

In the 4th century BC, two influential Greek philosophers wrote works based on the geocentric model. These were Plato and his student Aristotle. 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. In the "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. All heavenly bodies are attached to 56 concentric spheres which rotate around the Earth . (The number is so high because several transparent spheres are needed for each planet.) The Moon is on the innermost sphere. Thus it touches the realm of Earth, which contaminates it, causing the dark spots (macula) and the ability to go through lunar phases. It is not perfect like the other heavenly bodies, which shine by their own light.

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 parallax. In short, the shapes of the constellations should change considerably over the course of a year, or else the stars are so much further away than the Sun and the planets that this motion would be undetectable. Stellar parallax was not detected until the 19th century as the distances from the Earth to the stars made the effect extremely subtle, so the Greeks chose the simpler of the two explanations (either the Earth is not moving and so no effect exists, or the stars are so far away the effect was undetectable). The lack of any observable parallax was considered a fatal flaw of any non-geocentric theory. Another important observation was that Venus stays about the same brightness most of the time, implying that it is usually about the same distance from Earth, which is more consistent with geocentrism than heliocentrism. In reality, that is because the loss of light caused by its phases compensates for the increase in apparent size caused by its varying distance from Earth. Other objections included the idea, put forward by Aristotle, that the natural state of heavy objects like the Earth was at rest, and that some force was required to move them. It was also believed by some that the Earth's rotation on its axis would cause the air and objects in it (such as birds or clouds) to be left behind.

A major flaw in the Eudoxan and Aristotelian models based on concentric spheres was that they could not explain the changes in brightness of the planets caused by a change in distance.

Claudius Ptolemy

Although the basic tenets of Greek geocentrism were established by the time of Aristotle, the details of his system did not become standard. This honor was reserved for the Ptolemaic system, espoused by the Hellenistic astronomer Claudius Ptolemaeus in the 2nd century AD. His main astronomical book, 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, 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.

Ptolemaic system

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 two or more spheres: one sphere is its deferent. The deferent was a circle centered on a point halfway between the equant and the earth. Another sphere is the epicycle which is embedded in the deferent. The planet is embedded in the epicycle sphere. The deferent rotates around the Earth while the epicycle rotates within the deferent, causing the planet to move closer to and farther from Earth at different points in its orbit, and even to slow down, stop, and move backward (in retrograde motion). The epicycles of Venus and Mercury are always centered on a line between Earth and the Sun (Mercury being closer to Earth), which explains why they are 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 Latin ex- or e- meaning "from," and 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 prompted him 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, but many people did not like it because they did not think it was true to Plato's dictum of "uniform circular motion." The resultant system which eventually came to be widely accepted in the west was an unwieldy one to modern eyes; 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

Main articles: Maragheh observatory, Astronomy in medieval Islam, and Islamic cosmology

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

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, while Alpetragius proposed a planetary model that abandoned the equant, epicycle and eccentric mechanisms, though this resulted in a system that was mathematically less accurate. 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."

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 the geocentric model. 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. 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 al-Qushji (c. 1474), Al-Birjandi (d. 1525), and Shams al-Din al-Khafri (d. 1550). Ibn al-Shatir, the Damascene astronomer (1304–1375 A.D) 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 A.D)." 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. 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.

However, the Maragha school never made the paradigm shift to heliocentrism. 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.

Geocentrism and rival systems

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. 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. 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. Martianus Capella definitely put Mercury and Venus on epicycles around the Sun.

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. His theory was not popular, and he had one named follower, Seleucus of Seleucia.

Copernican system

Main article: Copernican heliocentrism

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.

With the invention of the telescope in 1609, observations made primarily by Galileo Galilei (such as that Jupiter has moons) called into question some of the tenets of geocentrism but did not seriously threaten it.

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

Johannes Kepler, after analysing Tycho Brahe's 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).

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 1838, astronomer Friedrich Wilhelm Bessel successfully measured the parallax of the star 61 Cygni, disproving Ptolemy's assertion that parallax motion did not exist.

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

Main article: Modern geocentrism

Individuals of some religions interpret their scriptures literally as stating that the Earth is the physical center of the universe. This requires the Sun to revolve around the Earth instead of the other way around because if the Earth were moving it could not continuously be in the center of the universe. This is known as modern geocentrism. Astrologers, while they may not believe in geocentrism as a principle, still employ the geocentric model in their calculations.

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.

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

Planetariums

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. The celestial sphere, still used for teaching purposes and sometimes for navigation, is also based on a geocentric system.

Geocentric models in science fiction

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

• Claudius Ptolemaeus
• Celestial spheres
• Firmament
• Heliocentrism
• Brahmanda (Earth is in middle planetary system)
• Hindu cosmology
• Religious_cosmology#Hindu

References

• Crowe, Michael J. (1990). Theories of the World from Antiquity to the Copernican Revolution. Mineola, NY: Dover Publications, Inc. ISBN 0-486-26173-5.
• Dreyer, J.L.E. (1953). A History of Astronomy from Thales to Kepler. New York, NY: Dover Publications.
• Evans, James. The History and Practice of Ancient Astronomy. New York: Oxford University Press, 1998.
• Heath, Thomas. Aristarchus of Samos. Oxford: Clarendon Press, 1913
• Hoyle, Fred, Nicolaus Copernicus, 1973.
• Koestler, Arthur The Sleepwalkers: A History of Man's Changing Vision of the Universe, 1959, Penguin Books, 1986 edition: ISBN 0-14-055212-X, 1990 reprint: ISBN 0-14-019246-8
• Kuhn, Thomas S. The Copernican Revolution. Cambridge: Harvard Univ. Pr., 1957. ISBN 0-674-17103-9
• Linton, Christopher M. (2004). From Eudoxus to Einstein—A History of Mathematical Astronomy. Cambridge: Cambridge University Press. ISBN 978-0-521-82750-8.
• Walker, Christopher, ed. Astronomy before the telescope. London: British Museum Press, 1996. ISBN 0-7141-1746-3

External links

• Another demonstration of the complexity of observed orbits when assuming a geocentric model of the solar system
• Geocentric Perspective animation of the Solar System in 150AD
• History of the Planetary Systems from Thales to Kepler by J. L. E. Dreyer
• Ptolemy's explanation for retrograde motion
• Ptolemy’s system of astronomy
• The Galileo Project - Ptolemaic System
• Interactive simulation of a heliocentric or geocentric representation of planetary paths