Geocentrism
Geocentrism is a superseded astronomical model description of the Universe with Earth at the center. It is also known as the geocentric model, often exemplified specifically by the Ptolemaic system. Under most geocentric models, the Sun, the Moon, stars, and planets all orbit Earth. The geocentric model was the predominant description of the cosmos in many European ancient civilizations, such as those of Aristotle in Classical Greece and Ptolemy in Roman Egypt, as well as during the Islamic Golden Age.
Two observations supported the idea that Earth was the center of the Universe. First, from anywhere on Earth, the Sun appears to revolve around Earth once per day. While the Moon and the planets have their own motions, they also appear to revolve around Earth about once per day. The stars appeared to be fixed on a celestial sphere rotating once each day about an axis through the geographical poles of Earth. Second, Earth seems to be unmoving from the perspective of an earthbound observer; it feels solid, stable, and stationary.
Ancient Greek, ancient Roman, and medieval philosophers usually combined the geocentric model with a spherical Earth, in contrast to the older flat-Earth model implied in some mythology. However, the Greek astronomer and mathematician Aristarchus of Samos developed a heliocentric model placing all of the then-known planets in their correct order around the Sun. The ancient Greeks believed that the motions of the planets were circular, a view that was not challenged in Western culture until the 17th century, when Johannes Kepler postulated that orbits were heliocentric and elliptical. In 1687, Isaac Newton showed that elliptical orbits could be derived from his laws of gravitation.
The astronomical predictions of [|Ptolemy's geocentric model], developed in the 2nd century, served as the basis for preparing astrological and astronomical charts for over 1,500 years. The geocentric model held sway into the early modern age, but from the late 16th century onward, it was gradually superseded by the heliocentric model of Copernicus, Galileo, and Kepler. There was much resistance to the transition between these two theories, since for a long time the geocentric postulate produced more accurate results. Additionally some felt that a new, unknown theory could not subvert an accepted consensus for geocentrism.
Ancient Greece
In the, Anaximander proposed a cosmology in which Earth is shaped like a section of a pillar, held aloft at the center of everything. The Sun, Moon, and planets were holes in invisible wheels which surround Earth, and through those holes, humans could see concealed fire. At around the same time, Pythagoras thought that Earth was a sphere, but not at the center; he believed that it was in motion around an unseen fire. Later these two concepts were combined, so that most of the educated Greeks from the 4th century BC onwards thought that Earth was a sphere at the center of the universe.In the 4th century BC 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 : 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. 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 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. Stellar parallax was not detected until the 19th century.
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. 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. 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
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 caculating the planet's latitude. By 1500 Nilakantha Somayaji developed a single approach for all of the planets. Among the ancient Indian astronomers Aryabhata argued for rotation of the Earth, but his system was otherwise geocentric.Ptolemaic model
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.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, 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
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 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, 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 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. Most noticeably the size of a planet's retrograde loop 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" 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 1,000 years of observations. The observed motions and his mechanisms for explaining them include:
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 that the Copernican, Ptolemaic and even the 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:
- Moon
- Mercury
- Venus
- Sun
- Mars
- Jupiter
- Saturn
- Fixed Stars
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