The Ptolemaic System - A Short History

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The Ptolemaic System - A Short History
« on: March 06, 2005, 11:08:24 AM »
by Francis Graham

Early in the history of civilization, peoples in the Nile and Tigris-Euphrates valleys developed an interest in astronomy and a concern about the nature and condition of the Universe they found themselves in. The earliest such models of the Universe developed there depicted a flat Earth, surrounded by high mountains, and a solid dome of a sky upon which stars were placed, and through which water canopies poured their rainfall. Planets, and the sun and the moon, were comparatively small
bodies controlled by divine forces. This model, in place at the time of the Akkadian Empire, and the cities of Ur, and Sumer, is called the Mesopotamian Model.

Other civilizations who adopted it modified it. The center of the flat Earth in became the capital of the adopting civilization. The divine forces behind the motions of the sun, moon and planets were caused by the god(s) and goddess(es) of the adopting civilizations. Sometimes the metallic canopy was personified, such as the Egyptian goddess Nuit becoming the sky.
The model is also presented in the Bible, as discussed by Robert Schadewald in an insightful article. There we find a water canopy, a great Deluge, and a flat earth depicted, with the sun and moon small objects that could stop over valleys (as in Joshua 10) and a tabernacle where the sun was placed at night (Psalm 19). It is particularly meaningful that Abraham, the founder of the Hebrew culture, is said to have been born in Ur.

The Greeks adopted the Mesopotamian model originally, and had their god Helios, and later Apollo, drive the sun chariot across the sky, over a flat Earth. This is clear in a reading of the Iliad, and the myths of Phaeton. However, the Greeks began to develop higher mathematics, particularly geometry, and logical reasoning. These two twin pillars enabled them to make discoveries which caused the Hellenistic Culture to reject the Mesopotamian model.

Earlier Hellenistic natural philosophers had suspected the Earth was a globe by analogy with the sun and moon, but Aristotle seems to have been the first to know this with certainty. Aristotle had gained reputation as the person who wrote down for the first time the comprehensive rules of logical analysis, rules which by and large stand today.  He also was the tutor of no less a person than Alexander the Great. Aristotle noticed that, during a lunar eclipse, the shadow of the Earth on the moon was a
section of a circle, no matter where the moon was in relation to the shadow:to the north, south, east or west. Hence the conclusion was inescapable, after observing many eclipses, that the Earth cast a circular shadow.  While circular flat objects can also cast circular shadows, Aristotle further noted that the shadow of the Earth was circular no matter in which direction the eclipse took place--in Aries, Capricorn, Gemini or Sagittarius-- it was circular in every orientation.  The only object that can
cast a circular shadow when illuminated in any direction is a sphere.  Hence Aristotle was led to the inescapable conclusion that the Earth is sensibly a sphere.

Aristotle's logical reasoning allowed him to postulate, with Eudoxus, that the spherical Earth was at the center of the Universe, with the sun, moon, planets and stars all circling around it on concentric crystal spheres. But the logical reasoning was based on premises developed from a faulty sense of physical processes and falling bodies and motion, which he
regarded as self-evident starting points. Hence, Aristotle was totally wrong about the nature of the Universe and the station of the Earth in it.

The multiple concentric shells of Aristotle and Eudoxus were by no means universally accepted, but became a majority view of most Hellenistic natural philosophers.

The next step in the development of Hellenistic science came from more precise observations of celestial bodies, using essentially moveable sighting holes on large protractors (the telescope was not invented, of course, until 1609) and marked sticks. This was possible with the creation of a large scientific institution, the Library and Museum at Alexandria.

Alexander the Great's conquering army had spread Hellenistic culture as far as India, and had subdued Persia, Babylonia, Palestine and Egypt. When he died young in Babylon, the vast empire was divided among his generals, and the general that received Egypt, was Ptolemy I. Ptolemy provided support for the founding of a large library and museum in Alexandria, a city founded by Alexander the Great.  In this scientific and literary arena, scientific accomplishments were examined and performed.
Eratosthenes measured the size of the Earth correctly. And astronomical observations were performed, Hipparchus, for example, making his large star catalog.

The results of this sequence of observations produced a paradox which was inconsistent with the concentric spheres of Eudoxus. The moving celestial bodies, the moon, the sun, the planets, exhibited an irregularity in motion that the uniformly moving concentric spheres would not explain. Particular among them was retrograde motion of the outer planets, Mars, Jupiter and Saturn (Uranus, Neptune and Pluto were unknown in pretelescopic times). Planets exhibit retrograde motion when they seem to stop their usual apparent motion from west to east along or near the ecliptic, reverse direction and for a while go from east to west among the "fixed" stars, and then stop and proceed prograde again.

Two explanations arose in ancient Hellenistic science to explain this phenomenon. The first, by Aristarchus of Samos,placed the sun at the center of the Universe and the Earth as one of the planets going around it, each planet completing its revolution around the sun in a shorter time period than the next planet farther out. As an inner planet, such as the Earth, passed a less speedy outer planet, such as Mars, the outer planet would be seen to lag behind and even move backwards relative to the
much more distant stars. As the Earth rounded the curve of its orbit, however, the outer planet would be seen to move forward again. Also, in Aristarchus' system, the fixed sun only appears to rise and set each day because of the rotation of the Earth.

Aristarchus' system explained retrograde motion well and was, as we now know, the correct choice. Other irregularities in the motion of the planets around the sun could be explained in Aristarchus' system by adding additional circular motions (heliocentric epicycles, as was done by Copernicus) or by assuming the planets orbit on ellipses (the correct choice, as was done by Kepler). However, another system was proposed which also explained retrograde motion.

Claudius Ptolemaeus, or Ptolemy (no relation to the earlier King Ptolemy) proposed such an alternative system around the year 60. In his view, the Earth was essentially near the center of the Universe, and exhibited no motion of any kind, the stars,sun and moon going around it every day. Retrograde planetary motion was explained by adding epicycles, or circles on circles. The main concentric crystal sphere of Eudoxus was preserved in the deferent, centered near the immobile Earth. The epicycle, or
circle on the circle, rotated backwards with respect to the deferent's motion and carried the planet imbedded in its circumference.

The inner planets (Mercury and Venus) in Ptolemy's system orbited on deferents with the same period of revolution as the sun. Their epicycles were large, and allowed them to be taken some angular distance from the sun corresponding to their points of greatest elongation. This was a necessary contrivance to explain why the planets Mercury and Venus can never be seen in opposition. In the Aristarchus (heliocentric) model, it is
obvious: they are inner planets, and cannot get on the opposite side of the Earth than the sun is on.  

Ptolemy first announced his system in a manuscript called the "Planetary Hypothesis". His full-blown theory, however, is found in his much more comprehensive work, "The Mathematical Syntaxis", more commonly called "The Almagest". Although Ptolemy's manuscripts are in Greek, and the "Planetary Hypothesis" only survives in an Arabic translation, you can read an English translation of Ptolemy's Almagest in Volume 16 of the Britannica
Great Books series, which most American libraries have. If you have learned geometry in high school you'll find it very readable.

Ptolemy's system had some early advantages over the Aristarchus system which facilitated its acceptance by Hellenistic natural philosophers. First, it preserved the idea of the Earth's immobility and the erroneous physics of Aristotle ; acceptance of the Aristarchus' system would have necessitated a renewed look at the underlying assumption of that physics. 1st -
Century natural philosophers were apparently unwilling to make those severe changes. Secondly, although there is evidence that Ptolemy fudged some numbers to make his system look more accurate, it could nonetheless be made accurate to any required degree by the addition of epicycles upon epicycles, as some Arabic scholars attempted to do.  This is because of a mathematically permissible technique, Fourier Analysis, which is based on the fact that ANY periodic motion can be described in
terms of a sum of a series of circular motions. In essence, then, Ptolemy's system Fourier-analyzed the Universe.

The last advantage was that, in Aristarchus system, a moving Earth would give a slightly different viewing angle to the stars when they were observed at points on the Earth's orbit six months apart. This effect, called parallax, was not observed by the ancient peephole-tubes and protractors used by the pretelescopic astronomers. The ancient astronomers could have observed parallax if the parallax angle were as large as 2 minutes of arc. For the parallax angle to not be detected, and Aristarchus' system to be true, the stars would have to be over 40 million times the Earth's radius in distance. The natural philosophers of classical times could not believe this; Ptolemy's much smaller, walled in Universe, had the star sphere only 20,000 times the Earth's radius. Much later, of course, in 1838, parallax was measured on the nearest stars, using a split-lens fitted with micrometers for which all previous errors, e.g. flexure, temperature expansion, etc., had been determined and subtracted. A parallax of three
quarters of one arc-second was thereby measured for the nearest star beyond the sun, and that corresponds to a distance of 6.3 billion Earth radii.

As the Roman Empire and Hellenistic civilization collapsed in western and central Europe, the Hellenistic scientific learning fell into the hands of the Christian Church, where it, as well as all other classical learning and mislearning, was filtered through a doctrinal filter. There was intense debate whether the flat-Earth depicted in the Bible was correct or not among the early Church fathers, Lactantus and Cosmas Indicopleustes
proposing a T-map of a flat Earth with Jerusalem at the center and Asia, Africa and Europe in the sections divided by the T, as the only cosmological view in literal accordance with scripture. However, in the revival of logical analysis and scholarship in Church Universities beginning in the 11th century, Aristotlean physics and Ptolemaic cosmology won out. Because the flat-earth cosmography was not explicitly spelled out in the non-Apocryphal works (and some Hellenistic elements creeping in the Canonical works, such as the "circle" of the Earth in Job) it was possible
for the Church to allow the spherodicity of the Earth, with some stipulations. For example, since ,it is said, upon Christ's return, all eyes are to be able to see him at once, St. Augustine considered that, although the Earth was spherical, nobody lived on the other side.  This is also in accordance with the story of Satan taking Christ to a high place and showing him all the Kingdoms of the world. While this statement is easily reconciled with a flat-earth cosmography, it can also be reconciled with a
spherical earth cosmography if there are no kingdoms on the hemisphere opposite Jerusalem.

With such compromises, the Church Universities were able to absorb Classical learning and generate new scholarship with a vigor unmatched in the earlier Middle Ages. William Occam developed Aristotlean logic, and used it to falsify Aristotle's own axioms about falling bodies. If a heavy body falls faster than a lighter one, he questioned, would a heavy body chained to a lighter one be buoyed up by the lighter body or together
constitute still a heavier body which would fall faster? The paradox was the crack in a movement which would shatter the erroneous physics that enabled Ptolemaic cosmology, as did Occam's Razor: "We cannot admit entities without necessity". The simplest model is the best ,it says, and that turned out to be Copernicus' reintroduction and elaboration of Aristarchus'.
But the universities also generated doctrinal justifications of the classical learning, for example, the immobility of the Earth is entirely justified by the literal meaning of Joshua 10 and Ecclesiastes 1:5 : it is the sun that is moving,not the Earth. "The Earth is stablished that it cannot be moved." says the King James translation of Psalm 93.  St. Thomas Aquinas knew this, and in his "Summa Theologia" he not only discusses the nature of
angels, and makes careful and cogent distinctions concerning the nature of sin, but, knowing the Ptolemaic system and no other, also tells us that the Earth is the center of the Universe.

The Copernican reintroduction of the heliocentric Universe, though itself with minor flaws, satisfied Occam's Razor over its competitor, the Ptolemaic System. The relationship between the sidereal period (the time from its presence at one longitude on the Celestial sphere to its return) and the synodic period of a planet (the time from opposition to opposition) could be demonstrated as a necessity from the heliocentric Copernican
model; in Ptolemy's model it was merely coincidental that all of the planets should have this relationship.  In Copernicus,outer planets must be nearer (and hence brighter) at opposition and farther (and hence dimmer) in conjunction. No such restraint exists for the Ptolemaic system; yet this relationship is observed to always be true.  Finally, with the invention of the telescope, the observation of the full phase of Venus (impossible with the Ptolemaic system as described in the "Almagest") and the satellites of Jupiter shattered the crystal spheres of Ptolemy forever.

The Church, however, reluctant to expose itself as capable of error in the teachings of its universities (if not centrally its doctrine), and also motivated by a theoretical cautiousness, used its powers of judicial process, policing, and censorship to attempt to stifle the teaching and acceptance of the Copernican view.  Well after Newton, the Cassinis, a family of Catholic astronomers, habituated themselves to think in a dual mode, both Copernican-Newtonian and Ptolemaic. Finally, with the
demonstration of the Foucault pendulum , and the impending discovery of parallax, the church rescinded its ban on Copernican thought in 1830. The Ptolemaic system was no more.At the present time, there are modern astrophysicists working at the new Vatican Observatory on Mt. Graham. Catholic education has by comparison become very progressive.

Today, there are still some adherents to the old views on religious grounds. W.G. Voliva wrote extensively favoring a flat earth in the newsletter of the Holy Apostolic Church in Zion in the 1930's. Prof. Hanson of Cleveland State University has spoken and written favorably on the Ptolemaic system, also on religious grounds, and the Tychonic system has a substantial body of religiously-inspired adherents. But these views are well outside the mainstream of science, since there is an enormous abundance of evidence that the Earth is, to a high approximation,
spherical, rotates, and revolves around the sun.