Claudius Ptolemy

Geographer and Astronomer: Entrenching

The Geocentric Concept

November 21^st 2005

Katherine McCracken

SCI199Y1

Claudius Ptolemy is unquestionably the last of the great scientists of ancient Greece. After all, he is commonly referred to as “the last important astronomer of classical antiquity.”[1] Although little conclusive evidence on Ptolemy’s life is known, various Arabic sources tell us he lived to the ripe age of 78 years old, and was probably born in Upper Egypt. The name Claudius Ptolemy is a mixture of Greek and Egyptian in his first name, ‘Ptolemy’, and ‘Claudius’ is considered ethnically Roman. This could possibly mean that he was a descendent from a Greek family, who resided in Egypt, and therefore, they were considered Roman citizens. It is believed that Ptolemy and his astronomical and geographical studies flourished in Alexandria during the 2^nd century AD. His research, development of new theories, and expansion on older ones, profoundly relied on other scientists and teachers of that time. We do know that Ptolemy relied heavily on the observations made by ‘Theon of Smyrna’, who was also known as ‘Theon the Mathematician’ and ‘Theon the Old’. He was most likely one of Ptolemy’s teachers.[2] Theon made astronomical observations of Mercury and Venus between 127 and 132. Ptolemy lists four observations which Theon made in 127, 129, 130 and 132; therefore, we know that Ptolemy used the observations made by Theon. From these observations, “Theon made estimates of the greatest angular distance that Mercury and Venus can reach from the Sun.” [3] Ptolemy also gave reference to ‘Marinos of Tyre’, one of the worlds first mathematical geographers. However, there was one scientist, who held the utmost importance for Ptolemy. The lifetime of work by the scientist Hipparchus was eventually taken over by Ptolemy. Hipparchus is often referred to as the founder of “systematic observational astronomy,” he also was one of the main developers of the mathematics of trigonometry. He applied this to his observations of celestial objects.[4] Hipparchus, “completed a star catalogue of 850 stars, [he] identified celestial latitude, longitude, and magnitude… and [calculated] the length of the tropical year (365 days 5 hours 55 minutes), and the sidereal year (365 days 6 hours and 10 minutes) to remarkably precise conclusions”[5] Ptolemy eventually expanded Hipparchus’s star catalogue and used many of Hipparchus’s observations to further develop his own. Because Ptolemy’s research heavily relied on the observations of others, his findings fell under the same problems as those before him, with common observational errors. When Ptolemy examined the theory of the sun, he used his own observations with those of Hipparchus’s. “[Ptolemy] was able to confirm that the length of the tropical year was 1/300 of a day less than 365 ¼ days, the precise value obtained by Hipparchus.”[6] In actual fact, the true value is 1/128 of a day less than 365 ¼ days. Based on these observations, he proposed a model for the sun, which he discussed in great detail in his encyclopaedia style book, The Almagest. It is quite astonishing to believe that Ptolemy’s greatest works have been able to survive through time. The most important of his long list of works, is entitled The Almagest, a written discourse in thirteen books. It was originally entitled The Mathematical Compilation, and then The Greatest Compilation. It was only when it was translated from its Greek form into Arabic, did the title become what it is commonly known as today. It is the earliest of Ptolemy’s works, and it “gives in detail the mathematical theory of the motions of the sun, Moon and Planets.”[7] Ptolemy’s main focus is his description of the universe, being centered around the Earth, a theory initialized by Aristotle. This concept of the universe is known as the ‘geocentric concept’ or as the ‘Ptolemaic system’. It was the leading theory in astronomy for over a millennium.

As noted earlier, The Almagest is a collection of thirteen books, each dealing with a variety of astronomical concepts, like the motions of the Earth, Moon, planets and stars. In addition, it explains mathematical problems, some of which were referenced from other mathematicians and others which were created by Ptolemy himself. It describes some of the physical geography observed at this time. Ptolemy’s mathematical knowledge was only possible with his complete understanding and access to the data collected by earlier scientists. Even without a list of reputable teachers, the Alexandrian library could have provided an affluent source of information for him. Even with all of his “borrowings” from other workers, Ptolemy was the first to develop a mathematical theory to explain the motions of the planets. After all, he was a mathematician above all else. With the help of Hipparchus’s observations and notes, Ptolemy formulated and improved the geocentric concept, or the Ptolemaic system, as it is also known. This theory is explained and described in the first two books of The Almagest. Ptolemy gives, with great detail, a mathematical theory of the Sun, Moon, and planetary movements. At this time, there were only five planets known in existence; Mercury, Venus, Mars, Jupiter, and Saturn. The Ptolemaic model was also designed to explain how the “heavens” moved. “Planets became associated traditionally with colour, metals, minerals, and parts of the human body.”[8] Ptolemy argued that the planets and other celestial objects had a certain “power” over earthly events and happenings. This system eventually became a basic pattern for astrology. According to this system, planet Earth was by far the largest of the planets, and it was located right in the centre of the universe. In this geocentric model, the Earth was successively being orbited by the Moon, Mercury, Venus, the Sun, Mars, Jupiter, and Saturn, as well as the “crystalline heavens” and stars.[9] The orbits of these celestial bodies were thought to be geocentric, measured with respect to the centre of the earth, and not concentric, having a common centre that is not the earth, as which was previously believed. Ptolemy had noticed that there was an “inequality” to the movements of the planets; there had to be something causing these unusual motions.

A Greek astronomer by the name of Apollonius of Perga, also known as ‘The Great Geometer’, was the first to devise a system to explain the uniform, circular movements of the planets. He was presumably the founder of Greek mathematical astronomy, and he used geometrical models (i.e. using geometry) to explain planetary theory. In Ptolemy’s book called Syntaxis (also known as The Almagest), he stated, “Apollonius introduced systems of eccentric and epicyclic motion to explain the apparent motion of the planets across the sky.”[10] It is believed that the theory of epicycles was not created by Apollonius; it was only improved by him. What we do know is that he was very interested in determining the points where the forward motion of planets appears to change to retrograde motion and vice versa. His ability to have mastered geometry certainly would have helped him in this study. In order to prove his theory of geocentricity, Ptolemy had to introduce, and attempt to explain, a number of different concepts. First of all, to begin to explain the geocentric concept, one must envision the Earth, eccentrically placed, and immobile at the centre of the universe. Revolving around this stationary earth, in order, were the Moon, Mercury, Venus, the Sun, Mars, Jupiter, and Saturn. Ptolemy had realized, along with Hipparchus, that there were inequalities in their motions and the only way to explain them was by applying a system of epicycles and deferent’s or one with eccentrics; both theories were suggested by Apollonius. At this time in the world’s history, people believed that Earth was no longer flat, but it was spherical. To accommodate what we now know as a heliocentric revolution, (where the planets revolve around the sun, not the earth); Ptolemy placed a series of epicycles on the general revolution path of each planet. Because the planets appeared to “wander” across a fixed field of stars, occasionally reversing direction; (what we now call retrograde motion), Aristotle suggested that the planets were attached to epicycles, which were attached to deferents. Therefore, the concurrent revolution of both the epicycles and deferents created the intermittent “reversal” of the movements of the planets around the earth. To further understand this concept it is important to know what epicycles and deferents are. “The planets were attached, not to the concentric spheres themselves, but to circles attached to the concentric spheres… these circles were called epicycles, and the concentric spheres to which they were attached were termed the deferents.”[11] In other words, a planet was placed on a circular path, an ‘epicycle’, and this epicycle revolved around a larger circular path, the ‘deferent’, which ultimately circled the Earth. Ptolemy, after careful analysis and consideration, added something more to Aristotle’s theory. First of all, he displaced the Earth from the centre of the universe, claiming that the planets actually revolved around an eccentric, a point which was near the earth, but not exactly on it. To prove this theory he suggested that the epicycles should be placed on other epicycles. “The motion was comparable to that of an eccentric valve gear on a steam locomotive.”[12] Even with all of these theories, there were still certain occurrences that could not be explained, such as the unusual and unaccounted for movements of the planets. Because of this, Ptolemy introduced another part to this geocentric concept. He suggested that there was an imaginary point “placed on the diameter of the deferent but at a position opposite to that of the Earth from the centre of the deferent.”[13] He called this point the equant. With the equant in place, the system now worked like this: the Earth was now located a short distance from the centre of each of the deferents, and the centre of each deferent and epicycle caused the circular motion of the planets around the equant. He also proposed that the distance from the earth to the centre of the deferent was equal to that of the distance between the centres of the deferent to the equant. With this new aspect to his theory, Ptolemy was able to explain the unaccounted for movements of the celestial bodies. However, there is still one more part to this Ptolemaic system. The sun’s annual path across the stars was given a name; it was called the plane of the ecliptic. Ptolemy stated that “the planes of the deferents” were inclined at small angles to this plane of the ecliptic, and the planes of the deferents epicycles were inclined by equal amounts to the deferents. Therefore the planes of the epicycles were parallel to that of the ecliptic. The idea of a geocentric universe was the leading theory for over a millennium. It was not until the year 1543 when Nicholas Copernicus published the book De Revolutionibus Orbium Caelestium did the end of the geocentric era arise.

After the publication of Copernicus’s treatise in 1543 the geocentric model of the universe was questioned thoroughly by astronomers and scientists alike. According to this new heliocentric model of the universe, the earth and the other planets revolved around the Sun, and not the Earth. In the beginning, this theory was not wholeheartedly believed because it lacked concrete experimental and observational results. In the Copernican theory the Earth was given the rank of a planet, and it did a full rotation on its axis once every twenty four hours. Copernicus replaced Ptolemy’s equant’s with the possibility of uniform motion. The planets were believed to move in ellipses with sun in the centre; i.e. the principle concept of uniform circular motion. This proved that the geocentric concept was wrong. Therefore, the orbits of the planets were no longer believed to be circular, they were oval; elliptical. This elliptical theory was first discovered by Johannes Kepler. This theory was hard to believe for some, because Ptolemy’s theory of a geocentric universe made a lot of sense, and seemed favourable to them for several reasons. One of which being the Earth was the largest celestial body in the sky, and it was located in the centre of the universe; a sign that God obviously purposely designed it that way. The sun and planets also revolved around it, showing the earth is central and the most important thing in the sky. That ideology however, was proved wrong. The geocentric concept that held the top rank for 1400 years was no longer believed. The most important concept Copernicus introduced was the possibility that man was no longer the most superior being in the universe; an idea Ptolemy’s geocentric model favoured greatly.

Claudius Ptolemy, a mathematician, geographer, and astronomer from Alexandria Egypt, who was presumably living during the years 87-150 AD, developed the geocentric concept of the universe and attempted to explain the motions of the planets. He was successfully able to introduce a remarkably supported theory to the world with the publication of his many books, most importantly, The Almagest. This collection of thirteen books explains his various theories “ranging from earth conceptions to sun, moon, and star movement as well as eclipses and a breakdown on the length of months. The Almagest also included a star catalogue containing 48 constellations, using the names we still use today.”[14] In Ptolemy’s fourth book, he attempted to describe how the moon relates to the length of the months. Although at this time the moons elliptical orbit and 8.849 year apsides cycle was already established, he discovered an inequality in the motion of the moon relative to the suns position. The equation of the centre was diminished when the moon was in opposition to the sun. When this happened, the angular distance between the moon and sun increased; thus, causing an irregularity in the motion of the moon. He constructed another epicycle with a deferent with the centre revolving eccentrically around the Earth. The fifth book was devoted to an astronomical instrument called the astrolabe. It was a common instrument used during this time, and it was Ptolemy’s principle instrument for celestial observation. Book six attempted to explain the lunar eclipse. Ptolemy, with the tables he constructed, was very successful in predicting their occurrences with a high precision. On the other hand, he found it difficult to predict solar eclipses. This was in part due to not knowing the correct solar distance. Books seven and eight explore equinoxes, and show a catalogue of the known stars in the sky, some of which he took from the observations of Hipparchus. The last five volumes in The Almagest dealt most in part with the motions of the planets. This large collection of work was not the only thing Ptolemy had accomplished. He had several other books to his name. Some of which included Analemma, a book in which he discusses projection points of celestial spheres. He wrote others on weather predictions and the risings and setting of stars, as well as books on geometry, geography, mechanics, and even “optical phenomena.” A well known book by Ptolemy was entitled Geographike Gyphegesis, which in English translates to “Guide to Geography”. It was divided into eight volumes, and it described how to construct maps and it listed places in Europe, Africa, Asia, which were all put into a table according to their latitude and longitude. This guide contained a lot of problems and contradictions, but it still was a valuable contribution to the history and development of the world. It was from Ptolemy’s Guide to Geography; Christopher Columbus was able to fuel his belief in a westward path to Asia. After the death of Ptolemy, work in Greek astronomy became practically nonexistent. Overtime, most of the astronomical discovery was being done in Islam. Claudius Ptolemy was one of the greatest astronomers from the classical period. Through his mathematical models, and celestial observations Ptolemy was able to develop a concept of the universe that explained the movements of the planets. He also “laid the methodological foundation for the Islamic and European mathematical astronomy of the middle ages and renaissance.”[15] After all, the geocentric concept of the universe that was improved and developed by Ptolemy was believed for over a millennium.

Works Cited

The Encyclopedia of Astronomy and Astrophysics, Volume 3, ed. Paul Murdin, IOP Publishing Ltd and Nature Publishing Group, London, UK, 2001
Encyclopedia of Planetary Sciences, ed. Shirley, H. James, Fairbridge, Rhodes, W., Chapman and Hall, London, UK, 1997

Connor, J.J., Robertson, E.F., Claudius Ptolemy, http://www-groups.dcs.st-and.ac.uk/~history/Printonly/Ptolemy.html, April 1999
Connor, J.J., Robertson, E.F., Theon of Smyrna, http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Theon_of_Smyrna.html, April 1999
Connor, J.J., Robertson, E.F., Apollonius of Perga, http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Apollonius.html 99, April 19
Claudius Ptolemaeus - 'Ptolemy' : 90-168 AD, http://www.acmi.net.au/AIC/PTOLEMY_BIO.html
The Solar System, http://www.phys.unt.edu/Astronomy/online_course_files/sample_pages/04_1.html
Arnett, B., http://obs.nineplanets.org/psc/theman.html, June 7^th, 2000