Ancient Astronomy: Ptolemy to Copernicus
(100 AD - 1543 AD)

The Template of Aristotle & Origin of Ancient Astronomy

Observation of the night sky is a most ancient activity; one that has been conducted throughout the world since time immemorial. In the history of Europe, for well over a thousand years prior to the Renaissance of the 15th century, among the most learned, a general understanding of the motion of the celestial bodies of the heavens rested primarily upon the ideas of Aristotle from the 4th century BC, and those of Ptolemy from the 2nd century AD [1].

From the former, came a well developed schemata as to the general ordering of the cosmos and of the observed bodies therein contained, upon which the latter, during his own age, established a most comprehensive mathematical model to chart the activity of the system; one that furnished a most detailed account of the movements of the then known planets against the perceived background star-field. It was an intricate system to be sure, but one that did possess a significant degree of predictive power in charting the positions of the major planets as viewed from the Earth.

Coming at the time when it did, and being somewhat superior to other similar models of the period, Ptolemy’s system rapidly became established as the standard model of the heavens throughout Europe. Its acceptance amongst the learned was such that it dominated astronomy throughout the region for well over a thousand years. Indeed, so ingrained did it become in the minds of men that it was not until the beginning of the 17th century that it was eventually overthrown in its entirety [2].

Of Ptolemy’s decision to actually use the ideas of Aristotle concerning the ordering of the celestial phenomena of the heavens, there was one most notable consequence. Namely, that he was bound to accept as true a certain idea, quite commonly held throughout Greece during the time of Aristotle, that the Earth as a physical body is fixed in space and unmoved; the central body of the entire cosmic arrangement [3]. Indeed, of ancient astronomy in general, many of the greatest thinkers of the age during this period were thoroughly convinced that the sun, moon, and all of the (then) known planets including the background stars, were all in orbit about a fixed, motionless Earth.

Under this general scheme, each of the various types of celestial phenomena were thought to orbit the Earth in transparent spherical shells at various set distances, with the background stars held to be the furthest away. Such was the very system then that Ptolemy was led mathematically to capture during his own age, some six centuries after the height of classical Greek culture. In the end, the downfall of the Ptolemaic system was inextricably bound up with the overthrow of the idea of a fixed Earth lying at the centre of the cosmos. The first serious challenges to the system outright began at the time of the Renaissance.

Ancient Astronomy Transformed

One of the first astronomers to deviate from the Ptolemaic system, almost 1300 years since its founder lived, was a man named Tycho Brahe (1546 - 1601 AD). During his life Brahe carried out many observations of the planets. And, operating without even the use of a telescope, his measurements were of a level of accuracy at least 10 times more precise than anyone else had obtained previously [4].

In contrast to Ptolemy who thought that all celestial bodies orbited the Earth directly, Brahe favoured an Earth centred system wherein the known celestial bodies did not orbit directly about the Earth, but instead about the sun, which itself was then held to possess a direct orbit about the Earth. The only exception to this general scheme concerned the moon. Of this particular body, Brahe held that like the sun, it too possessed its own direct orbit about the Earth [5], but one that was much closer. Concerning the background stars, they were held to be far more distant than any of the major celestial bodies, just as under the Ptolemaic system.

One can easily see then that Brahe’s system was only a slight variation upon that of Ptolemy with regard to the issue of the general orbits of the planets. He still considered the Earth to be unmoved. However, a near contemporary of Brahe who also developed an alternative to the Ptolemaic system, Nicholas Copernicus (1473-1543), was indeed willing to ‘set the Earth in motion’.

In the system of Copernicus, the sun was placed at the centre of the cosmos, with all of the known planets, including the Earth, held to orbit the sun in circular paths of various sizes; each body engaging in uniform circular motion about the sun [6]. Indeed, circles were thought to be perfect and that it was quite natural that God would proscribe such orbits to the planets.

In comparing the various systems, a clear disagreement obviously existed between Copernicus, Brahe and Ptolemy, as to the general ordering of the planets within the heavens. Contrasting in particular the Ptolemaic system with that of Copernicus, one can also note certain key points of difference in the way that they each dealt with or accounted for the observed movements of the planets, which to an observer upon the ground looking up at the night sky, do appear most unusual.

Indeed, when astronomical observations of the sky are carried out from the Earth, even by modern astronomers today, they are done so from the perspective of plotting the positions of various bodies upon the inside of a large sphere, the technical term for which is the Celestial Sphere. An observer at night will have the horizon line all around them, and will usually note the angle up from the horizon of a star or planet, and the angle from an established direction line on the ground e.g. facing north.

In this way the positions of celestial bodies may be plotted and their movements recorded. When actual observations are made of the planets over extended periods of time though, a number of distinct peculiarities can be seen in their movements. Viewed from the Earth they appear to trace out periodic zigzag like patterns in the sky, constantly changing their direction of movement. They are also seen to speed up and slow down in a non-uniform manner, even to the point of coming to an apparent standstill at certain times, before moving back the way they came – what astronomers refer to as retrograde motion.

One of the primary differences between the Ptolemaic and Copernican systems is how they each deal with the retrograde motion of the observed planets. Under the Ptolemaic system, this is done by the introduction of what are known as epicycles.

Essentially, although the observed planets, including the sun and the moon, are said to orbit the Earth in circles at various distances, Ptolemy held that their orbits were in fact governed not by just one large circle, but by the interplay of two circles; one large, and one much smaller. The larger of the two is the deferent, whilst the smaller circle is known as the epicycle [7]. Employing the use of an epicycle then in addition to the main or primary orbital circle of a planet did give an apparent solution to the seemingly bizarre retrograde motion as observed from the Earth:

Diagram 1 (The Ptolemaic Model): If a planet is engaged in a smaller orbit (epicycle) in addition to its main orbit (deferent) about a central Earth; then at those times when the planet moves in the same direction in its smaller orbit as with its main orbit, it will appear to move quite rapidly though the star-filled sky from the view of an Earth bound observer. However, when the planet begins to turn about in its smaller orbit so as to move in the opposite direction to that of its main deferential path, it will seem to slow down in the sky from an observer’s point of view; briefly stopping and going back the way it came, before turning once more to resume its journey through the sky at a more rapid pace.

In contrast to the Ptolemaic system, the Copernican system did not require at all the use of epicycles to account for observed retrograde motion, because under a sun-centred system retrograde motion amongst the observed planets is naturally accounted for [8]. This is due to the fact that the planets each possess different orbital periods, with those furthest away taking the longest to orbit the sun. As a result of this they are given to ‘overtake’ one another at various intervals of time; the very mechanics of such overtaking readily accounting for retrograde motion in a far more elegant way than under an Earth-centred system.

Diagram 2 (The Copernican Model): Here it can be seen that the Earth, being much closer to the sun than Planet 2, possesses a much faster orbital speed, as indicated by the different sized arrows. As a result, at some point the Earth will catch up to Planet 2; such an event occurring when there is a conjunction between both planets and the sun. From the perspective of an Earth based observer, as the conjunction is approaching, Planet 2 will appear to slow down as viewed in space against the background star field.

At the exact point of the conjunction, it will briefly cease to move, before appearing to go backwards as the Earth overtakes. However, as the Earth continues in its orbit it will eventually turn such that its direction of motion is directly opposed to that of Planet 2, the most extreme point being when the sun is exactly in between both bodies. As this occurs, Planet 2 will appear to speed up and move quite rapidly through space as a result (were it possible to observe it in the absence of the light of the Sun). From the dynamics of the planetary bodies, such an ongoing recurring cycle readily accounts for apparent retrograde motion.

In the Copernican system, it can be seen then that epicycles are unnecessary as a means to explain retrograde motion. However, it is interesting to note though that Copernicus nevertheless did still retain the use of them, even within a newly formulated sun centred system [9]. His actual reason for this was because planetary observations indicated that even when the slowing down and speeding up of the observed planets due to retrograde motion was precisely accounted for, the planets still nevertheless did not seem to travel at uniform speed about the sun. Rather, the observations clearly demonstrated that they appeared to travel faster through space when closer to the sun and slower when further away from it.

Indeed, this noted fact that the planets did not maintain a constant distance from the sun at all times in their orbits led Copernicus to offset his major orbital circles so that they were not precisely centred on the sun. Thus, in holding fast to his circles, and through his conviction that the speed of the planets was uniform, he was forced to retain small planetary epicyclical orbits as a subtle way to account for the continued presence of their apparent non-uniform motion about the sun.

This was really nothing more though than a mathematical manipulation employed in order not to have to discard the primary aspects of his system; to allow it to better match actual observations; and also to allow him to claim that any observed non-uniform motion was not real, but illusory. A more detailed example of Copernicus’s system with the inclusion of an epicycle is as follows:

Diagram 3 (Epicycles within the Copernican Model): A planet in orbit about the sun is travelling anti-clockwise in its epicycle and also anti-clockwise in its main orbital circle; the centre of the smaller circle moving in uniform motion upon the circumference of the larger circle. When positioned at P1 the combined speeds of both ‘orbital circles’ are pointed in the same direction and thus are added. This necessitates that the planet is at this moment travelling at its fastest in orbit about the sun. From this initial position, as the planet moves yet further about the sun on its main circle, the uniform speed of the planet in its epicycle is such that by completing half of its main orbit about the sun, reaching point P2, it has completed one orbit of its epicycle.

At this point, the main orbit is counter to the direction of that of the epicycle, and thus the planet, at its most extreme position from the sun, is travelling at its slowest. If one were to plot the actual path of one full orbit about the sun, the planet would be found to trace out an elongated circular path as opposed to an exact circle. Such is the result of combining two uniform circular orbits in the proscribed manner.

Of Accuracy and Underlying Method

Upon the issue of system accuracy, one should note that the Copernican system actually afforded no greater level of precision than that of the Ptolemaic system [10]. Indeed, Copernicus’s continued use of epicycles was in fact necessary simply to allow it to achieve the same level of accuracy as was present under the Ptolemaic system. Without them, although the general ordering of the planets about the sun would have been correct, the predictive power of the system would have been very much weaker.

Upon comparison then, both systems possessed a corresponding level of accuracy; neither one being greatly superior to the other. In terms of their margin of error, both could be up to 5 degrees off the mark [11] with respect to observations. It was not simply the case though that this was attributable to inaccurate observations as such. Rather, one has to understand that the comparable level of error in both systems was due in actuality to an identical flaw inherent to them both.

Essentially, it was the very method underlying their development and construction that was flawed; the choice of such method by Copernicus and Ptolemy being itself governed by their failure to understand the proper nature of the task they had set themselves. In essence, they had a certain false objective, in that what they both sought to attain in charting the course of the heavens was the means to develop nothing more than simply a precise mathematically descriptive model of its primary bodies; a goal, that by necessity thus determined the very nature of their attempts to capture the course of the planets; and for whose reason, when evaluating their respective systems, whether Earth centred or sun centred, it is impossible to know which if any is based upon truth.

For all of their efforts, all that Ptolemy and Copernicus had sought to uncover was nothing more than a comprehensive series of mathematical functions to capture the apparent movement of the planets as seen against the background stars. Essentially, this is exactly akin to someone attempting to determine some future position of an object moving across their field of vision by conducting a limited number of observations of the object as it moves, so as to uncover a relationship between the spatial separation between the object at various points, and the corresponding time interval between those points i.e. how much time it takes to get from one observed point to another.

In the case of an object engaged in apparent uniform motion, one would be hoping to discover a simple equation for the speed of the object: distance / time. Once obtained, the object’s future position could then be calculated from any observed point given the passage of a certain amount of time. Indeed, the observer may have no actual knowledge of the true speed of the object at all, and simply measure the angle it sweeps out in the distance, such as is the case with the movement of planets upon the inside of the Celestial Sphere.

Either way, the method employed here is simply one wherein a mathematical function for speed is sought; whether true speed or angular speed; the aim being to ‘superimpose’ it upon an object perceived by the senses and so capture its apparent movement. With this method, Ptolemy and Copernicus thus charted the blind progress of the planets through the sky.

They concerned themselves with appearance only and of ‘connecting the dots’ of planetary positions to work out mathematical functions from which to determine a future position. In sum: They did not look into causes. If true advancement in understanding the planets was thus to be achieved, what was needed was someone who was indeed inclined to focus upon the underlying causes that governed their activity [12].


Such a man was Johannes Kepler:


Astronomy Beyond the Renaissance: Johannes Kepler (1571 - 1630 AD)


References

[1] http://www.stetson.edu/~efriedma/periodictable/html/Pm.html.
Internet Article: Claudius Ptolemy Primarily, Ptolemy’s actual description of the universe is based upon the Earth centred theories of Aristotle.

[2] Of the Longevity of the Ptolemaic system: The reasons for this are no doubt many and varied, but are bound to include such as the lack of strong communications networks between the learned men of the age, and also too much reverence being given to both Ptolemy and Aristotle. However, one must not forget to mention also the fact that during these times alternative thinking upon such matters was forcefully discouraged quite frequently by those who had sizable ruling power over the continent. Thus indeed, the Roman Church, a most active power in Europe during the middle-ages and a known enemy of truth, was so strongly intent upon upholding the Ptolemaic Earth-centred system for dogmatic reasons that they persecuted, sometimes to the point of death, those who thought to develop and publicise other ideas. Nevertheless, even in spite of such strong opposition, as is evident from history, the ancient Ptolemaic system did eventually meet its end, though its death was a slow process and did take several successive generations of great and courageous thinkers.

[3]http://www.321books.co.uk/encyclopedia/astronomy/ancient/ greek-astronomy.html.
Internet Article: Greek astronomy

[4] http://www.astronomynotes.com/history/s4.html.
Internet Article: History and philosophy of western astronomy: Renaissance

[5] P. Moore (General Editor) (1987) p.84 Ibid

[6] P. Moore (1987) p.106 Ibid

[7] P. Moore (1987) p.114 Ibid

[8] http://astro.wsu.edu/allen/courses/astr150/Notes/week7.html
Internet Article: ASTR 150 Course Pages

[9] http://astro.wsu.edu/allen/courses/astr150/Notes/week7.html Ibid

[10] http://astro.wsu.edu/allen/courses/astr150/Notes/week7.html Ibid

[11] http://astro.wsu.edu/allen/courses/astr150/Notes/week7.html Ibid

[12] Science of Kepler & Fermat. EIRVI – 2001-12 (Video)