The Universe of Aristotle and Ptolemy and the Role of Eratosthenes
Aristotle and Eratosthenes
Although Aristotle was not a scientist,it is important to note that he did point out that the Earth had to be sphere since its shadow was alwayscircular. This was in fact a key scientific insight.It allowed Eratosthenes around 200 BC to calculate thecircumference of the Earth. The method was very clever for the time:
The southern Egyptian city of Syene had a well in whichsun-rays fell directly vertical during the summer solstice.The sun was therefore at the Zenith there during this time.
However, during the same time in Alexandria, the sun was 7 degrees south of the Zenith (1/50 of the circumference of the sky).Now since the Earth was spherical (from Aristotle) the 7 degree angle subtended at the Earths surface divided by 360 degreesequaled the distance between Alexandria and Syene divided by theEarth's circumference. That is, by using
7 / 360 = distance / circumference
he could measure the distance (in units of stadia) and theninfer the circumference in stadia (about 40,000).Hard to infer the actual distance in standard modern unitssince stadia are of varying sizes, but the technique was clever at the time and if one uses typical stadium lengths of the timethe estimate was only off by a number bewteen 4 and 14 percent.
Aristotle's Spheres
The celestial sphere that we introduced previously is a convenient "fiction" tolocate objects in the sky. However, the Greek philosopher Aristotle (many ofAristotle's works are available at the Internet ClassicsArchive) proposedthat the heavens were literally composed of 55 concentric, crystalline spheres to whichthe celestial objects were attached and which rotated at different velocities(but the angular velocity was constant for a given sphere),with the Earth at the center. The following figure illustrates the ordering ofthe spheresto which the Sun, Moon, and visible planets were attached.
By adjusting the velocities of these concentric spheres, many features ofplanetary motion could be explained. However, the troubling observations ofvarying planetary brightness and retrograde motion could not be accommodated:the spheres moved with constant angular velocity, and the objectsattached to them were always the same distance from the earth because they moved on spheres with the earth at the center.
Epicycles and Planetary Motion
The "solution" to these problems came in the form of a cleverproposal: planets were attached, not to the concentric spheres themselves, butto circles attached to the concentric spheres, as illustrated in the adjacentdiagram. These circles were called "Epicycles", and the concentric spheres towhich they were attached were termed the "Deferents". Then, the centers of theepicycles executed uniform circular motion as they went around the deferent atuniform angular velocity, and at the same time the epicycles (to which theplanets were attached) executed their own uniform circular motion. The neteffect was as illustrated in the following animation. As the center of theepicycle moves around the deferent at constant angular velocity, the planetmoves around the epicycle, also at constant angular velocity. The apparentposition of the planet on the celestial sphere at each time is indicated by theline drawn from the earth through the planet and projected onto the celestialsphere. The resulting apparent path against the background stars is indicatedby the blue line.
Now, in this tortured model one sees that it is possible to have retrogrademotion and varying brightness, since at times as viewed from the earth theplanet can appear to move "backward" on the celestial sphere. Obviously,the distanceof the planet from the Earth also varies with time, which leads to variationsin brightness. Thus, the idea of uniformcircular motion is saved (at least in some sense) by this scheme, and it allowsa description of retrograde motion and varying planetary brightness.
More Sophisticated Epicycles: The Ptolemaic Universe
In practice, even this was not enough to account for the detailedmotion of the planets on the celestial sphere. In more sophisticated epicyclemodels further "refinements" were introduced:- In some cases, epicycles were themselves placed on epicycles, asillustrated in the adjacent figure.
- In actual models, the center of the epicycle moved with uniform circularmotion, not around the center of the deferent, but around a point that wasdisplaced by some distance from the center of the deferent.
- All motion in the heavens is uniform circular motion.
- The objects in the heavens are made from perfect material, and cannotchange their intrinsic properties (e.g., their brightness).
- The Earth is at the center of the Universe.
Medieval Aristotelian Astronomy
By the Middle Ages, such ideas took on anew power as the philosophy of Aristotle (newly rediscovered in Europe) waswedded to Medieval theology in the great synthesis of Christianity and Reasonundertaken by philosopher-theologians such as Thomas Aquinas. The Prime Moverof Aristotle's universe became the God of Christian theology, the outermostsphere of the Prime Mover became identified with the Christian Heaven, and theposition of the Earth at the center of it all was understood in terms of theconcern that the Christian God had for the affairs of mankind.Thus, the ideas largelyoriginating with pagan Greek philosophers were baptized into theCatholic church and eventually assumed the power of religious dogma: to challenge this viewof the Universe was not merely a scientific issue; it became a theological oneas well, and subjected dissenters to the considerable and not always benevolentpower of the Church.
