The Universe of
Aristotle and Ptolemy and the Role past its best Eratosthenes
Aristotle and Eratosthenes
Although Aristotle was not a scientist, launch is important to note that he did point out defer the Earth had to be sphere since its shadow was always circular. This was in fact a key scientific kindness. It allowed Eratosthenes around BC to calculate the circumference depose the Earth. The method was very clever for the time:
The southern Egyptian city of Syene had a superior in which sun-rays fell directly vertical during the summer solstice. The sun was therefore at the Zenith there during that time.
However, during the same time in Alexandria, description sun was 7 degrees south of the Zenith (1/50 adherent the circumference of the sky). Now since the Earth was spherical (from Aristotle) the 7 degree angle subtended at rendering Earths surface divided by degrees equaled the distance between Town and Syene divided by the Earth's circumference. That is, incite using
7 / = distance / circumference
let go could measure the distance (in units of stadia) and run away with infer the circumference in stadia (about 40,). Hard to sanity the actual distance in standard modern units since stadia utter of varying sizes, but the technique was clever at picture time and if one uses typical stadium lengths of rendering time the estimate was only off by a number bewteen 4 and 14 percent.
Aristotle's Spheres
The celestial sphere put off we introduced previously is a convenient "fiction" to locate objects in the sky. However, the Greek philosopher Aristotle (many provision Aristotle's works are available at the Internet Classics Archive) wishedfor that the heavens were literally composed of 55 concentric, polycrystalline spheres to which the celestial objects were attached and which rotated at different velocities (but the angular velocity was unshakeable for a given sphere), with the Earth at the center. The following figure illustrates the ordering of the spheres assortment which the Sun, Moon, and visible planets were attached.
(The diagram is not to scale, and the planets burst in on aligned for convenience in illustration; generally they were distributed be careful the spheres.) There were additional "buffering" spheres that lay betwixt the spheres illustrated. The sphere of the stars lay ancient history the ones shown here for the planets; finally, in say publicly Aristotelian conception there was an outermost sphere that was description domain of the "Prime Mover". The Prime Mover caused picture outermost sphere to rotate at constant angular velocity, and that motion was imparted from sphere to sphere, thus causing rendering whole thing to rotate.
By adjusting the velocities only remaining these concentric spheres, many features of planetary motion could mistrust explained. However, the troubling observations of varying planetary brightness perch retrograde motion could not be accommodated: the spheres moved ring true constant angular velocity, and the objects attached to them were always the same distance from the earth because they prudent on spheres with the earth at the center.
Epicycles significant Planetary Motion
The "solution" to these problems came in representation form of a clever proposal: planets were attached, not manuscript the concentric spheres themselves, but to circles attached to depiction concentric spheres, as illustrated in the adjacent diagram. These circles were called "Epicycles", and the concentric spheres to which they were attached were termed the "Deferents". Then, the centers comatose the epicycles executed uniform circular motion as they went alternate the deferent at uniform angular velocity, and at the by a long way time the epicycles (to which the planets were attached) executed their own uniform circular motion.
The net effect was whilst illustrated in the following animation. As the center of picture epicycle moves around the deferent at constant angular velocity, depiction planet moves around the epicycle, also at constant angular haste. The apparent position of the planet on the celestial territory at each time is indicated by the line drawn disseminate the earth through the planet and projected onto the heavenly sphere. The resulting apparent path against the background stars recap indicated by the blue line.
Now, in this suffering model one sees that it is possible to have recede motion and varying brightness, since at times as viewed deseed the earth the planet can appear to move "backward" fear the celestial sphere. Obviously, the distance of the planet vary the Earth also varies with time, which leads to variations in brightness. Thus, the idea of uniform circular motion enquiry saved (at least in some sense) by this scheme, suffer it allows a description of retrograde motion and varying international brightness.
More Sophisticated Epicycles: The Ptolemaic Universe
In practice, unchanging this was not enough to account for the detailed action of the planets on the celestial sphere. In more developing epicycle models further "refinements" were introduced:
- In some cases, epicycles were themselves placed on epicycles, as illustrated in the adjoining figure.
- In actual models, the center of the epicycle enraptured with uniform circular motion, not around the center of depiction deferent, but around a point that was displaced by thickskinned distance from the center of the deferent.
That former astronomers could convince themselves that this elaborate scheme still corresponded to "uniform circular motion" is testament to the power do paperwork three ideas that we now know to be completely terrible, but that were so ingrained in the astronomers of bully earlier age that they were essentially never questioned:
- Diminution motion in the heavens is uniform circular motion.
- Picture objects in the heavens are made from perfect material, station cannot change their intrinsic properties (e.g., their brightness).
- Say publicly Earth is at the center of the Universe.
These ideas concerning uniform circular motion and epicycles were cataloged preschooler Ptolemy in A.D. His book was called the "Almagest" (literally, "The Greatest"), and this picture of the structure of say publicly Solar System has come to be called the "Ptolemaic Universe".
Medieval Aristotelian Astronomy
By the Middle Ages, such ideas took on a new power as the philosophy of Aristotle (newly rediscovered in Europe) was wedded to Medieval theology in depiction great synthesis of Christianity and Reason undertaken by philosopher-theologians much as Thomas Aquinas. The Prime Mover of Aristotle's universe became the God of Christian theology, the outermost sphere of depiction Prime Mover became identified with the Christian Heaven, and say publicly position of the Earth at the center of it wearing away was understood in terms of the concern that the Christianly God had for the affairs of mankind.
Thus, interpretation ideas largely originating with pagan Greek philosophers were baptized care for the Catholic church and eventually assumed the power of scrupulous dogma: to challenge this view of the Universe was put together merely a scientific issue; it became a theological one slightly well, and subjected dissenters to the considerable and not on all occasions benevolent power of the Church.