Epicyclic theory

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The epicyclic theory says that a moving star moves on a small circular path - called epicyclic ("outcircle") - which in turn moves on a large circular path - called deferent ("carrier circle") - around a fixed center. The epicyclic (Greek epi "on", kyklos "circle") is therefore "a circle circling on a circle". This theory was probably supported by Apollonios von Perge towards the end of the 3rd century BC. BC and was predominant in astronomy for almost 2000 years until the 17th century. With the epicyclic theory it was possible to explain why the planets move at varying speeds compared to the fixed stars and why some of them sometimes even run backwards on a loop . Because of the religiously motivated belief in a relationship between stars and gods, such movements, but also close encounters between the planets or with certain stars, were classified as extremely important events (→ astrology ).

The basis of the epicyclic theory is the teaching of Aristotle that there can be no changes in the sky apart from the phases of the moon , and that among the movements only the uniform circular movement is perfect and takes place without external influence. Accordingly, all movements outside the lunar orbit sphere must be uniform circular movements.

In the Ptolemaic worldview , the epicyclic theory was systematically expanded to explain the movements of the moon , sun and planets in relation to the starry sky as they appear from the earth (→ geocentric worldview ). In the heliocentric view of the world according to Nicolaus Copernicus , epicycles were also used, whereby the defenders for the planets now had the central sun as the focus.

The epicyclic theory was only replaced by Johannes Kepler's theory of elliptical planetary orbits.


Ptolemaic worldview

Depiction of deferent and epicyclic after Ptolemy. The point-shaped earth is located in the Centrum Mundi. The Centrum Deferentis is above it, offset by the eccentricity of the planet. The Equantis Center is at the same distance above. From this point the epicyclic moves with constant angular velocity on the deferent, which is symbolized by the blue colored areas. The superposition of epicyclic movement and deferent movement can be seen as a dashed red line. The green line shows the true location of the planet on the ecliptic. In addition, the so-called aux of the planet is indicated on the extension of the line of the centers; the angle between this point on the ecliptic and the vernal equinox is also called the aux.

Ptolemy collected many mathematical models from antiquity in the Almagest . In doing so, he created a usable manual that was binding for the subsequent generations of science in the Arab and Latin Middle Ages. The planetary movements are explained on the basis of the epicyclic movement.

According to the epicyclic theory, the planets move - in addition to their daily orbit around the earth - along a small circle , the epicyclic (Greek epíkyklos, “secondary or upstream circle”), which in turn moves along a larger circle called the deferent (also deferent Circle ; from Latin deferre "carry away", "take with you"). The circles are roughly parallel to the plane of the earth's orbit (plane of the ecliptic ). The movement along each circle is counterclockwise at a constant speed. The planetary orbits in this system are similar to epicycloids .

If the earth is located in the center of the deferent, then the planet would initially move counterclockwise with the movement on the deferent, which corresponds to the average movement of the planet through the starry sky. During half of the time, this movement is also added to the counterclockwise movement on the epicyclic. In the rest of the time, however, the planet on the epicyclic runs in the opposite direction to the movement on the deferent, which means that its overall movement in the sky slows down and finally reverses for a short time, so that the planetary orbit finally completes a loop .

However, this arithmetical device was insufficient to fully describe the precisely observed movement of the planets. Therefore the epicyclical theory was connected by Ptolemy at the latest with the eccentric theory of Hipparchus , in which the earth is offset from the center of the defender.Furthermore, Ptolemy introduced the equant or "balance point", a point that was assumed to be equidistant from the center of the defender to the earth. Only seen from the equant does the orbit on the deferent appear to be uniform. As Nicolaus Copernicus showed, these additional assumptions can also be represented by further, suitably chosen epicycles (epicycles on epicycles). Nonetheless, Copernicus achieved the same accuracy overall with a significantly lower number of epicycles for the planetary system by using the heliocentric worldview as a basis. In this, he did not, as required in the geocentric world view , also take into account the motion of the earth including its irregularities in each individual planetary orbit.

Comparison with Keplerbahnen

Alternative description of an elliptical orbit through an epicyclical movement

With the arithmetic trick of an epicyclic one can also describe an exactly elliptical orbit (with the opposite direction of rotation, see illustration), as it was recognized by Johannes Kepler in the 17th century to be correct. These trajectories therefore also result in the observed positions correctly if the observer or the sun is not placed in the center, but in a focus of the ellipse. This corresponds to the epicyclic model with the eccentric theory mentioned. With the assumption prescribed at the time that all circular movements had to run uniformly, the points in time would be wrong. This can be corrected by varying the web speed; Kepler formulated this with the sentence that the line connecting the focus to the planet sweeps over equal areas at the same time ( Second Kepler's law ). Seen from the other focus, this movement actually appears to be almost uniform (the error lies in the area of ​​the eccentricity of the orbit ellipse to the square, i.e. even under one percent on Mars). In epicyclic theory, this was the role of the equant, whose position was usually set in such a way that the result was exactly at the other focus. Given such close correspondence, Kepler's discovery appears particularly remarkable.

Ptolemy's theory for the orbits of the sun, moon and planets

For the planets Venus , Mars , Jupiter and Saturn , Ptolemy gave a unified theory for describing the planetary motion in the Almagest . In the center of the universe, the Centrum Mundi , is the punctiform earth, from which the observer sees the movements of the planet in front of the fixed star sphere. The starting point of the considerations is the ecliptic , which is divided into twelve sections according to the signs of the zodiac . Each of these sections is in turn divided into 30 degrees. The center of the defender of a planet is shifted by the so-called eccentricity compared to the Centrum Mundi . The movement of the epicyclic center on the deferent takes place unevenly compared to the earthly observer in the Centrum Mundi , but the movement is also uneven in relation to the Centrum Deferentis . However, there is another place, the Centrum Equantis , from which the epicyclic center moves at a constant angular velocity. All three points lie on the line of the centers , which in turn assumes a certain angle, the so-called aux , on the ecliptic compared to the vernal equinox . The planet orbits the center of the epicyclic at a constant angular velocity. A projection beam going through the planet from Centrum Mundi projects the true location of the planet onto the ecliptical coordinate system. Since in this model both the deferent and the epicyclic are inclined in relation to the ecliptic, the movement of the planet can be specified in ecliptical longitude and ecliptical latitude . The aux of the planet is not constant, but according to Ptolemy moves clockwise through the ecliptic at a speed of 1 ° per century. This movement is caused by the precession of the earth's axis. Modern measurements show that the described movement occurs at a speed of about 1 ° within about 70 years (a complete revolution takes about 25,800 years).

Since the sun has only one anomaly, i.e. only has a temporally variable speed of movement within a year, the Ptolemaic solar model can be represented with the help of an eccentric as well as with the help of an epicyclic. The equivalence of both theories is proven in the Almagest .

More complicated models are required for the moon and Mercury . The lunar orbit is so strongly disturbed by the sun that, according to the epicyclic theory, it would have to have such a large epicyclic that its distance from the earth and thus its (apparent) size would have to vary considerably. Mercury has such a strongly elliptical orbit that it can no longer be reproduced well with the approximation of epicycles.

According to its principle, the epicyclic theory can be viewed as an approximation of the actual planetary orbits by Fourier series , at least in the case of uniform movements such as those found in the moon model as well as in the model of the sun. This parallel was discovered at the latest by Giovanni Schiaparelli and formally proved by Giovanni Gallavotti .

Overcoming by Copernicus and Kepler

The heliocentric view of the world explains the loops of the planetary orbits by superimposing the earth's motion and therefore seems to be able to do without epicycles. Since the new model was still based on circular orbits for the planets, discrepancies had to be explained again by using the epicyclics. Copernicus still used 34 epicycles in his world system , but was able to provide a conclusive explanation for the connection of the orbit of Mercury and Venus to the sun.

It was only through Johannes Kepler that the epicyclic theory became superfluous: The “natural” model of the planets on elliptical “ Kepler orbits ” around the sun does not require any correction by superimposed epicycles.

See also

Web links

Individual evidence

  1. See also George Saliba : Ibn Sīnā and Abū ʿUbayd al-Jūzjānī : The Problem of the Ptolemaic Equant. In: Journal for the History of Arabic Science. Volume 4, 1980, pp. 376-403.
  2. Poulle, Sendet, Scharsin, Hasselmeyer: The planetary clock . A masterpiece of astronomy and Renaissance technology created by Eberhard Baldewein 1563–1568 . German Society for Chronometry, Stuttgart 2008, ISBN 978-3-89870-548-6 , p. 21 ff.
  3. Karl Manitius : Ptolemy's Handbook of Astronomy . BG Teubner Verlagsgesellschaft, Leipzig 1963, translation by Manitius with corrections by Otto Neugebauer .
  4. ^ Giovanni Gallavotti: Quasi periodic motions from Hipparchus to Kolmogorov. In: Rendiconti Lincei - Matematica e Applicazioni. Series 9, Volume 12, No. 2, 2001, pp. 125–152 ( PDF ( Memento of the original dated December 18, 2005 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this note .; 205 kB). @1@ 2Template: Webachiv / IABot / www.lincei.it
  5. Lucio Russo: The forgotten revolution. How science was born in 300 BC and why it had to be reborn. Springer, Berlin et al. 2004, ISBN 3-540-20068-1 , p. 91.