Ptolemaic Astronomy, Islamic Planetary Theory, and Copernicus's Debt to the Maragha School
Ptolemaic Astronomy, Islamic Planetary Theory, and Copernicus's Debt to the Maragha School
Ptolemy's (100?-170?) Almagest was first translated into Arabic during the early ninth century. Islamic astronomers initially accepted and worked within the Ptolemaic framework, isolating and correcting erroneous parameters. Objections were later raised concerning Ptolemy's failure to reconcile the mathematical models of the Almagest with the physical spheres they were intended to represent. A group of thirteenth-century Islamic astronomers, known as the Maragha school, revolutionized medieval theoretical astronomy by developing planetary models that resolved the Ptolemaic difficulties. The chief concerns and technical solutions of the Maragha school are evident in the later work of Nicolaus Copernicus (1473-1543).
Plato (428?-347 b.c.) first challenged astronomers to explain the apparently irregular movements of celestial bodies in terms of uniform circular motions. Eudoxus (408?-355? b.c.) accepted this challenge "to save the phenomena" and developed a system of concentric spheres with Earth as their common center. Each planet, as well as the Sun and Moon, was attached to a single sphere. This, in turn, was part of a set of interconnected spheres, each of which rotated about its own axis at a different rate and orientation. The combined motions were then adjusted to approximate the observed movements of the body in question. Eudoxus employed 27 spheres: three each for the Sun and Moon, four each for the five planets, and one for the fixed stars.
Callipus (370?-300?) improved the Eudoxian system by adding spheres. Aristotle (384-322 b.c.) further modified it, but, unlike Eudoxus, he maintained that the spheres were material bodies. Accordingly, certain presuppositions of Aristotelian physics needed to be satisfied. This required 22 additional spheres. Unfortunately, these models failed to explain certain phenomena.
In the second century a.d. Ptolemy proposed a more satisfactory system in the Almagest. He endorsed Aristotelian physics and its conclusions regarding Earth being at rest and the center of a spherical universe. He also acknowledged that planetary motions could only be explained kinematically by uniform circular motion or combinations thereof. However, instead of concentric spheres, Ptolemy employed eccentric orbits, epicycles, and equants.
In its simplest form, a planet's motion might be represented by an eccentric orbit—a circle about Earth, known as the deferent, with Earth offset from the center. In addition, a planet could be made to travel on an epicycle—a smaller circular orbit whose center moves along the circumference of the deferent. These geometrical devices had been exploited to great effect by Hipparchus (170?-120? b.c.). In fact, Ptolemy adopted Hipparchus's solar model without alteration and refined his lunar and stellar models. Ptolemy's planetary models, though, were the product of his own genius.
To account for the anomalous behavior of the planets, Ptolemy introduced the equant. The equant lies along the diameter defined by Earth and the deferent center. It is the same distance as Earth from, but on the opposite side of, the deferent center. According to the Almagest, uniform circular motion was about the equant, not the deferent center.
In Planetary Hypotheses Ptolemy supported a physical interpretation of the system propounded in the Almagest. He accepted that the universe was composed of physically real, concentric spheres, but made no attempt to correlate the motions of these bodies with his mathematical models.
The Almagest was first translated into Arabic in the early ninth century. Islamic astronomers quickly adopted Ptolemy's geocentric view and directed their researches toward refining his mathematical models. Thabit ibn Qurra (836-901), al-Battani (858?-929), and others associated with al-Ma'mun's (786-833) House of Wisdom uncovered erroneous parameters and provided corrected values based on new observations. Attention then shifted to deeper methodological and theoretical considerations, especially the relationship between Ptolemy's models and their physical interpretation.
The reexamination of Ptolemaic astronomy reached its full maturity during the eleventh century. The most extensive and sophisticated attack on it was leveled by Ibn al-Haytham (965-1040?), also known as Alhazen, in al-Shukuk ala Batlamyus. Al-Haytham's objective was to harmonize the mathematical and physical aspects of astronomy. Accordingly, he rejected the use of mathematical models whose motions could not be realized by physical bodies. In particular, he objected to Ptolemy's use of the equant because it required uniform circular motion of a sphere about a point other than its center. Since this was physically impossible, the models of the Almagest could not be describing the actual motions of celestial bodies. Al-Haytham argued that they should therefore be abandoned in favor of more adequate models. The Persian Abu Ubayd al-Juzjani (?-1070?) went a step further by constructing his own non-Ptolemaic models.
Al-Juzjani's efforts were ultimately unsuccessful, but the search for alternate models continued during the twelfth century in the Islamic west. Astronomers of Andalusian Spain rejected geometric models that failed to satisfy Aristotle's axiom of uniform circular motion about a fixed point. According to Aristotelian physics, this fixed point was the center of the universe and coincided with Earth's center. Ptolemy's eccentrics, epicycles, and equants all violated the principle because they required the celestial spheres to revolve about fixed points other than Earth's center. Thus, the Ptolemaic approach was rejected as fundamentally flawed.
Sometimes referred to as the "Averröist critique," this line of criticism received its canonical formulation in the work of Ibn Rushd (1126-1198), or Averröes, who had been a student of Abu Bakr ibn Tufayl (1105?-1184). Ibn Tufayl claimed to have devised an arrangement that satisfied the philosophical presuppositions of Aristotelian physics without recourse to eccentrics or epicycles. Though nothing remains of this work, Ibn Tufayl's ideas inspired another of his students, al-Bitruji (1100?-1190?). Al-Bitruji proposed a system of concentric spheres reminiscent of that of Eudoxus. However, neither this nor any other configuration devised by the Andalusian school succeeded in making numerical predictions of planetary positions as accurate as Ptolemy's. The Andalusian approach was soon abandoned and the Ptolemaic system remained dominate.
The Golden Age of Islamic astronomy extended from the mid-thirteenth to the mid-fourteenth century. During this time, attempts were made to reform Ptolemaic astronomy by Nasir al-Din al-Tusi (1201-1274), Mu'ayyad al-Din al-Urdi (?-1266), Qutb al-Din al-Shirazi (1236-1311), Ibn al-Shatir (1305?-1375?), and others. Since the first three of these astronomers were associated with the Maragha observatory in northern Iran, and the last, Ibn al-Shatir, subsequently continued their work, they are today referred to as the Maragha school. The models they developed resolved the Ptolemaic problems regarding uniform circular motion.
Al-Tusi was the first to formulate a model of uniform circular motion that had the same predictive accuracy as Ptolemy's. He achieved this result with a device of his own invention—the "Tusi Couple." Consisting of two spheres rolling one within the other, the Tusi Couple was placed at the end of the equant vector—the line extending from the equant point to the center of an epicycle. When set in motion, the couple caused the length of the equant vector to vary, which caused the epicycle to trace out a path very close to that of the Ptolemaic deferent. Thus, the introduction of the deferent circle and non-uniform circular motion about it could be avoided. Furthermore, all component circular motions in al-Tusi's models were uniform about their own centers.
Al-Urdi, independent of and possibly prior to al-Tusi, developed a variant solution. His method proved mathematically equivalent to al-Tusi's, but required one less rotating sphere. This arrangement was later adopted by one of al-Tusi's disciples, al-Shirazi. The fourteenth-century Damascus astronomer Ibn al-Shatir continued the Maragha reforms. He combined the geometrical devices of al-Tusi and al-Urdi together with secondary epicycles to construct more accurate planetary models. His models retained the effect of the equant, but with the celestial bodies now rotating with uniform circular motion about Earth's center.
The motivation behind the Maragha school's tradition of model building has often been misunderstood. Though their models did restore uniform circular motion, they did not criticize Ptolemy because his models violated this principle. Their planetary models were designed to overcome the much more serious and fundamental problem of internal inconsistency.
Ptolemy accepted uniform circular motion as the only means of explaining the movements of celestial bodies. Nevertheless, he then introduced into his mathematical models the equant, which made such motions physically impossible. The latter point had been previously noted by al-Haytham. But, unlike al-Haytham, the Maragha school was not concerned with restoring uniform circular motion as such. Their goal was a mathematical methodology capable of accounting for the observable world in a manner consistent with whatever assumptions were made about the universe's physical nature. Thus, the Maragha school revolutionized medieval theoretical astronomy by rejecting Plato's limited goal of "saving the phenomena."
The question of Copernicus's debt to the Maragha school was raised in 1957 in an article by Victor Roberts. Roberts showed that the lunar model of Copernicus was essentially identical to that of Ibn al-Shatir's. Since then, ongoing research has established further similarities. In the Commentariolus, Copernicus presented planetary models that substituted the combination of two epicycles and a deferent for the Ptolemaic deferent-equant arrangement just as Ibn al-Shatir had done. A more striking resemblance appears in their models for Mercury. Here, Copernicus employs the Tusi Couple to vary Mercury's orbital radius exactly as in Ibn al-Shatir's model. Finally, Copernicus's solar model was mathematically equivalent to Ibn al-Shatir's, except that the positions of the Sun and Earth were reversed.
Copernicus and the Maragha school thus used the same mathematical devices and often applied them at precisely the same points. But there is a much deeper connection. They both stressed the need for internally consistent mathematical models that can be physically interpreted. Though no direct connection has yet been established, scholarly opinion suggests that these similarities cannot be attributed to mere coincidence. However, as significant as the Maragha influence might have been, it in no way diminishes the originality of Copernicus's heliocentric hypothesis.
STEPHEN D. NORTON
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