In much popular writing on the history of science Copernicus has been portrayed as a heroic genius who overturned 2000 years of prejudice and launched a revolution in science that continues to the present day. The word "Copernicus" has entered the Western vocabulary to refer to that rare individual who initiates a truly fundamental change in some subject or field of investigation. Immanuel Kant was the Copernicus of philosophy for his introduction of the method of critical philosophy; Nikolai Lobachevsky was the Copernicus of geometry for his invention of non-Euclidean geometry in the nineteenth century; and Edwin Hubble was the Copernicus of modern cosmology for his identification of galaxies and universal expansion in the twentieth century.

This picture of Copernicus was largely based on a general understanding of what he had done and not on a particularly close study of his actual writings. As historians over the past 50 years have analyzed the original Copernican texts and documents, a rather different and less admiring portrait has emerged. A sharp critique was advanced by Arthur Koestler (1963, 201-202) in a book on the history of early modern astronomy:

The figure of Copernicus, seen from the distance, is that of an intrepid, revolutionary hero of thought. As we come closer, it gradually changes into that of a stuffy pedant, without the flair, the sleepwalking intuition of the original genius; who, having got hold of a good idea, expanded it into a bad system, patiently plodding on, piling more epicycles and deferents into the dreariest and most unreadable among the books that made history.

Koestler was primarily a literary biographer rather than a scientist. Historians of science have also been very critical of Copernicus, including scholars who have studied closely the mathematical development of the heliocentric idea. Although he wrote for mathematicians and regarded himself as one of them, Copernicus displayed a lack of technical skill and creativity in comparison with Ptolemy. Some of the technical devices that he introduced were in fact almost certainly obtained from Islamic sources, with no acknowledgment of this fact, and he contributed relatively little to the field of observational astronomy. Although his contributions to cosmology were undeniable, even here it is suggested that his achievement was only the result of "a fortunate philosophical guess," to use a dismissive phrase of historian Derek Price (1959, 256). Copernicus is seen as the last medieval astronomer, someone who was mentally shackled by traditional conceptions of natural philosophy and slow to appreciate the possibilities opened up by his new system. His ideas entered the public domain slowly and through the efforts of friends; his famous book, written in a somewhat emotionless style, did not appear until he was on his deathbed. His reluctance to publish has been attributed variously to a fear of controversy, to his own recognition of technical weaknesses in his system, or simply to a weakness of character and an inability to assert himself as a man and a thinker.

The truth about Copernicus lies somewhere between the heroic portrait of popular history and the critical disparagement of contemporary scholarship. Copernicus worked in relative isolation in the single-minded pursuit of a great idea. Furthermore, unlike in modern cosmology, where the major advances have consisted of discoveries (often fortuitous) by skilled observers using advanced technology, Copernicus's achievement was an intellectual one carried out by a single individual working on the northern periphery of christendom. Whatever his limitations as a technical astronomer, he grasped the essential cogency of the heliocentric hypothesis and possessed the tenacity to pursue this idea to the end. That he did so in the circumstances of his time makes him a truly extraordinary figure of the history of science.

Publication of On the Revolutions of the Heavenly Spheres

Copernicus's interest in mathematics and astronomy was aroused at the University of Cracow, where he studied for several years in the 1490s. At the encouragement of his maternal uncle, the Bishop of Ermeland, he moved at the end of 1496 to northern Italy to train for a career in the church. Over the next nine years he studied canon law, medicine, and astronomy, obtaining a degree in canon law from the University of Ferrara in 1503. From 1506 until his death in 1543 he occupied the post of canon of the cathedral of Frauenberg in northern Poland by the Baltic Sea. Copernicus devoted his career to his administrative duties, to the practice of medicine, and to the pursuit of astronomy. A notable moment in his career occurred in 1514, when he was asked to participate in a project to reform the calendar. Although Copernicus declined on the grounds that the current state of knowledge of the motions of the Sun and the Moon was too uncertain to provide a reliable basis for calen-drical reform, the request indicated that by this early point in his career he possessed a substantial reputation as an astronomer.

The heliocentric system was set forth by Copernicus in 1543 in his great work On the Revolutions of the Heavenly Spheres. It was written in a technical style and was aimed at specialists; as he wrote in the dedication, "Mathematics is written for mathematicians." Revolutions was preceded by the unpublished Commentary of 1530, an outline of the new system that enjoyed a limited circulation and helped make his ideas known to the community of astronomers. A young Lutheran scholar named Georg Rheticus (1514-1574) studied with Copernicus for two years, from 1539 to 1541, and became an advocate for the new astronomy. In 1540 Rheticus published an expository account of the Copernican system under the title First Narrative. It was at Rheticus's instigation and with the encouragement of Copernicus's friend Bishop Giese that the Polish canon carried out the final preparations for the publication of his book.

Copernicus came to the study of astronomy following a period of growing interest in the mathematical and observational work of Ptolemy, al-Battani, al-Biruni, and al-Tusi. In the fifteenth century, there was a general revival of astronomy in Europe, and important accounts of Ptolemaic astronomy were published by Georg Peurbach (1423-1461) and his pupil Johannes Müller (1436-1476), also known as Regiomontanus. The latter wrote the Epitome of the Almagest of 1496, a book that moved beyond commentary to the level of original research in astronomical theory and technique. Regiomontanus also compiled a major manual of trigonometry, a work that helped to establish him as the leading mathematician of the fifteenth century.

In the first book of Revolutions Copernicus called attention to some anticipations of the new astronomy in ancient Greek and Roman writings. It is fair to say that he was giving prominence to some fairly obscure sources in order to build a rhetorical basis for the presentation of his own new system. Copernicus referred to the Pythagorean Philolaus and to Heraclides (387312 b.c.), the latter a pupil of Plato, who reputedly posited the rotation of the Earth as an explanation of the diurnal motion of the heavens. The late Roman writer Martianus Capella (ca. 470 a.d.) had suggested an alternative to the traditional ordering of the planets (Moon-Mercury-Venus-Sun-Mars-Jupiter-Saturn), suggesting that Venus and Mercury revolve about the Sun as the Sun revolves about the Earth. The proposed arrangement is an example of what is called a geoheliocentric system, the most famous of which is the more fully developed Tychonic system, considered in the next chapter. In comments echoing the sentiments of contemporary Hermetic and neo-Platonic authors Copernicus emphasized the special significance of the Sun in the universe.

Copernican System

The Copernican system was based on two distinct insights, both of which involved imparting a motion to the Earth: first, the daily 24-hour motion from east to west that all celestial bodies undergo may be attributed to the rotation of the Earth; second, certain striking and apparently unaccountable features of the Ptolemaic system can be explained by placing the Sun at the center and having the planets revolve about the Sun. These astronomical insights, and, in particular, the movement of the Earth that they implied, raised fundamental questions for traditional Aristotelian physics and would lead to new and revolutionary lines of investigation in natural philosophy.

There is a basic difference between ancient astronomy and Copernican cosmology that derives from the different interpretations in the two systems of the daily motion of the heavens. In the Ptolemaic system, each celestial body completes a revolution about the Earth in 24 hours, independently of its distance from the Earth. The fantastic speed with which the planets and sphere of fixed stars move implies a qualitative difference between them and objects found in our terrestrial world. Celestial bodies are composed of a mysterious and perfect fifth element, the ether, a conclusion largely derived from the fact of this daily motion. In ancient cosmology, there was a contrast between the world of the Earth and the world of the heavens based on the kinds of motion characteristic of objects in the two domains. By imparting a rotation to the Earth to explain the apparent daily motion of the heavens, Copernicus logically eliminated an assumption underpinning the traditional antithesis of the terrestrial and celestial domains.

It is worth noting that it was easier for astronomers of Copernicus's time to accept the daily rotation of the Earth than it was to accept its annual motion about the Sun. The Earth's rotation had already been discussed in some detail by al-Biruni and by late medieval writers such as Oresme. Independently of Copernicus, a professor at the University of Ferrara, one Celio Calcagnini (1479-1541), reasoned that it made more sense to suppose that the Earth revolves in 24 hours than to assume the entire heavens complete a revolution in the same period. Francesco Patrizio argued the same point later in the century, suggesting it was implausible to assume that the solid spheres of the planets and fixed stars could move with the incredible velocities required by the daily rotations stipulated in traditional cosmology. Both Calgagnini and Patrizio were otherwise firm believers in a geocentric universe. William Gilbert (1544-1603), the English natural philosopher and author of a seminal work on magnetism, was also convinced of the Earth's rotation, a motion he speculated was produced by the Earth's magnetic energies. On the question of the Earth's annual motion about the Sun Gilbert remained noncommittal.

Putting the Earth in motion about the Sun meant that the Earth was no longer the center of the universe and was just another celestial body. The fact that thinkers were willing to consider the Earth's rotation but not its annual revolution about the Sun indicates that the latter assumption represented a more radical departure from orthodoxy. The annual motion was the cornerstone of Copernicus's new world system. The motivation for this assumption derived from certain special features of the Ptolemaic system, in particular, the curious role in this system occupied by the Sun in relation to the planets. For each of the three superior planets the line joining the center of the epicycle to the planet always remains parallel to the line joining the Earth to the Sun. For the

Copernican Cosmology
Figure 4.4: The Copernican system. The Thomas Fisher Rare Book Library, University of Toronto.

two inferior planets the centers of their epicycles always lie on the line joining the Earth to the Sun. Hence the planets and the Sun move about the Earth in a very specific way, a fact that simply expresses what is seen in nature and has no explanation.

As we saw in chapter 3, there are simple transformations that relate the Ptolemaic and Copernican models of planetary motion. For each of the superior planets the epicycle of the planet becomes the Earth's orbit about the Sun, while its deferent becomes the planet's orbit about the Sun. In the case of the inferior planets the epicycle becomes the planet's orbit about the Sun, while its deferent becomes the Earth's orbit about the Sun. In the Copernican system the three epicycles for the superior planets are replaced by one circle, the Earth's orbit about the Sun, while the two deferents for the inferior planets are replaced by one circle, once again, the Earth's orbit. The Copernican system, which is depicted in figure 4.4 in an original illustration from Revolutions, possesses a definite economy with respect to the Ptolemaic system, having replaced three planetary epicycles and two planetary deferents by the Earth's orbit. There is, in the Copernican system, no longer the curious coincidence concerning the directions of the radii of the superior epicycles and the centers of the inferior deferents. The superior epicyclic radii point in the direction of the Sun because they are simply the radius joining the Earth to the Sun, while the centers of the inferior planets lie on the radius joining the Earth to the Sun because these centers coincide with the Sun, and the radii of the deferents coincide with the line joining the Earth to the Sun.

The naturalness and coherence of the Copernican system provided strong internal evidence in favor of the heliocentric hypothesis. There are also some indications (discussed in Goldstein (2002)) that Copernicus may have been motivated to develop a system in which the planets, as one moves out from the central body, decrease in angular velocity. In the Ptolemaic system this was the case for Mars, Jupiter, and Saturn; however, Mercury, Venus, and the Sun move about the Earth with the same average angular velocity. Although the Sun is farther than Mercury from the Earth, they both complete a circuit around the ecliptic in one year. In the Copernican system the rule of decreasing angular velocity is satisfied by all the planets.

In the Ptolemaic system the distances of the planets were regulated by the nesting principle, according to which there is no empty space between the successive spheres of movement of each of the planets. In the Copernican universe, there is no need to invoke such a principle: once the distance from the Earth to the Sun is set, all the other distances and dimensions of the system are determined. This fact is sometimes expressed by saying that Copernican astronomy has very natural and inherent system-like features.

Viewed purely as a work of geometrical astronomy, the Copernican theory was, in certain respects, characterized by a stronger sense of physical realism than its classical Ptolemaic counterpart. Copernicus seems to have been influenced by Islamic Ptolemaists, who modified some of Ptolemy's technical devices to make them physically more plausible. Of course, the Arabic treatises all supposed that the Earth was at the center of the universe. Because there were already such Islamic geocentric precedents, it is difficult to relate the heliocentric idea in and of itself with any particular push for a physically realistic astronomy. Nevertheless, an emphasis on producing mechanisms that were physically plausible as well as mathematically effective influenced how Copernicus developed his heliocentric scheme.

The Equant and the Earth's Third Motion

Ptolemy had introduced the equant to account for certain irregularities in the motions of the planets. The equant involved uniform angular motion of a circle about a point offset from the center of the circle. Although mathematically useful, it seemed difficult to reconcile with how material spheres actually move. As we saw earlier, Islamic astronomers devised ingenious techniques that allowed one to replace the equant by a combination of circular motions that were strictly uniform about their center. Copernicus was strongly opposed to the equant and attempted within his system of a heliocentric astronomy to produce mechanisms that avoided it. The basic innovation was to introduce a secondary epicycle to account for the small variations in motion that the equant was intended to produce. The end result of this modification of the original idea was a system with a substantially increased number of epicycles. According to some commentators, this fact diminished the essential economy and simplicity of the Copernican system.

In both the Ptolemaic and Copernican systems the motion of the Moon is geocentric, and it might be thought that there would be no significant differences between the two lunar theories. Nevertheless, the realism of Copernicus in comparison to Ptolemy is evident in the theory presented in book four of Revolutions. Ptolemy had supposed that the center of the lunar deferent was located on a small circle or eccenter whose center was the Earth so that the lunar epicycle was periodically drawn closer to the Earth by a kind of crank mechanism. Although effective in accounting for the observed variations in lunar position, this model had the disadvantage that the distance of the Moon from the Earth varied by as much as a factor of two, something that was at odds with the observed constancy in the size of the moon and could not be in accord with actual lunar distances. The model of the fourteenth-century Damascus astronomer al-Shatir, described above, had avoided this problem by placing the Moon on a secondary epicyclet. In this model the lunar distances varied within a much smaller range, and the lunar positions were also given with appropriate accuracy. In Revolutions Copernicus presented what was essentially al-Shatir's model. Although no mention of his predecessor was made, it is believed that he must have been familiar, if only indirectly from some sources, with al-Shatir's model.

Copernicus believed in the existence of material spheres that carried the planets about the Sun. One of the strongest pieces of evidence for this belief is the third motion Copernicus assigned to the Earth. Assume that the Earth is affixed in some way to a sphere that rotates in one year about the Sun. As the Earth is carried around the Sun, it rotates each day on its axis. It is evident that the direction of this axis of rotation will continuously change: if the axis is initially inclined at an angle to the axis of the ecliptic sphere, then it will, in the course of a year, trace out a circle on the celestial sphere whose center is the north ecliptic pole. If the northern hemisphere were initially inclined toward the Sun, it would stay inclined in this way throughout the year, and we would enjoy perpetual summer. Of course, observation reveals that the direction of the Earth's axis remains fixed on the celestial sphere at a point close to the pole star, a fact which explains the changing elevation of the Sun in the sky during the year and the occurrence of the seasons. Copernicus found it necessary to add a third motion to the Earth, a small conical movement of its axis, which has the effect of causing the axis of the Earth to remain parallel to itself as the Earth revolves about the Sun. In later astronomy the use of material spheres to produce planetary motion was found to be unnecessary, and the parallelism of the Earth's axis was understood to be a natural consequence of the Earth's inertial motion. The Copernican third motion of the Earth was rooted in medieval conceptions about how the planets moved on spheres, conceptions that were present in both Aristotelian cosmology and in the cosmology of Ptolemy's Planetary Hypotheses.

Nowhere are Copernicus's technical limitations more apparent than in the latitude theory developed in the final book of Revolutions. In reference to this theory Kepler wrote, "Copernicus, ignorant of his own riches, took it upon himself for the most part to represent Ptolemy, not nature, to which he had nevertheless come the closest of all" (Swerdlow and Neugebauer 1984, 483). By collapsing the superior epicycles and inferior deferents to the circle of the Earth's orbit, the Copernican hypothesis should have effected a substantial simplification in the Ptolemaic latitude theory. The orientation of the different planes could be reduced to their relation to one and the same reference plane, the plane of the Earth's orbit. Furthermore, the latter occupies no special conceptual place in the theory other than to act as a reference plane for the analysis of planetary motion. Nevertheless, Copernicus placed the center of the Earth's orbit at the center of each of the planetary orbits and essentially duplicated the Ptolemaic latitude theory for each of these orbits. As Kepler observed, he failed to take advantage of the opportunities and simplifications that his system afforded. In fairness to Copernicus, it should be noted that all observations are of necessity made from the Earth so that his assumption may be viewed as a pragmatic one resulting from the practical needs of observation. Furthermore, latitude theory is the most technically difficult part of planetary astronomy, and a satisfactory treatment of it would challenge not just Copernicus but his most skilled successors.

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