The development of European science entered a new phase in 1543, when the heliocentric theory of Nicholaus Copernicus (1473–1543) was published, with the planets orbiting around the sun and not the earth.
Copernicus was born on 19 February 1473 at Torun, a town on the Vistula 110 miles north-west of Warsaw. His name was originally Niklas Koppernigk, which he latinised as Nicholaus Copernicus in 1491 when he enrolled at the University of Cracow, where he studied for three or four years without taking a degree. He then went to Italy to study at the universities of Bologna, Padua and Ferrara before returning to spend the rest of his days in what he called ‘this remote corner of the earth’, in what was then Prussia and is now Poland. During the years 1505–12 he lived at Heilsburg Castle, 140 miles north-east of Torun, where his uncle Lucas was bishop. After his uncle died in 1512 he moved to Frauenburg (Frombork), east of Danzig (Gdańsk), where he served as a canon in the cathedral for the rest of his days, making observations of the heavens and developing the mathematical basis of his new astronomical theory.
When Copernicus was at the University of Cracow the astronomer Albert Brudzewski was lecturing there, although there is no record of their having met. Brudzewski had published a commentary on the planetary theory of Peurbach, in which he put forward Ptolemy’s theory that the celestial orbs are not spheres but circles. Brudzewski also used a mathematical method analogous to one employed by the Arabic astronomers Nasir al-Din al-Tusi and ‘Ala’ al-Din ibn al-Shatir, similar to a model that Copernicus would later use in his heliocentric theory.
The textbooks that Copernicus read in his courses at the University of Cracow in mathematics, astronomy and astrology included works by Euclid, Ptolemy, Peurbach and Regiomontanus. The works of a number of Arabic astrologers and philosophers were available in Cracow at that time, including those of Masha’allah, al-Farghani, al-Kindi, Thabit ibn Qurra and Jabir ibn Aflah. Copernicus also bought a number of books in Johann Haller’s bookshop in Cracow, including the Alphonsine Tables and the Tabulae directionum of Regiomontanus, which he had bound together with parts of Peurbach’s Tables of Eclipses and tables of planetary latitudes.
Around 1512 Copernicus began writing a work entitled Nicolai Copernici de hypothesibus motuum caelestium a se constitutis commentariolus (Nicholas Copernicus, Sketch of his Hypotheses for the Celestial Motions). This came to be known as the Commentariolus, or ‘Little Commentary’, the first notice of the new astronomical theory that Copernicus had been developing. He gave written copies of this short treatise to a few friends but never published it in book form. Only two manuscript copies have survived, one of which was first published in Vienna in 1878. The earliest record of the Commentariolus is a note made in May 1514 by a Cracow professor, Matthias de Miechow, who writes that he had in his library ‘a manuscript of six leaves expounding the theory of an author who asserts that the earth moves while the sun stands still’. Matthew was unable to identify the author of this treatise, since Copernicus, with his customary caution, had not written his name on the manuscript. But there is no doubt that the manuscript was by Copernicus, because the author made a marginal note that he reduced all his calculations ‘to the meridian of Cracow, because...Frombork...where I made most of my observations...is on this meridian as I infer from lunar and solar eclipses observed at the same time in both places.’
The introduction to the Commentariolus discusses the theories of Greek astronomers concerning ‘the apparent motion of the planets’, noting that the homocentric spheres of Eudoxus were ‘unable to account for all the planetary motions’, and were supplanted by Ptolemy’s ‘eccentrics and epicycles, a system which most scholars finally accepted’. But Copernicus took exception to Ptolemy’s use of the equant, which led him to think of formulating his own planetary theory, ‘in which everything would move uniformly about its proper center, as the rule of absolute motion requires’.
Copernicus goes on to say that after setting out to solve ‘this very difficult and almost insoluble problem’, he finally arrived at a solution which involved ‘fewer and much simpler constructions than were formerly used’, provided that he could make certain assumptions, seven in number.
The assumptions are, that there is not a single centre for all the celestial circles, or spheres; that the earth is not the centre of the universe, but only of its own gravity and of the lunar sphere; that the sun is the centre of all the planetary spheres and of the universe; that the earth’s radius is negligible compared to its distance from the sun, which in turn is ‘imperceptible in comparison to the height of the firmament’; that the apparent diurnal motion of the stellar sphere is due to the rotation of the earth on its axis; that the daily motion of the sun is due to the combined effect of the earth’s rotation and its revolution around the sun; and that ‘the apparent retrograde and direct motion of the planets arise not from their motion but from the earth’s’. He then concludes that ‘the motion of the earth alone, therefore, suffices to explain so many inequalities in the heavens’.
Copernicus then goes on to describe the ‘Order of the Spheres’ in his heliocentric system, in which the time taken by a planetary sphere to make one revolution increases with the radius of its orbit.
The celestial spheres are arranged in the following order. The highest is the immovable sphere of the fixed stars, which contains and gives position to all things. Beneath it is Saturn, which Jupiter follows, then Mars. Below Mars is the sphere on which we revolve, then Venus; last is Mercury. The lunar sphere revolves around the center of the earth and moves with the earth like an epicycle. In the same order, also, one planet surpasses another in speed of revolution, accordingly as they trace greater or smaller circles. Thus Saturn completes its revolution in thirty years, Jupiter in twelve, Mars in two and one-half, and the earth in one year; Venus in nine months, Mercury in three.
Copernicus used the same system of epicycles that Ptolemy and all of his successors had employed in the geocentric model. He concludes the Commentariolus by summarising the number of circles; i.e., deferents, or primary circles, and epicycles, or secondary loops, required to describe all of the celestial motions in his heliocentric system: ‘Then Mercury runs on seven circles in all; Venus on five; the earth on three, and round it the moon on four; finally Mars, Jupiter and Saturn on five each. Altogether, therefore, thirty-four circles suffice to explain the entire structure of the universe and the entire ballet of the planets.’
The first indication that the new theories of Copernicus had reached Rome came in the summer of 1533, when the papal secretary Johann Widmanstadt gave a lecture entitled Copernicana de motuu terra sentential explicani (An Explanation of Copernicus’ Opinion of the Earth’s Motion) before Pope Clement VI and a group that included two cardinals and a bishop. After the death of Pope Clement, on 25 September 1534, Widmanstadt entered the service of Cardinal Nicholas Schönberg, who as papal nuncio in Prussia and Poland had undoubtedly heard of Copernicus years before. Schönberg wrote to Copernicus on 1 November 1536, in a letter that may have been drafted by Widmanstadt, urging Copernicus to publish a book on his new cosmology and to send him a copy.
Despite this encouragement Copernicus made no move to publish his researches, but then his attitude changed in the spring of 1539, when he received an unexpected visit from a young German scholar, Georg Joachim van Lauchen, who called himself Rheticus (1514–74). Rheticus, who although only twenty-five was already professor of mathematics at the Protestant University of Wittenberg, explained that he was deeply interested in the new cosmology of Copernicus, who received him hospitably and permitted him to study the manuscript that he had written to explain his theories. During the next ten weeks Rheticus worked with Copernicus in studying the manuscript, which he then summarised in a treatise entitled Narratio prima (First Narrative), intended as an introduction to the Copernican theory. This was written in the form of a letter from Rheticus to his friend Johann Schöner, under whom he had studied at Wittenberg. The Narratio prima was published at Danzig in 1540 with the approval of Copernicus, who is referred to by Rheticus as ‘my teacher’ in the introductory section where he describes the scope of the Copernican cosmology.
Rheticus does not mention the heliocentric theory until after the section on ‘General Considerations Regarding the Motions of the Moon, Together with the New Lunar Hypotheses.’ There he says that the new model explains the retrograde motion of the planets ‘by having the sun occupy the center of the universe, while the earth revolves instead of the sun on the eccentric’.
The Narratio prima proved to be so popular that a second edition was published at Basel the following year. But Copernicus still hesitated to publish his manuscript, which he sent for safekeeping to his old friend Tiedemann Giese, Bishop of Culm. Finally, in the autumn of 1541, Giese received permission from Copernicus to send his manuscript to Rheticus, who was to take it to the press of Johannes Petreius in Nuremberg for publication. The title chosen for the book was De Revolutionibus Orbium Coelestium Libri VI (Six Books Concerning the Revolutions of the Heavenly Spheres). The title stems from the fact that Copernicus believed the celestial bodies to be embedded in the same crystalline spheres, or rather spherical shells, as those first proposed by Aristotle, though he had them revolving around the sun rather than the earth.
Toward the end of the following year Copernicus suffered a series of strokes that left him half-paralysed, and it was obvious to his friends that his end was near. Meanwhile Rheticus had taken a leave of absence from the University of Wittenberg in May 1542 to supervise the printing of De Revolutionibus in Nuremberg. Five months later he left Nuremberg to take up a post at the University of Leipzig, leaving responsibility for the book in the hands of Andreas Osiander, a local Lutheran clergyman. Osiander took it upon himself to add an anonymous introduction entitled Ad lectorem (To the Reader), which was to be the cause of considerable controversy regarding the Copernican theory.
De Revolutionibus finally came off the press in the spring of 1543. The first printed copy was sent to Copernicus, and according to tradition it reached him a few hours before he died, on 24 May 1543. Tiedemann Giese describes the last days of Copernicus in a letter to Rheticus: ‘He had lost his memory and mental vigor many days before; and he saw his completed work only at his last breath upon the day that he died.’
The introduction to De Revolutionibus, the Ad lectorum written by Osiander, is entitled ‘To the Reader Concerning the Hypotheses of this Work.’ This says that the book is designed as a mathematical device for calculation and not as a real description of nature. The Ad lectorum was intended to deflect criticism of the heliocentric cosmology by those who thought that it contradicted the Bible, particularly the passage in the Book of Joshua that says ‘The sun stood still in the middle of the sky and delayed its setting for almost a whole day.’ Martin Luther, referring to the Copernican theory, had already been quoted as saying that ‘People give ear to an upstart astrologer who strove to show that the earth revolves, not the heavens, or the firmament, the sun and the moon. This fool wishes to reverse the entire science of astronomy, but sacred Scripture tells us that Joshua commanded the Sun to stand still and not the Earth.’ Copernicus himself had been worried about such criticism, as evidenced by his statement in the Preface of De Revolutionibus, which he dedicated to Pope Paul III: ‘I can reckon easily enough, Most Holy Father, that as soon as certain people learn that in these books of mine which I have written about the revolutions of the spheres of the world I attribute certain motions to the terrestrial globe they will immediately shout to have me and my opinion hooted off the stage.’
The first eight chapters of Book I of De Revolutionibus give a greatly simplified description of the Copernican cosmology and its philosophical basis. Copernicus begins with arguments for the spherical nature of the universe; the sphericity of the earth, moon, sun and planets; and the uniform circular motion of the planets around the sun. He shows how the rotation of the earth on its axis, together with its revolution about the sun, can easily explain the observed motions of the celestial bodies. The absence of stellar parallax he explains by the fact that the radius of the earth’s orbit is negligible compared to the distance of the fixed stars.
Chapter 9 is entitled ‘Whether many movements can be attributed to the Earth, and concerning the center of the world.’ Here Copernicus abandons the Aristotelian doctrine that the earth is the sole source of gravity, and instead takes the first step toward the Newtonian theory of universal gravitation, writing that ‘I myself think that gravity or heaviness is nothing except a certain natural appetency implanted in the parts by the divine providence of the universal Artisan, in order that they should unite with one another in their oneness and wholeness and come together in the form of a globe.’
Chapter 10 is entitled ‘On the order of the celestial orbital circles.’ Here Copernicus removes the ambiguity concerning Mercury and Venus, which in the Ptolemaic model were sometimes placed ‘above’ the sun and sometimes ‘below’. The Copernican system has Mercury as the closest planet to the sun, followed by Venus, Earth, Mars, Jupiter and Saturn, surrounded by the sphere of the fixed stars, and with the moon orbiting the earth. This model is simpler and more harmonious than Ptolemy’s, for all of the planets revolve in the same sense, with velocities decreasing with their distance from the sun, which, as Copernicus writes, sits enthroned at the centre of the cosmos.
In the center of all the celestial bodies rests the Sun. For who would place this lamp of a very beautiful temple in another or better place than this where from it can illuminate everything at the same time. As a matter of fact, not unhappily do some call it the lantern, others the mind and still others, the pilot of the world...And so the sun, as if resting on a kingly throne, governs the family of stars which wheel around.
Chapter 11 is ‘A Demonstration of the Threefold Movement of the Earth,’ while the remaining three chapters of Book One are concerned with the application of plane and spherical geometry and trigonometry to problems in astronomy. The three motions to which Copernicus refers are the earth’s rotation on its axis, its revolution around the sun, and a third conical motion, which he introduced to keep the earth’s axis pointing in the same direction while the crystalline sphere in which it was embedded rotated annually. The period of this supposed third motion he took to be slightly different than the time it takes the earth to rotate around the sun, the difference being due to the very slow precession of the equinoxes.
Book Two is a detailed introduction to astronomy and spherical trigonometry, together with mathematical tables and a catalogue of the celestial coordinates of 1,024 stars, most of them derived from Ptolemy, adjusted for the precession of the equinoxes.
Book Three is concerned with the precession of the equinoxes and the movement of the earth around the sun. Here the theory is unnecessarily complicated, since Copernicus, besides combining precession with his ‘third motion’ of the earth, inherited two effects from his predecessors, one of them spurious. The first effect was the mistaken notion, stemming from the trepidation theory, that the precession was not constant but variable, and the other was the variation in the inclination of the ecliptic.
Book Four deals with the motion of the moon around the earth; Books Five and Six study the motions of the planets. Here, as with the motions of the sun, Copernicus used eccentrics and epicycles just as Ptolemy had done, though his conviction that the celestial motions were combinations of circular motion at constant angular velocity made him refrain from using the Ptolemaic device of the equant. Because of the complexity of the celestial motions, Copernicus was forced to use about as many circles as had Ptolemy, and so there was little to choose from between the two theories so far as economy was concerned, and both were capable of giving results of comparable accuracy. The advantages of the Copernican system were that it was more harmonious; it removed the ambiguity about the order of the inner planets; it explained the retrograde motion of the planets as well as their variation in brightness; and it allowed both the order and relative sizes of the planetary orbits to be determined from observation without any additional assumptions.
Copernicus refers to Aristarchus of Samos thrice in De Revolutionibus, twice regarding his predecessor’s measurement of the inclination of the ecliptic and once concerning his measurement of the length of the solar year. But nowhere does he mention that Aristarchus had in the mid-third century BC proposed that the sun and not the earth was the centre of the cosmos. Copernicus had referred to the heliocentric theory of Aristarchus in his original manuscript, but deleted it from the edition of De Revolutionibus printed in 1543.
Copernicus is known to have possessed a copy of George Valla’s Outline of Knowledge, printed by Aldus Manutius at Venice in 1501, which included a translation of a work of Aetius (Pseudo-Plutarch) containing two references to Aristarchus. One has Aristarchus ‘assuming that the heavens are at rest while the earth revolves along the ecliptic, simultaneously rotating about its own axis’; the other says that in his theory the earth ‘spins and turns, which Seleucus afterwards advanced as an established opinion’.
Copernicus was almost certainly familiar with Archimedes’ Sand-Reckoner, which contains the earliest reference to the heliocentric theory of Aristarchus. There Archimedes says that Aristarchus explains the lack of stellar parallax in his heliocentric theory by supposing that the radius of the earth’s move around the sun is negligible compared to the distance of the stars. This is essentially the same explanation given by Copernicus in his Commentariolus, where in the fourth of his assumptions he states that ‘the distance from the earth to the sun is imperceptible in comparison to the height of the firmament’. Copernicus uses this same argument in De Revolutionibus, where at the end of Book One, chapter 10 he contrasts the retrograde motion of the planets with the unchanging array of the stars, noting that ‘How exceedingly fine is the godlike work of the Best and Greatest Artist!’
Thus it is possible that Copernicus was aware of the heliocentric theory of Aristarchus and that he chose to suppress mention of it in De Revolutionibus, perhaps so as not to lessen the importance of his own life’s work, setting the celestial orbs in motion around the sun rather than the earth.
Copernicus mentions some of the Arabic astronomers whose observations and theories he used in De Revolutionibus, namely al-Battani, al-Bitruji, al-Zarqallu, Ibn Rushd (Averroës) and Thabit ibn Qurra. He also mentions al-Battani in his Commentariolus. But he does not mention Nasir al-Din al-Tusi, Mu’ayyad al-Din al’-Urdi, Qutb al-Din al-Shirazi and Ala’ al-Din ibn al-Shatir. F. Jamil Ragep describes the advances made by these Arabic astronomers in the thirteenth and fourteenth centuries:
In essence, these astronomers developed mathematical tools (such as the ‘Tusi couple’ and the ‘Urdi lemma’) that allowed connected circular motions to reproduce approximately the effects brought about by devices such as Ptolemy’s equant...What this allowed Tusi and his successors to do was to isolate the aspect of Ptolemy’s equant model that brought about a variation in distance between the epicycle center and the earth’s center from the aspect that resulted in a variation in speed of the epicycle center about the Earth. Such mathematical dexterity allowed these astronomers to present models that to a great extent restored uniform circular motion to the heavens while at the same time producing motions of the planets that were almost equivalent to those of Ptolemy.
Ragep goes on to quote from an article by Noel Swerdlow and Otto Neugebauer, which indicates that some of the mathematical methods used by Copernicus were based on those of Arabic, Iranian and Turkic astronomers.
The planetary models for longitude in the Commentariolus are all based upon the models of Ibn al-Shatir – although the arrangements for the inferior planets is incorrect – while those for the superior planets in De Revolutionibus use the same arrangement as ‘Urdi’s and Shirazi’s model, and for the interior planets the smaller epicycle is converted into an equivalent rotating eccentricity that constitutes a correct interpretation of Ibn al-Shatir’s model. In both the Commentariolus and De revolutionibus the lunar model is identical to Ibn al-Shatir’s and finally in both works Copernicus makes it clear that he was addressing the same physical problems as his predecessors. It is obvious that with regard to these problems, his solutions were the same.
Ragep then quotes Swerdlow on the question of how Copernicus might have acquired the theories of these Arabic astronomers, where he says ‘How Copernicus learned of the models of his [Arabic] predecessors is not known – a transmission through Italy is the most likely path – but the relation between the models is so close that independent invention by Copernicus is all but impossible.’
All that someone like Copernicus had to do was take any of Ibn al-Shatir’s models, hold the sun fixed and then allow the Earth’s sphere, together with all the other planetary spheres that were centered on it, to revolve around the sun instead...that was the very step taken by Copernicus when he seems to have adopted the same geocentric models as those of Ibn al-Shatir and then translated them to heliocentric ones whenever the situation called for it.
Thus the Copernican theory seems to have been based on mathematical models that he acquired from his Arabic predecessors, though he took the revolutionary step of putting the sun at the centre of the planetary orbits rather than the earth.