THE REVIVAL OF ASTRONOMY CULMINATED WITH THE PARADIGM-shifting work of Nicolaus Copernicus (1473–1543), whose life spanned the transition period between the twilight of the medieval era and the dawn of the Renaissance. He was born twenty years after the fall of Constantinople, capital of the Byzantine Empire, the Christian continuation of the Roman Empire. Two years later the Gutenberg Bible was printed, stimulating an unprecedented spread of the new learning that had developed in western Europe. Copernicus’s teenage years saw monumental changes such as Columbus’s discovery of America, opening up a new world at the beginning of a new age.
Copernicus was born on February 19, 1473, in Torun, a town on the Vistula 110 miles northwest of Warsaw, in what was then the Duchy of Prussia and is now Poland. His name was originally Niklas Koppernigk, which he Latinized as Nicolaus Copernicus after he went to university. The youngest of four children of a prosperous merchant, his father died in 1483, whereupon he and his siblings were adopted by their maternal uncle Lucas Watzenrode, a priest who had studied at the universities of Cracow, Cologne, and Bologna.
In 1489 Lucas become bishop of Ermland, also known as Warmia, one of the four provinces into which the Duchy of Prussia was then divided, with the kingdom of Prussia to its west and the kingdom of Poland to its south. Copernicus and his older brother, Andreas, stayed with their uncle Lucas at his palace in Heilsburg, 140 miles northeast of Torun, while their sister Barbara entered a convent. Their other sister, Maria, married a merchant in Cracow.
In the autumn of 1491 Nicolaus and Andreas were sent by their uncle Lucas to the University of Cracow, where they enrolled in the faculty of arts. They remained there for about three or four years, but left without taking a degree. During that time Nicolaus is known to have taken courses in mathematics, astronomy, astrology, and geography. According to his first biographer, the French astronomer Pierre Gassendi (1592–1655), his reading also included Cicero, Virgil, Ovid, and Seneca, for the curriculum at Cracow was in tune with the spirit of the Renaissance, where the emphasis was on the humanities rather than science.
The renowned Polish astronomer Albert Brudzewski was lecturing in the University of Cracow at the time and Nicolaus would undoubtedly have read his works, although there is no record of their having met. Brudzewski had published a commentary on the Theorica novae planetarum of Peurbach, in which he put forward his own 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 ibn al-Shatir, similar to a model that Copernicus would later use in his heliocentric theory. Brudzewski may have obtained this theory from a work written in Cracow in 1430 by the Polish astronomer Sandivogius of Czecel. This suggests that the works of Nasir al-Din al-Tusi and ibn al-Shatir were available at the University of Cracow when Copernicus was studying there.
According to Gassendi, the textbooks that Copernicus read in his courses in mathematics, astronomy, and astrology included works by Euclid, Ptolemy, Sacrobosco, Peurbach, and Regiomontanus. In addition, the works of a number of Arabic astronomers were available in Cracow at that time, including those of al-Farghani, al-Kindi, Thabit ibn Qurra, al-Tusi, and al-Shatir. Copernicus also frequented Johann Haller’s bookshop in Cracow, where he purchased the Alphonsine Tables and the Tabulae directionum of Regiomontanus and had them bound together with parts of Peurbach’s Tables of Eclipses and tables of planetary latitudes.
Nicolaus and Andreas left Cracow early in 1496 to live with their uncle Lucas in the bishop’s palace at Heilsburg. Lucas nominated Nicholas and Andreas to be canons of Frauenburg Cathedral, that is, resident clergy who were not required to take holy orders or a vow of celibacy, but at first his efforts were unsuccessful. Nicolaus was finally made a canon in 1497 and Andreas was elected in 1499. Both of them were elected in absentia, for in the fall of 1496 Nicolaus had gone off to study at the University of Bologna, where Andreas joined him two years later. There, both joined the faculty of law and enrolled in the Natio Germanorum, the largest of the “nations” into which foreign students were organized at Bologna.
The brothers seem to have stayed as paying guests in the house of Domenico Maria da Novara (1454–1504) of Ferrara, a professor of astronomy at the university. Nicolaus believed that he was “not so much the pupil as the assistant and witness of observations of the learned Dominicus Maria,” as his friend Rheticus later quotes Copernicus. One of the observations in Bologna concerned a lunar occultation of the star Aldabaran, which Copernicus says they made “after sunset on the seventh day before the Ides of March, in the year of Christ 1497.”
Copernicus received his master’s degree in law at Bologna in 1499. He then went to Rome early in 1500 to take part in the celebration of the Jubilee, or Holy Year, that had been proclaimed by Pope Alexander VI. According to Rheticus, while in Rome Copernicus “lectured on mathematics before a large audience of students and a throng of great men and experts in this branch of knowledge.” Copernicus notes in De revolutionibus that he observed a lunar eclipse in Rome on November 6, 1500. He compared it to an eclipse observed by Ptolemy in Alexandria in the “nineteenth year of Hadrian” (AD 136/137), his purpose being “to determine the positions of the moon’s movement in relation to the established beginnings of calendar years.”
Nicolaus and Andreas returned to Poland in May 1501. On July 27 of that year they made an appeal to the authorities of their chapter in Frauenburg, asking for a two-year extension of their leave so that they could complete their studies in Italy. The chapter accepted and in August they left Frauenburg for Italy, Andreas to complete his degree in canon law in Bologna and Nicolaus to study medicine in Padua.
Nicolaus enrolled at the University of Padua in the fall of 1501, studying law as well as medicine. He interrupted his studies in Padua after two years to enroll at the University of Ferrara, where on May 31, 1503, he received the degree of doctor of canon law. Copernicus practiced medicine for the rest of his career in addition to continuing his work in astronomy. He was truly a Renaissance man before the term was coined, for to him and other scholars of his time there were no boundaries between the academic disciplines, and he brought the same attitude of mind to his medical work as he did to his astronomical researches.
Copernicus returned to Poland later in 1503, first rejoining his fellow canons at Frauenberg and soon afterward going on to live with his uncle Lucas at Heilsburg Castle (Lidzbark Warminski), the official residence of the bishops of Warmia, about forty miles southeast of Frauenburg. He remained at Heilsburg for six years, serving as secretary of state and personal physician to his uncle Lucas. Copernicus also participated in the local Prussian diets, or parliaments, as a member of the group of canons called the Chapter of Warmia.
On January 1, 1504, Copernicus went to Marienburg (Malbork) to attend a meeting of the Land Diet of the Prussian States, at which Bishop Lucas presided. The assembly decided to convene another meeting twenty days later in Elbing (Elblag), where the Prussian states solemnly refused to make a pledge of loyalty to King Alexander, grandson of Wladyslaw II Jagiello, who had become Grand Duke of Lithuania in 1492 and succeeded his childless elder brother, John I Albert, as king of Poland in 1501, reuniting the two states.
In May 1504 Nicolaus went with Lucas to a meeting of the Prussian delegates with King Alexander in Thorn, after which they accompanied the king to Danzig. He attended another assembly of the Prussian states with his uncle in 1506 from August 20, to September 15. Nicolaus probably also accompanied Lucas to Cracow on January 24, 1507, to attend the coronation of Sigismund I, who had succeeded his brother Alexander as king of Poland the previous year.
Nicolaus Copernicus, from the 1554 Paris edition of his biography by Pierre Gassendi
On January 24, 1507, Nicolaus was appointed personal physician of the bishop of Warmia, with a salary of 15 marks a year in addition to his income as a canon, which in 1519 was 98 marks. Soon afterward Bishop Lucas became seriously ill, but Nicolaus nursed him back to health, and he accompanied his uncle to an assembly of the Prussian states from September 1 through September 4 of that year, the last one they would attend together.
Around 1509 Nicolaus left his uncle’s service in Heilsberg and rejoined the cathedral chapter in Frauenburg, where he would spend most of the remainder of his life. It may be that by then he had decided to return to the astronomical research he had begun in Italy, which he would not have had the time to do while serving as his uncle’s minister of state.
Early in 1512 he accompanied his uncle to Cracow to attend the wedding of King Sigismund and the coronation of his bride. But on the way home Bishop Lucas died in Torun, on March 29, 1512. His body was brought back to Frauenburg and, as was the custom at the time, he was buried in the cathedral, where his tomb can still be seen, with an epitaph composed by Copernicus.
When Copernicus returned to Frauenburg, he was one of sixteen canons in the cathedral chapter of Warmia. Most of the canons lived in a dormitory beside the cathedral. Each of them also had a curia, a house in the town outside the walls on Cathedral Hill, and some also had a villa in the countryside. In 1514 Copernicus bought a house just outside the west gate of Cathedral Hill. The previous year he had moved out of the dormitory inside the fortress and took up residence within the defense tower in the northwest corner of the fortress walls, which he had purchased from the cathedral chapter. The tower had three floors, the uppermost of which had windows on all sides, so that he could look out over the town and the surrounding countryside. Nearby he also built an observatory in the form of a viewing platform, where he set up his astronomical instruments with an unobstructed view of the celestial sphere. The observatory was built at his own expense, as recorded in the chapter archives, which note that in April 1513, he paid money into the chapter treasury for eight hundred bricks and a barrel of chlorinated lime from the cathedral work yard.
In De revolutionibus Copernicus refers to three instruments that he may have used in his observations. One was a sighting device called a triquetrum, or Ptolemy’s ruler, used for measuring parallax. Another was a quadrant, a kind of sundial set in a wooden block, used to measure the altitude of the sun at noon. The third was an armillary astrolabe, also known as an armillary sphere, which Copernicus describes as a set of nested rings, one set of which contained sights for measuring the position of a star or planet. He undoubtedly also had a regular astrolabe, although he does not mention it in De revolutionibus.
Looking up from his tower on June 5, 1512, Copernicus noted that Mars was in opposition, that is, the planet rose at sunset and set at sunrise, since it was diametrically opposite the sun in the celestial sphere. This was the first of at least twenty-five observations that Copernicus would make at Frauenburg, where he also developed the mathematical methods that he used in his new astronomical theory.
Around this time Copernicus began writing a work entitled De hypothesibus motuum coelestium a se constitutis commentariolus (Sketch of 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.” He 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 had reduced all his calculations “to the meridian of Cracow, because … Frombork [Frauenburg] … 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.” (Frombork is actually about ¼° west of Cracow.)
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 “the center of the earth is not the center of the universe.” He said that “we revolve around the sun like any other planet” and that the apparent daily rotation of the heavens results from the real diurnal rotation of the earth in the opposite sense.
Copernicus went on to say that after setting out to solve “this very difficult and almost insoluble problem,” he finally arrived at a solution that involved “fewer and much simpler constructions than were formerly used,” provided that he could make certain assumptions.
The assumptions, seven in number, were: (1) that there is not a single center for all the celestial circles, or spheres; (2) that the earth is not the center of the universe, but only of its own gravity and of the lunar sphere; (3) that the sun is the center of all the planetary spheres and of the universe; (4) 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”; (5) that the apparent diurnal motion of the stellar sphere is due to the rotation of the earth on its axis; (6) 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 (7) that “the apparent retrograde and direct motion of the planets arise not from their motion but from the earth’s.” He then concluded that “the motion of the earth alone, therefore, suffices to explain so many inequalities in the heavens.”
Copernicus later described 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.
Thus Mars, Jupiter, and Saturn revolve around the sun in orbits larger in size and longer in period than the earth’s, while Mercury and Venus have smaller orbits with shorter periods. Copernicus shows how this can be used to explain the apparent retrograde motion of the planets, starting with Mars, Jupiter, and Saturn. He says each of the outer planets:
seems from time to time to retrograde, and often to become stationary. This happens by reason of the motion, not of the planet, but of the earth changing its position in the grand circle. For since the earth moves more rapidly than the planet, the line of sight directed [from the earth] toward [the planet and] the firmament regresses, and the earth more than neutralizes the motion of the planet. This regression is most notable when the earth is nearest to the planet, that is, when it comes between the plant and the sun at the evening rising of the planet. On the other hand, when the planet is setting in the evening or rising in the morning, the earth makes the observed motion greater than the actual. But when the line of sight is moving in the direction opposite to that of the planets and at an equal rate, the planets appear to be stationary, since the opposed motions neutralize each other.
The apparent retrograde motion of the inner planets, focusing on Venus, he explained as follows:
Venus seems at times retrograde, particularly when it is nearest the earth, like the superior planets, but for the opposite reason. For the regression of the superior planets happens because the motion of the earth is more rapid than theirs, because it [the earth] is slower; and because the superior planets enclose the grand circle [earth’s orbit], whereas Venus is enclosed within it. Hence Venus is never in opposition to the sun [i.e., on the opposite side of the sun], and since the earth cannot come between them, but it [Venus] moves within fixed distances on either side of the sun. These distances are determined by tangents to the circumference drawn from the center of the earth, and never exceed 48° in our observations.
Copernicus used the same system of epicycles that Ptolemy and all of his successors had employed in the geocentric model. He did so because this was a highly effective method for representing the orbits of the planets as seen from the earth, which he adapted to his heliocentric system by changing the reference point to the sun as the center rather than the earth, which then became one of the planets. This was a stroke of genius, I think, for now he could put the mathematical methods of Ptolemy to use in his heliocentric theory.
Copernicus concluded the Commentariolus by summarizing the number of circles, that is, deferents, or primary circles, and epicycles, or secondary loops, required to describe all of the planetary 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.”
Despite its brevity, the Commentariolus contains all of the main ideas that Copernicus would later introduce in De revolutionibus, most notably the revelation that the sun and not the earth was the center of the universe. Although he says in the beginning of the Commentariolus that he will leave mathematical demonstrations for his larger work, he describes the motions of the celestial bodies at some length, indicating that he had already worked out the details of his system, though he would alter parts of his planetary model in the final version of De revolutionibus.
Thus some three decades before the appearance of De revolutionibus Copernicus had fully developed his heliocentric theory. This involved a tremendous amount of work, which he would have done in the first decade after his return from Italy, during most of which he was extremely busy in the service of his uncle Lucas. It would then seem as if he indeed left his uncle’s service so as to return to the cathedral at Frauenburg, where he would have more time for his astronomical observations and calculations.
Aside from the mathematical details of the Ptolemaic and Copernican theories, which even modern astronomers find formidable, it seems to me that Copernicus conceived the truly revolutionary idea of the rotating sun at the center of the universe very early in his career, probably when he was at the University of Cracow. There he had become deeply influenced by the Pythagorean notion of celestial harmony, which he expressed throughout his work, and he was also aware of the heliocentric theory that Aristarchus of Samos had put forward in around 250 BC. Since he took the trouble to acquire and bind together the Alphonsine Tables with the works of Peurbach and Regiomontanus, we can be sure that Copernicus had followed the developing ideas of his medieval predecessors. So I am convinced that from his undergraduate days Copernicus was committed to the idea that the sun and not the earth was the center of the universe, a revolutionary theory that he spent the rest of his days developing mathematically and verifying by observation, applying the scientific method developed by Robert Grosseteste and his followers. Thus Copernicus represents the culmination of medieval European science and at the same time the beginning of the Scientific Revolution, working away quietly in his “obscure corner of the earth.”
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’s 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 September 25, 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 November 1, 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 research. His attitude abruptly changed, though, in the spring of 1539, when he received an unexpected visit from a young German scholar, Georg Joachim van Lauchen, who called himself Rheticus (1514–1574). Rheticus, only twenty-five, 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 studied the manuscript alongside Copernicus. He then summarized the work 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 in Wittenberg. The Narratio prima was published at Danzig in 1540 with the approval of Copernicus, who was referred to by Rheticus as “my teacher” in the introductory section where he described the scope of the Copernican cosmology.
Rheticus then went into each of the books in detail, adding an astrological prediction of his own after his account of the Copernican theory of “The Eccentricity of the Sun and the Motion of the Solar Apogee.” Rheticus believed that world history followed the same cycle as the eccentricity of the sun’s orbit (observed from the earth) and that the completion of its next cycle would coincide with the downfall of the Mohammedan faith, following which, he says, “We look forward to the coming of our Lord Jesus Christ when the center of the eccentric reaches the other boundary of mean value, for it was in that position at the creation of the world.”
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 said 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 in 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. A letter, now lost, that Copernicus wrote on July 1, 1540, indicates that he was afraid that his theory would be criticized by both Aristotelians and theologians, for it contradicted the accepted geocentric astronomical of Ptolemy as well as the world picture of both Catholic and Protestant theologians, and at a most critical time, at the beginning of the Reformation. At a more fundamental level, or so I believe, was Copernicus’s fear of being ridiculed for proposing such a counterintuitive theory, particularly since he was such a private and modest person. As we will see, he admitted this in the dedicatory preface of De revolitionibus, addressed to Pope Paul III.
Finally, in the autumn of 1541, Giese received permission from Copernicus to send his manuscript to Rheticus, who took 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).
Toward the end of the following year Copernicus suffered a series of strokes that left him half-paralyzed, and it was obvious to his friends that his end was near. Tiedemann Giese wrote on December 8, 1542, to George Donner, one of the canons at Frauenburg, asking him to look after Copernicus in his last illness. “I know that he always counted you among his truest friends. I pray therefore, that if his occasions require, you will stand by him and take care of the man whom you, with me, have ever loved, so that he may not lack brotherly help in his distress, and that we may not appear ungrateful to a friend who has richly deserved our love and gratitude.”
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, with the publisher’s blurb, probably also written by Osiander, printed directly below the title. “You have in this recent work, studious reader, the motion of both the fixed stars and the planets recovered from ancient as well as recent observations and outfitted with wonderful new and admirable hypotheses. You also have most expeditious tables from which you can easily compute the positions of the planets for any time. Therefore buy, read, profit.”
The first printed copy of De revolutionibus was sent to Copernicus, and according to tradition it reached him a few hours before he died, on May 24, 1543. Tiedemann Giese described 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.” Here, Osiander cautions 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.”
De revolutionibus begins with a greatly simplified description of the Copernican cosmology and its philosophical basis. Copernicus 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, an argument first used by Archimedes in discussing the heliocentric theory proposed by Aristarchus. All of the arguments on physical grounds against the earth’s motion are then refuted, using in most cases the explanations given by Nicholas of Cusa. 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:
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. It is believable that this affect is present in the sun, moon, and the other bright planets and that through its efficacy they remain in a spherical figure in which they are visible, though they nevertheless follow their circular motions in many different ways.
One of the advances made by Copernicus deals with 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 sits enthroned at the center 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 wherefrom 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.
Copernicus refers to what he calls “the three motions” of the earth. These 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.
Copernicus goes on to give 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. This is the data to which he would apply his mathematical theory, which was much the same as that of Ptolemy, but with the sun at the center rather than the earth, which thus becomes one of the planets.
Copernicus then turned his attention to 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. As a result, his explanation of precession is flawed.
Another problem that Copernicus faced was the irregularity in the sun’s motion as observed from the earth. This is due to the fact that the center of the orbit does not coincide with the center of the sun and that the velocity of the sun in its apparent orbit around the earth is variable. He solved the problem by using a combination of an eccentric circle and an epicycle, in this way avoiding the use of an equant, his principal objection to Ptolemy’s mathematical method.
Next Copernicus dealt with the irregularity in the motion of the moon around the earth. Here he solved the problem by using an eccentric circle along with an epicycle together with a second, smaller epicyclet carrying the moon, similar to the model that had been used by the Arabic astronomer ibn al-Shatir, which Copernicus may have seen when he was studying at the University of Cracow.
He then went on to study the motions of the planets. Here again 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 sizes of the planetary orbits to be determined from observation without any additional assumptions.
Historian Angus Armitage noted that the great contribution that Copernicus made to astronomy was not just the notion that the sun was the center of the cosmos, but “lay rather in his development of those ideas into a systematic theory, capable of furnishing tables of an accuracy not before attained, and embodying a principal the adoption of which was to make possible the triumphs of Kepler and Newton in the following century.”
The sizes of the planetary orbits were determined relative to the mean radius of the earth’s orbit, known today as an astronomical unit (a.u.), where for each planet he computed the greatest, mean, and least values. The distance from the sun of either Mercury and Venus, the inner planets, was determined from its maximum elongation from the sun, that is, the largest angle it makes with the sun as seen from the earth. In the case of Venus the maximum elongation is 48°, from which Copernicus computed that its mean distance from the sun was 0.719 a.u., which is in remarkably good agreement with the modern value of 0.723 a.u. He used the same method for Mercury, where the maximum elongation is 22°, determining that its mean distance from the sun was 0.376 a.u., as compared to the modern value of 0.387 a.u., the larger discrepancy being due to the greater difficulty in observing Mercury because it is so close to the sun.
Copernicus determined the orbital radii of the outer planets using slightly different geometrical procedures. The values that he found for the mean values, in astronomical units, were very close to the modern values, an extraordinary accomplishment considering the primitive instruments he was using.
The next task was to convert these relative distances to absolute values. Using the methods of Aristarchus, Ptolemy, and al-Battani, along with his own innovations, Copernicus found that the sun’s mean distance was 1,142 earth radii (e.r.), as compared to Ptolemy’s value of 1,179 e.r. He could then have converted the known radius of the earth into miles, but he chose not to do so, for he felt that his new planetary model was so complete and self-consistent that such tasks could be left to his followers. In his dedicatory preface to Pope Paul III he stressed the internal consistency of his theory.
And so, having laid down the movements which I attribute to the Earth farther on in the work, I finally discovered by the help of long and numerous observations that if the movements of the other wandering stars are correlated with the circular movement of the Earth, and if the movements are computed in accordance with the revolution of each planet, not only do all their phenomena follow from that but also this correlation binds together the order and magnitude of all the planets and of their spheres or orbital circles and the heavens themselves that nothing can be shifted around in any part of them without disrupting the remaining parts and the universe as a whole.
Copernicus mentions some of the Arabic astronomers whose observations and theories he used in De revolutionibus, namely al-Battani, al-Bitruji, al-Zarqali, ibn Rushd (Averroës), and Thabit ibn-Qurra. He does not refer to ibn al-Shatir, though in his lunar theory he used a model similar to one that his predecessor had developed. Neither does he cite the thirteenth-century Arabic astronomer Nasir al-Din al-Tusi, although recent research shows that Copernicus used a mathematical method that had been invented by him. This is the so-called al-Tusi couple, which Copernicus also used in his lunar theory. There is no definite evidence that Copernicus knew of al-Tusi’s theory, which was apparently known to some of his contemporaries.
Copernicus referred to Aristarchus of Samos six times in the original manuscript of De revolutionibus, but four of these were erroneous and a fifth was probably incorrect. The only correct reference was near the end of book 1, where Copernicus wrote:
Though the courses of the Sun and the Moon can surely be demonstrated on the assumption that the Earth does not move, it does not work so well with the other planets. Probably for this and other reasons, Philolaus perceived the mobility of the Earth, a view also shared by Aristarchus of Samos, so some say, not impressed by that reasoning which Aristotle cites and refutes. Yet, since only keen wits and long efforts can probe such things, it was then hidden from most philosophers, and, as Plato said, only a few grasped the real cause of planetary motion.
But in the final editing of the manuscript this passage was removed and, instead, another passage was rewritten into the preface to Pope Paul III, in which Copernicus mentions Greek astronomers who had the earth in motion, though omitting Aristarchus. The new passage reads:
Some think that the Earth is at rest; but Philolaus the Pythagorean says that it moves around the fire, with an obliquely circular motion, like the sun and moon. Herakleides of Pontus and Ekphantus the Pythagorean do not give the earth any movement of locomotion, but rather a limited movement of rising and setting around its center like a wheel.
Copernicus cited Plutarch as the reference for this passage, but the source is actually from a work by Aetius (Pseudo-Plutarch) entitled Placita philosophorum. Copernicus is known to have possessed a copy of George Valla’s Outline of Knowledge, printed by Aldus Manutius in Venice in 1501, which included the Placita. The Placita contained two other references concerning the motion of the earth, neither of which was used by Copernicus. 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.”
Very little was known in western Europe of the heliocentric theory of Aristarchus until the publication of Archimedes’ Sand Reckoner in 1544, the year after Copernicus died. According to astronomer Owen Gingerich: “Had Copernicus known more [about Aristarchus’ heliocentric theory] he surely would have been happy to mention it, since he needed all the support he could muster for his own unorthodox views, and since he quotes with enthusiasm other possible geokineticists from Antiquity with less reputable credentials.”
Gingerich went on to say: “There is no question but that Aristarchus had the priority of the heliocentric idea. Yet there is no evidence that Copernicus owed him anything. As far as we can tell, both the idea and its justification were found independently by Copernicus.”
There is no question in my own mind that Copernicus conceived his sun-centered cosmology on his own, and that had he known more about Aristarchus he certainly would have given him credit. So far as I am concerned, Gingerich says the last word on the question of who should get credit for the heliocentric theory:
It is not really the task of the historian of science to assess the comparative originality of these two scientific giants. The heliocentric cosmology was convincing neither to the contemporaries of Aristarchus nor to those of Copernicus, but Copernicus had the good luck to be born not only at a time when science was beginning to reach, so to speak, a critical mass, but also at a time when scientific works were beginning to be printed; therefore his arguments survived and convinced a later generation of astronomers.
Astronomy and cosmology would never again be the same after the publication of De revolutionibus. The world picture was now irrevocably changed, an intellectual revolution started by an obscure canon, reviving a theory that had first been proposed eighteen centuries before by an almost forgotten Greek astronomer.
But Copernicus would not be forgotten because the revolution that he started made him immortal. He was certainly my hero when I first began reading books on astronomy in my youth. My admiration was and still is not just for his scientific achievement but for his persistent courage in working away on his revolutionary theory in his “remote corner of the earth,” his life’s work rescued from oblivion in the last years of his life by an idealistic young mathematician who saw to the printing of De revolutionibus, planting the seed that would blossom in the new astronomy and physics of the following century.
Copernicus never taught at a university, and so he never had a pupil in the formal sense, but Rheticus was in effect his student when they worked together on the final version of De revolutionibus, and he is so listed in the Math-Physics Genealogy website. And it is through this tenuous link that I and my students and their students trace our scientific ancestry back to Copernicus through Galileo and Newton.