Copernicus and Kepler: Towards a Heliocentric Theory
This paper will compare and contrast the approaches that Copernicus and Kepler took toward establishing the heliocentric theory and the mobility of the earth. Attention will be given to their evaluation of ancient and current astronomical thought.
Copernicus took pains to read everything he could find from the ancient Greek and Roman astronomers and philosophers. He was well read in Aristotle, the Pythagoreans, Ptolemy and the Scholastics. In 1474, Regiomontanus (1436 – 1376), the first astronomer-printer, published an advanced list of important works soon to come from his press in Nuremberg – among them, many mathematical and astronomical works, with which Copernicus was surely familiar.1 Regiomontanus’ own Epitome of the Almagest (printed in 1496) was used by Copernicus in his studies. However, the confusion of the competing astronomical theories of his day led Copernicus to think that there must be an alternative explanation. As Copernicus himself confesses to Pope Paul III in the preface to De Revolutionibus,
“For a long time, then, I reflected on this confusion in the astronomical traditions…I began to be annoyed…For this reason I undertook the task of rereading the works of all the philosophers which I could obtain to learn whether anyone had ever proposed other motions of the universe’s spheres than those expounded by the teachers of astronomy in the schools.”2
His “rereading” did not disappoint him. He found that in one of Cicero’s works a certain Hicetas had believed the earth moved. Later on he discovered that Plutarch mentioned at least three Pythagoreans who believed the same: Philolaus, Ecphantus and Heraclides of Pontus. In addition, during his time there were some novel ideas circulating about the nature of the universe. For example, Nicholas of Cusa (c. 1401 – 1464) had proposed an infinite and centerless universe 100 years before the publication of De Revolutionibus. Nicole Oresme (c. 1323 – 1392) theorized, but ultimately rejected, the possibility that the earth rotated on its axis in a commentary on Aristotle’s in his non-published tract entitled, Traité du ciel et du monde, written in 1377 at the request of King Charles V. Such views were the grand exceptions, however, and the accepted and majority view held that Ptolemy had gotten it right, with only some corrections needed to his theory. Copernicus came at the problem from this point of view.
Rheticus in his Narratio Prima relates to us Copernicus’ thinking in rejecting the main features of the Ptolemaic system.3 Firstly, the indisputable precession of the equinoxes and the change in the obliquity of the ecliptic was most satisfactorily explained by the motion of the earth. Secondly, the diminution of the eccentricity of the sun is explained more readily by the same reason. Thirdly, the planets have the centers of their deferents in the sun, as the center of the universe, and not the earth as the center of the universe. This is so because of the observed motion of Mars. Mars sometimes shows a parallax greater than the sun’s, an observation inconsistent with the earth at the center of the universe. Fourthly, to preserve the principle of uniform circular motion, only with the sun at the center could all the circles in the universe be made to revolve uniformly about their own centers and not about other centers (epicycles). Fifthly, the simple motion of the earth satisfies an innumerable number of appearances, and this is consistent with the principle of simplicity where one cause can satisfy the many. Sixthly, and lastly, Rheticus says that we should regard the rule that “the order and motions of the heavenly spheres agree in an absolute system.” This, according to Copernicus, is true only when the sun is placed in its rightful place in the center of the universe.
In spite of the novelty of Copernicus’ new vision, he still retained many features of the old Ptolemaic system. Indeed, it is Kuhn’s judgment that Copernicus’ De Revolutionibus
“…is a relatively staid, sober and unrevolutionary work. Most of the essential elements by which we know the Copernican Revolution – easy and accurate computations of planetary position, the abolition of epicycles and eccentrics, the dissolution of the spheres, the sun a star, the infinite expansion of the universe – these and many others are not to be found anywhere in Copernicus’ work.”4
bold on Copernicus’ part was his notion of putting the sun in the center of the universe with our earth and the rest of the planets revolving around it. It is true as Kuhn and others have pointed out that he did retain some key Ptolemaic ideas such as epicycles and uniform circular motion. However, I think that on balance, given the conventional wisdom supporting the Ptolemaic theory and the culture of a tradition-driven Church not fond of novelty, his heliocentric and mobile earth ideas were certainly innovative and bold when evaluated in his own setting.
Cohen concludes that Copernicus’ significance
“…lay not so much in the system he propounded as in the fact that the system he did propound would ignite the great revolution in physics that we associate with the names of Galileo, Johannes Kepler and Isaac Newton.”5
We must start by noting that Kepler was an early convert to the Copernican theory and remained an unabashed Copernican throughout his life. His teacher and mentor, Michael Maestlin, favorably reviewed Copernicus in his lectures at the University of Tubingen, where Kepler attended, beginning in 1589.
Kepler’s major works, Mysterium Cosmographicum (1596), Astronomia Nova (1609) and Harmonices Mundi (1619) display an interesting curiosity in numbers and geometrical and mathematical relationships. Why are there only 6 planets and no more or less? Why are the distances between the planets as they are and not another? Kepler even once penned an essay on why the snowflake had six sides and not five or seven.6 He went to great lengths in explaining various geometrical reasons for its appearance. This same curiosity drove his astronomical thinking.
In Mysterium Cosmographicum Kepler presented the first published defense of the Copernican system and posited that Euclid’s five platonic solids serve to explain the distance relationships among the six planets. Kepler has the same issue as Copernicus regarding the Ptolemaic theory: it simply does not account for a number of observed phenomena.
“I reply first that the old hypotheses simply do not account at all for a number of outstanding features. For instance, they do not give the reasons for the number, extent, and time of the retrogressions, and why they agree precisely, as they do, with the positions and mean motion of the Sun.”7
And so in the same way Kepler accepts the presumption that nature should be explained by simpler explanations, not more difficult ones.
“…these hypotheses of Copernicus not only do not offend against the Nature of things, but do much more to assist her. She loves simplicity, she loves unity. Nothing ever exists in her which is useless or superfluous, but more often she uses one cause for many effects…And although all these motions, eleven in number, are banished from the universe by the substitution of this single motion of the Earth, nevertheless reasons are supplied for a great many other matters for which Ptolemy for all his many motions could give no reason.”8
Kepler also makes an argument from common sense regarding the speed of the supposed revolutions of the bodies in the universe (an argument Copernicus also used). He explains that it is easier to suppose that the earth rotates in one direction in a twenty-four-hour period than to believe that the rest of the universe move at incredible speed about the motionless earth.
“Consequently there disappears that incredibly lofty and swift tenth and starless sphere, the swiftness of which and of the whole universe would be so great according to Ptolemy that it would traverse several thousand miles in the blinking of an eye…finally decide whether it is easier for it to happen and to be believed that that small point within the little circle A, and hence the Earth, rotate in one direction, or that the complete universe goes with ten distinct motions (as there are ten mutually independent circles) with inconceivable rapidity, and is subject to nothing but that small point, which along is motionless, because there is nothing outside.” 9
Here we have two thinkers, pushing forward our understanding of our place in the universe. Copernicus provided the sun-centered, mobile earth and Kepler agrees, adding the elliptical paths for planetary orbits. Once this new paradigm was in place, it needed an answer to the question: How to the planets move? On their own or from another source? A new physics was born from these questions.
Although Kepler, which Gilbert’s assistance, moved toward the notion of action at a distance, it was not until Newton that the answer was finally explained. Nonetheless, both Copernicus and Kepler were able to establish the heliocentric theory and mobility of the earth, with both observational and mathematical evidence. By questioning the reasoning of the ancients and working from fresh perspectives, which so many were unable or unwilling to try, a revolution was in the making, thanks to them both.
1 Elizabeth L. Eisenstein, The Printing Revolution in Early Modern Europe, Cambridge University Press, Cambridge, 1993, p.210.
2 Nicholas Copernicus, On the Revolution of the Heavenly Spheres, translated by Charles Glenn Wallis, Prometheus Books, Amherst, NY, 1995, Preface.
3 Joachim Rheticus, Narratio Prima, as found in Edward Rosen, Three Copernican Treatises, 2nd edition, Dover Publications, Mineola, NY, 1959, p.131.
4 Thomas S. Kuhn, The Copernican Revolution, Random House, New York, 1959, p. 135.
5 I. Bernard Cohen, The Birth of a New Physics, W.W. Norton & Company, New York, 1985, p.52.
6 Johannes Kepler, The Six Cornered Snowflake, translated by Colin Hardie, Oxford University Press, Oxford, 1996.
7 Johannes Kepler, Mysterium Cosmographicum, translated by A. M. Duncan, Abaris Books, New York, 1981.