Michael Maestlin's Mystery: Theory Building with Diagrams

Abstract

BEGINNINGS, QUESTIONS AND APPENDICESIn his 1973 article, Anthony Grafton described the intensive collaborative work undertaken between Johannes Kepler and his former university professor, Michael Maestlin, during the writing of Kepler's Mysterium cosmographicum. Kepler had left the University of Tubingen, Germany, to work as a mathematics teacher in Graz, Austria, where he had immediately begun to conduct his first independent research in astronomy. The book took the form of a collection of works by contributors: besides Kepler's main contribution, it contains the Narrano prima of Rheticus, which consisted of a comprehensive representation of the doctrine of Nicolaus Copernicus, with corrections and additions, followed by an appendix by Maestlin in which the latter presented an advanced version of Copernican planetary theory, the improved parameters of which he had reconstructed from Erasmus Reinhold's Prutenic tables. Grafton writes:For in the Mysterium Kepler began the work which led to his discovery of the true nature of planetary motion; it was there that he first posed the questions to which his three laws were the answers. Yet no one seems to have discussed the treatise which Kepler's teacher, Michael Maestlin, added to the Mysterium when he edited his student's work for publication - namely, Maestlin's appendix On the Dimensions of the Heavenly Circles and Spheres, according to the Prutenic Tables, after the theory of Nicolaus Copernicus.1Clearly, praise is due to Kepler as the author of the Mysterium, but were Maestlin's contributions confined to the appendix, leaving it ambiguous to what extent Maestlin 'edited' Kepler's text? Kepler was able to answer his own questions only in his later works, Astronomia nova and Harmonics. And were the research questions, whose pursuit led later to the so-called 'Kepler's laws', perhaps answered differently in the Mysterium!The intense exchange of letters between Kepler and Maestlin in fact tells us more about Kepler's ignorance of astronomy than of his knowledge, and highlights the indispensable role that Maestlin played in Kepler's research. Maestlin is more than just the author of an appendix: he was responsible for working out the underlying astronomical theory of Kepler's first major work. Maestlin can, therefore, be rightly regarded as the co-author of the Mysterium, a fact that Kepler himself acknowledged in one of his letters to his former teacher.DIMENSIONS OF THE COSMOSThe fact that the Copernican Revolution changed the astronomical and physical conception of the world in many different ways is often overlooked. Displacing the Earth from the centre of the universe was only a minor change; it involved no more than a small geometrical reconfiguration, the consequences of which had been discussed in Antiquity. The consequences, of course, were crucial. Of dynamical importance is the fact that, from a geometrical viewpoint, the Earth rotates around its own axis every 24 hours. Kepler, as well as Maestlin, indicated that this alternative theory of a daily rotating celestial sphere implied that the rotating bodies would have far greater velocities. Grave difficulties then arose when it came to laying the foundations of classical mechanics, which had to describe and explain the movement of heavy bodies on the Earth's rotating surface under the influence of the Earth's heaviness. Copernicus recognized these consequences in De revolutionibus orbium coelestium (1543); however, he stressed that it was up to future researchers to deal with them. Neither Kepler nor Maestlin addressed these issues as such in the Mysterium; they examined the consequences, which were astronomically far more radical.The idea - that one can obtain much more empirical data on the positions of the planets on their way around the Sun from the movement of the Earth and from observers on the Earth - was clear to all mathematical astronomers of the time. It was impossible to deduce the sizes of the planetary orbits on the basis of empirical astronomical observations using the Ptolemaic view of the world, as the projected positions of the planets moving around the Earth (with an observer at the centre of the universe) were independent of the presumed distances of the planets from the Earth. …