Reading Johannes Kepler's Mysterium Cosmographicum
Johannes Kepler’s first major work is called Mysterium cosmographicum [The Secret of the Universe1]. Two editions were published, the first in 1596, and the second in 1621, after he had derived his most important results.
The English translation follows the second edition, and it is a fascinating read, because we get to read the 1596 text, along with the notes that Kepler added in 1621, which refer to major results, thoughts or amendments made over that period of 25 years, published in the following major astronomical works:
Astronomiae pars optica [The Optical Part of Astronomy] (1604)
De stella nova [Of the New Star] (1606)
Astronomia nova [New Astronomy] (1609)
Harmonices mundi [Harmony of the World] (1618)
Epitome astronomiae Copernicae [Epitome of Copernican astronomy] (1618, 1620, 1621)
As I wrote in the post Kepler's First Steps Towards a Theory of Gravity, Kepler’s first two laws are first presented in the Astronomia nova, while the third law is first presented in the Harmonices mundi.
In Kepler’s time, only six planets were known; Uranus would only be discovered in 1781 and Neptune in 1846. The Mysterium cosmographicum is best known for the proposal that the spheres of the six planets of the solar system are separated by the five Platonic solids. Hence Kepler proposed the following structure, from outside in:
sphere of Saturn
cube
sphere of Jupiter
tetrahedron
sphere of Mars
dodecahedron
sphere of Earth
icosahedron
sphere of Venus
octahedron
sphere of Mercury
the sun at the center.
Kepler’s idea was that each Platonic solid defines a circumscribed sphere and an inscribed sphere, and that the radii of these spheres correspond to the midpoints of the eccentricities of the planets. He then compares these radii with the data available in Copernicus’s De revolutionibus.
It should be noted that notwithstanding his highly original a priori thinking, he only considered it to be of value if it was supported by the empirical data:
So far all that has been said is that certain signs agree with the theorem and make it probable. Let us now pass to the distances between the astronomical spheres and the geometrical derivations: if they do not agree, the whole of the preceding work has undoubtedly been a delusion. [p.149]
The fit is surprisingly good, although by no means perfect. Kepler examines in detail the differences, and discusses the quality of data used by Copernicus, some of which comes from Ptolemy’s Almagest, some from the Alfonsine tables. Still he concludes:
Indeed the human failings of Copernicus himself in accepting any sort of figures which suit him up to a point and help his case will be found out by the careful reader of Copernicus. He does not repudiate values which though derived in different ways ought according to a theoretical proof to have agreed exactly, even though they differ by a few minutes…. To overcome them, and unhampered to aspire to the establishment of knowledge with the least possible detriment, as Copernicus dared to do, is the part of a brave man. It is for a lazy man to shirk it, for a coward to give up hope and to reject all this trouble. Hence even Copernicus himself neither tries to hide his own failings, which have just been recounted, nor shows shame in admitting them. He arms himself with the example of Ptolemy and the ancients; he excuses himself by the difficulty of observing; and everywhere he sets a precedent for others of scorning these petty little shortcomings in the process of establishing splendid discoveries. If that had not been done previously, Ptolemy would never have brought forth for us his Almagest, Copernicus his books On the Revolutions, Rheingold his Prutenic Tables. [pp.181,183]
Of course, the entire edifice was based on the idea that there are exactly six planets in the solar system, not the eight planets and myriad dwarf planets, moons, asteroids and comets we know of today. In addition, there is a chapter on astrology and another one on numerology. Furthermore, Kepler was working from a teleological perspective, assuming that the entire universe was created for humanity, either 5557 or 5572 years before 1595, with all the planets initially lined up in Aries. So one might be tempted to simply dismiss the work.
However, perhaps we should consider that there is really no fundamental difference in supposing that the universe was created some six millennia ago, or that it began some 13.8 billion years ago in a Big Bang, and that we can calculate what happened in the first fractions of a second after that moment. Yet, that is what we are repeatedly told today.
Furthermore, in the Mysterium cosmographicum, Kepler did not just write about the static geometry of the spheres in the solar system, but also the motions of the planets. He explains in his notes in the second edition that by trying to reconcile the static and dynamic natures of the solar system, and by working with better quality data, once he had access to the observations conducted under Tycho Brahe, he was ultimately capable of deriving his laws of motion of the planets, and, most importantly, his harmonic law, what we call today his third law.
In future posts, I will be writing about the development of these laws, by examining the Astronomia nova and the Harmonices mundi.
Johannes Kepler. Mysterium Cosmographicum: The Secret of the Universe. Translation by A.M. Duncan. Introduction and Commentary by E.J. Aiton. With a Preface by I. Bernard Cohen. New York: Abaris, 1981.