Mysterium Cosmographicum

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Mysterium Cosmographicum, (lit The Cosmographic Mystery, alternately translated Cosmic Mystery, The Secret of the World or some variation) is an astronomy book by the German astronomer Johannes Kepler, published at Tübingen in 1596 and in a second edition in 1621. The full title being Forerunner of the Cosmological Essays, Which Contains the Secret of the Universe; on the Marvelous Proportion of the Celestial Spheres, and on the True and Particular Causes of the Number, Magnitude, and Periodic Motions of the Heavens; Established by Means of the Five Regular Geometric Solids (Latin: Prodromus dissertationum cosmographicarum, continens mysterium cosmographicum, de admirabili proportione orbium coelestium, de que causis coelorum numeri, magnitudinis, motuumque periodicorum genuinis & proprijs, demonstratum, per quinque regularia corpora geometrica). Kepler proposed that the distance relationships between the six planets known at that time could be understood in terms of the five Platonic solids, enclosed within a sphere that represented the orbit of Saturn. This book explains Kepler's cosmological theory, based on the Copernican system, in which the five Pythagorean regular polyhedra dictate the structure of the universe and reflect God's plan through geometry.This was the first attempt since Copernicus to say that the theory of Heliocentrism is physically true.[1] According to Kepler's account from this text, the ratio was brought to his attention accidentally while demonstrating the calculation of the ratio between a circle and a circle created by a rotated inscribed circle. From this he realized that he had stumbled on the same ratio between the orbits of Saturn and Jupiter. He wrote, “By a certain mere accident I chanced to come closer to the actual state of affairs. I thought it was by divine intervention that I gained fortuitously what I was never able to obtain by any amount of toil.” But after doing further calculations he realized he could not use the two-dimensional polygons to represent all the planets, but instead he had to use the five Platonic solids.

Detailed view of the inner sphere

Shapes and the planets[edit]

Kepler's Platonic solid model of the Solar system from Mysterium Cosmographicum (1600)


Theological and philosophical foundation[edit]




Epistemology and philosophy of sciences[edit]

Many of Kepler's thoughts about epistemology can be found in his Defense of Tycho against Ursus or Contra Ursum (CU), a work which emerged from a polemical framework, the plagiarism conflict between Nicolaus Raimarus Ursus (1551–1600) and Tycho Brahe: causality and physicalization of astronomical theories, the concept and status of astronomical hypotheses, the polemic “realism-instrumentalism”, his criticism of skepticism in general, the epistemological role of history, etc. Jardine has pointed out that it would be sounder to read Kepler's CU more as a work against skepticism than in the context of the modern realism/instrumentalism debate.[citation needed]



In terms of the impact of Mysterium, it can be seen as an important first step in modernizing the theory proposed by Nicolaus Copernicus in his "De Revolutionibus". Whilst Copernicus sought to advance a helio-centric system in this book, he resorted to Ptolemaic devices (viz., epicycles and eccentric circles) in order to explain the change in planets' orbital speed, and also continued to use as a point of reference the center of the earth's orbit rather than that of the sun "as an aid to calculation and in order not to confuse the reader by diverging too much from Ptolemy." Kepler regarded Copernicus' arguments as being merely a posteriori and set out to provide the a priori demonstrations of the astronomical phenomena.[6] Modern astronomy owes much to "Mysterium Cosmographicum", despite flaws in its main thesis, "since it represents the first step in cleansing the Copernican system of the remnants of the Ptolemaic theory still clinging to it." [7] Especially when dealing with the geometry of the universe, Kepler consistently utilizes Platonic and Neo-Platonic frameworks of thought. The entirety of the polyhedral idea is based on the same "formal cause" postulated by Plato for the structure of the universe. In addition, an "efficient cause" is need to answer the underlying reason for the structure. In an argument from design, Kepler postulates the existence and necessity of God the Creator as this "efficient cause."[8]


In response to Mysterium Cosmographicum, the Danish astronomer Tycho Brahe said the ideas were intriguing but could only be verified through the observations Brahe himself had been making the past 30 years. Because he was promised use of these observations by Brahe, Kepler he sought him out in the beginning of 1600. However, Brahe, however, only gave him the data on Mars.[9]

In popular culture[edit]

The Mysterium Cosmographicum was featured on the Austrian 10 euro Johannes Kepler silver commemorative coin minted in 2002.[10]


  • George W. Hart, "Johannes Kepler's polyhedra"
  • Johannes Kepler
  • Caspar. Kepler, pp. 65–71.
  • Field. Kepler's Geometrical Cosmology, Chapter IV, p 73ff.
  • Dreyer, J. L. E., A History of Astronomy from Thales to Kepler, Dover Publications, 1953, pp. 331, 377–379.
  1. ^ James R. Voekel. "Classics of Astronomy by Johannes Kepler". 2010.
  4. ^ Caspar. Kepler, pp. 65–71.
  5. ^ Field. Kepler's Geometrical Cosmology, Chapter IV, p 73ff.
  6. ^ Barker and Goldstein, “Theological Foundations of Kepler’s Astronomy”
  8. ^ "Johannes Kepler". Stanford Encyclopedia of Philosophy. May 2, 2011.
  9. ^ James R. Voekel. Classics of Astronomy by Johannes Kepler. 2010.
  10. ^, 10 euro: Eggenberg Palace.

External links[edit]