Mysterium Cosmographicum (lit. The Cosmographic Mystery, alternately translated as Cosmic Mystery, The Secret of the World, or some variation) is an astronomy book by the German astronomer Johannes Kepler, published at Tübingen in late 1596 and in a second edition in 1621. 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 Platonic solids dictate the structure of the universe and reflect God's plan through geometry. This was virtually the first attempt since Copernicus to say that the theory of heliocentrism is physically true. Thomas Digges had published a defense of Copernicus in an appendix in 1576. According to Kepler's account, he discovered the basis of the model while demonstrating the geometrical relationship between two circles. From this he realized that he had stumbled on a similar ratio to the one between the orbits of Saturn and Jupiter. He wrote, "I believe it was by divine ordinance that I obtained by chance that which previously I could not reach by any pains." But after doing further calculations he realized he could not use two-dimensional polygons to represent all the planets, and instead had to use the five Platonic solids.
Shapes and the planets
Johannes Kepler's first major astronomical work, Mysterium Cosmographicum (The Cosmographic Mystery), was the second published defence of the Copernican system. Kepler claimed to have had an epiphany on July 19, 1595, while teaching in Graz, demonstrating the periodic conjunction of Saturn and Jupiter in the zodiac: he realized that regular polygons bound one inscribed and one circumscribed circle at definite ratios, which, he reasoned, might be the geometrical basis of the universe. After failing to find a unique arrangement of polygons that fit known astronomical observations (even with extra planets added to the system), Kepler began experimenting with 3-dimensional polyhedra. He found that each of the five Platonic solids could be uniquely inscribed and circumscribed by spherical orbs; nesting these solids, each encased in a sphere, within one another would produce six layers, corresponding to the six known planets—Mercury, Venus, Earth, Mars, Jupiter, and Saturn. By ordering the solids correctly—octahedron, icosahedron, dodecahedron, tetrahedron, and cube—Kepler found that the spheres correspond to the relative sizes of each planet's path around the Sun, generally varying from astronomical observations by less than 10%. He attributed most of the variances to inaccuracies in measurement.
Kepler also found a formula relating the size of each planet's orbit to the length of its orbital period: from inner to outer planets, the ratio of increase in orbital period is twice the difference in orb radius. However, Kepler later rejected this formula because it was not precise enough.
Theological and philosophical foundation
As he indicated in the title, Kepler thought he had revealed God’s geometrical plan for the universe. Much of Kepler's enthusiasm for the Copernican system stemmed from his theological convictions about the connection between the physical and the spiritual; the universe itself was an image of God, with the Sun corresponding to the Father, the stellar sphere to the Son, and the intervening space between to the Holy Spirit. His first manuscript of Mysterium contained an extensive chapter reconciling heliocentrism with biblical passages that seemed to support geocentrism.
With the support of his mentor Michael Maestlin, Kepler received permission from the Tübingen university senate to publish his manuscript, pending removal of the Bible exegesis and the addition of a simpler, more understandable description of the Copernican system (the Narratio prima by Rheticus) as an appendix. Mysterium was published late in 1596, and Kepler received his copies and began sending them to prominent astronomers and patrons early in 1597; it was not widely read, but it established Kepler's reputation as a highly skilled astronomer. The effusive dedication, to powerful patrons as well as to the men who controlled his position in Graz, also provided a crucial doorway into the patronage system.