In July 1595, a 23-year-old **Johannes Kepler** was demonstrating how conjunctions of Jupiter and Saturn moved through different constellations of the zodiac when the illustration he had drawn for his audience suddenly hit him with a force he described as akin to divine revelation. The triangular progression of these planets’ alignments over time would gradually sketch out a circular figure that resembled a planetary orbit on its inside. What if this and other similarly inscribed shapes were the ultimate reason behind the order and spacing of all the celestial spheres in the heavens?

Kepler transformed this initial two-dimensional idea into three-dimensional geometry and then published it in his *Mysterium Cosmographicum* – roughly translated, the “Secret of the Cosmos” – one of the most unusual works in the history of early modern astronomy. It was the first really spirited and systematic defense of Nicholas Copernicus’s heliocentric theory to be printed since the publication of Copernicus’s own book 50 years earlier, but today it is best remembered for the beauty and haunting strangeness of Kepler’s geometrical representation of the entire cosmos, shown below.

The solid figures nested inside circles represent the five ideal Platonic solids, which Kepler thought corresponded to the exact amount of space between each celestial sphere bearing the Earth and other planets. With five gaps to account for between six planets, this arrangement explained why there were exactly six planets and no more, as well as why these planets were positioned at their respective distances. In addition, because this system worked only under the heliocentric rather than geocentric system, Kepler argued it was further proof that Copernicus’s theory must be true.

To modern eyes, Kepler’s vision of a perfectly Platonic heliocentric cosmos may suggest mysticism or even wishful thinking. Yet even this somewhat fanciful geometric model encapsulated a critical central insight in its insistence that a truly successful model of the cosmos must account for the entire three-dimensional space of the heavens, rather than just the linear order of the celestial spheres. Consider by comparison the illustration of the heavens that had appeared in Copernicus’s book of 1543:

In this image, each sphere representing one of the planets simply envelops the sphere inside it in an even progression of circles from the Sun to the distant stars. Despite this apparent simplicity, the details of the heliocentric system – buried deep inside Copernicus’s mathematics but made more explicit in Kepler’s work – were much more complicated.

Under the old geocentric cosmology, the order of planets in the heavens was based largely on conventions related to their speed of movement. Nothing in the calculations that predicted where individual planets would appear in the night sky implied a necessary sequence for their celestial spheres, and indeed ancient writers sometimes disagreed on their arrangement, particularly in regard to the locations of Venus and Mercury.

Copernicus, however, took what had once been a purely algorithmic calculation of each planet’s position relative to the Sun’s direction and turned it into a physical location relative to the center of the cosmos. In doing so, he locked each of the planets into orbits at specific relative distances from the Sun, creating for the first time a truly interconnected model of the cosmos under which nothing could be moved without upsetting all the other parts, as Copernicus described it in his preface to Pope Paul III.

This vision of a unified and interconnected cosmos was one of the things that most attracted Kepler to the heliocentric theory, but it also produced highly uneven spacing between the different planets. Even if no one from this era could yet measure the exact distances, the heliocentric theory clearly indicated that inner planets should be clustered much more closely together than the large gaps between the orbits of Mars, Jupiter, and Saturn. In a well-ordered universe, what possible reason could there be for the existence of such wide empty spaces?

By highlighting this problem, Kepler’s *Mysterium Cosmographicum* emphasized that the “new astronomy” (as he would title his most influential later work) would only be more accurate than its predecessors if it went beyond algorithms and rearranging circles and instead tried to fully explain both the celestial bodies and the spaces between them. His first attempt to match these spaces to the geometry of Platonic solids may seem a bit quaint in retrospect, although Kepler never gave up on this idea and indeed published a second edition of the *Mysterium Cosmographicum* 25 years later. Nevertheless, his ability to imagine celestial bodies from different points in the cosmos – note for example the perspective cones in the illustration above – ultimately led him to focus on how a force emanating from the sun would dissipate in law-like fashion as it moved farther and farther outward from the center.

From this last insight, it was a relatively straightforward intellectual leap to Kepler’s famous three laws of planetary motion, which described the behavior of this force, established ellipses rather than circles as the ideal form of planetary movements, and ultimately laid the foundations for Isaac Newton’s theory of gravity. In this manner, an empirically inaccurate but aesthetically beautiful example of three-dimensional thinking was a key stepping stone toward our modern understanding of the cosmos.

## Further reading

J.V. Field, *Kepler’s Geometrical Cosmology* (Chicago: University of Chicago Press, 1988).

Jaroslav Folta, ed., *Mysterium Cosmographicum 1596-1996* (Prague Studies in the History of Science and Technology, vol. 2, 1998).

Johannes Kepler, *Mysterium Cosmographicum – The Secret of the Universe*, translated by A.N. Duncan with an introduction and commentary by E.J. Aiton (New York: Abaris Books, 1981).

Fully digitised copy from ETH-Bibliothek Zürich available **here**.