Guided Pathway

Model of the Solar System from Kepler’s Mysterium, A Modern Diagram after Kepler, the Solar System from Brockhaus 1908

The sequence 1, 2 & 3 illustrates what for Warburg was the historic watershed in the human being’s relation to the cosmos: Johannes Kepler’s discovery of the elliptical orbit of Mars. With this discovery Kepler (1571−1630) was able to disprove the principle that a recurrent movement must be circular. In 1924 Warburg had recognized Kepler’s discovery – published in the Astronomia nova (with the subtitle De motibus stellae Martis) of 1609 – as the decisive breakthrough to modern astronomy and modern science in general. He illustrates its impact on the history of astronomy by a contemporary diagram of the solar system (# 3). The diagram was detached from page 55 of volume 15 of Warburg’s personal copy of Brockhaus’ Konversations-Lexikon (14th edition, Leipzig 1908). By accepting the heliocentric system – plausibly explained in his De revolutionibus orbium coelestium libri VI of 1543 by Nicolaus Copernicus (1473−1543) – and analyzing the mathematical charts which the older Danish astronomer Tycho Brahe (1546−1601) had compiled through new observation techniques, Kepler had noticed the divergence of Mars’s orbit from the ideal figure of the circle. Through painstaking calculations he came to the conclusion that its orbit was indeed elliptical. The results of these calculations are known as Kepler’s First Planetary Law. The revolutionary aspect of Kepler’s work, however, was not just the discovery of the real movement of the planets, buts also its description in geometrical-mathematical terms.

Warburg’s sequence begins with Kepler’s earliest model of the solar system (# 1), published as the frontispiece to the Mysterium Cosmographicum whose first edition came out in 1596 and the second, used here, in 1621. The model depicts a heliocentric system in which the distances between the six known planets that circulate around the sun are understood in terms of the five Platonic solids or of the Pythagorean regular polyhedra; according to Plato these solids are in permanent movement and can change their shape through collision. The enclosing sphere represents the orbit of Saturn. The model was the result of Kepler’s attempt to investigate the divine plan behind the creation of the cosmos. For Warburg this was proof that the belief in the harmonic structure of the universe, based on numerical ratios which determine concordant intervals, persisted up to Kepler’s time. Although the three-dimensional model was a constitutive precursor for the correct representation of the solar system, only the introduction of the telescope at the beginning of the 17^th century allowed a correction of the Aristotelian axiom that the recurrent ‘natural’ movement is circular.

Image # 2 is meant to illustrate Kepler’s First and Second Planetary Law. It has been noticed by Field that the diagram is inaccurate and differs decisively from the diagrams Kepler published in his Astronomia nova. One the one hand it implies that the orbits of Mars and the earth are situated on the same plane, and on the other it contains information unknown to Kepler such as the seasons on Mars which depend on the aberration of the planes. The abbreviation Ap (Aphelium) and the letter π (Perihelium) refer to the opposition between the sun, the earth, and Mars. Π marks the closest, Ap the most distant position of Mars in relation to the sun. Kepler defined the area circumscribed by the elliptical orbit of the planet in relation to the sun in his Second Planetary Law.