Johannes Kepler

Johannes Kepler Kopie eines verlorengegangenen Originals von 1610

A 1610 portrait of Johannes Kepler by an unknown artist. Wikimedia Commons.

One of the very first people to accept the physical reality of the Copernican system was the German astronomer and mathematician Johannes Kepler (1571 – 1630). Kepler was introduced to Copernicus’ work as a student at the University of Tübingen by his professor Michael Maestlin (1550 – 1631). He puzzled for a long time over the question of why there were gaps between the celestial orbs in the Copernican system, and he also wondered why there were six planets, as opposed to some other number. In 1595, while he was working as a mathematics teacher in the Austrian city of Graz, he hit upon the answer. Kepler’s flash of insight, which he describes in terms evocative of divine revelation, was that the spaces between the orbs of the six planets were delimited by the five regular geometric solids. The five regular solids, also known as the Platonic solids, are symmetrical polyhedrons in which each face is the same regular polygon. They are the tetrahedron, made of four equilateral triangles; the cube, made of six squares; the octahedron, made of eight equilateral triangles; the dodecahedron, made of twelve pentagons; and the icosahedron, made of twenty equilateral triangles. It had been known since antiquity that there are only five such regular solids. (Plato made these geometrical shapes the basic components of his cosmos in the Timaeus.) Kepler began with the sphere of the earth. Around the sphere of the earth, which was a solid sphere large enough to contain both the earth and the moon, he inscribed a dodecahedron. Then around the dodecahedron he inscribed a sphere, which was the inner surface of the orb of Mars. Around the outer surface of the orb of Mars, he inscribed a tetrahedron. Around the tetrahedron he inscribed a sphere, which was the inner surface of the orb of Jupiter. Around the outer surface of the orb of Jupiter he inscribed a cube. Around the cube he inscribed a sphere, which was the inner surface of the orb of Saturn. Moving inwards from the earth, he inscribed an icosahedron inside the inner surface of the earth/moon orb. Inside the icosahedron he inscribed a sphere, which was the outer surface of the orb of Venus. Inside the inner surface of the orb of Venus he inscribed an octahedron, and inside this he inscribed a sphere that was the outer surface of the orb of Mercury.  If you’re having trouble visualizing this (and I’m really impressed if you’re NOT having trouble!), watch this video.  Kepler published this work in 1596 under the title The Secret of the Universe (Mysterium Cosmographicum). This was one of the very first published defenses of the Copernican system.

Kepler-1596-024-pl-sm

Kepler’s model of the cosmos from the Mysterium Cosmographicum (1596). Courtesy of OU History of Science Collections.

For Kepler, the aesthetic perfection of this system was clear proof that it was true. Here was a clear explanation for why God had created a cosmos with space between the orbs of the planets. God was a geometer and He had created the cosmos in the most symmetrical, beautiful, geometrically perfect way imaginable. Further, not only did Kepler’s system explain why there were spaces between the orbs, it also explained why there were exactly six planets. There were six and only six planets because there were five and only five Platonic solids to delimit the intervals between the planets. For Kepler, this gave the Copernican system a definite edge over the Ptolemaic system, because Ptolemy could not explain why there were seven planets (counting the sun and the moon), instead of six or eight or ten.

Kepler sent a copy of The Secret of the Universe to Tycho, and while the book did not convince the Dane to accept a heliocentric cosmos, it did impress him enough to secure Kepler an invitation to work with him at the court of the Emperor Rudolph II in Prague, where Tycho had recently been appointed imperial astronomer. Kepler arrived in Prague in 1600 and Tycho asked him to develop a more accurate model for the orb of Mars using the newer and better observational data Tycho had accumulated. Tycho died a year later so he never saw the end result of Kepler’s long and painful “war with Mars.” In 1609, Kepler finally published the results of his study of Mars in a groundbreaking book aptly titled New Astronomy (Nova Astronomia). In the New Astronomy, Kepler broke with the nearly two thousand year old tradition of uniform circular motion in the heavens. He declared that Mars moved in an ellipse with the sun at one focus.  And he asserted that Mars moved in such a way that a line drawn from Mars to the sun swept out equal areas in equal times. This meant that Mars moved faster when it was closer to the sun and slower when it was farther away.  These are now known as Kepler’s first and second laws of planetary motion. In subsequent work he demonstrated their applicability to all the planets.

Kepler1

Kepler’s first law. A planet moves around an ellipse with the sun at one focus. Wikimedia Commons.

Kepler2

Kepler’s second law. A line drawn from the planet to the sun sweeps out equal areas in equal times. Wikimedia Commons.

The New Astronomy is also significant because in it Kepler introduced the concept of a “orbit.” All the astronomers whose work I have discussed used the term “orb” (Latin: orbis), a tern that signified a hollow sphere in which a celestial body was embedded. The entire orb rotated around the earth (or the sun). Kepler was the first to employ the term orbit (Latin: orbita). The Latin word orbita means “a track or rut made in the ground by a wheel.” By the time he wrote the New Astronomy, Kepler had adopted Tycho’s position that the heavens are fluid and that planets move through the heavens like fish swim through water. Kepler was the first astronomer to describe the path of a planet through the heavens. Finally, Kepler sought to answer another one of the questions that plagued the Copernican system: what made the earth move if it was not made of ether? Based on his analysis of Mars, Kepler noted that planets move faster when they are closer to the sun. This, combined with the much older observation that planets appear to move more slowly the farther away they are from the sun, led Kepler to posit that the sun itself had a kind of motive power. It generated not just heat and light, but also motion, and caused all of the celestial bodies to move around it.

References:

Bernard R. Goldstein and Giora Hon, “Kepler’s Move from Orbs to Orbits: Documenting a Revolutionary Scientific Concept” Perspectives on Science 13 (2005) 74-111.

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