Kevin T. Kelly
Department of Philosophy
Carnegie Mellon University
Johannes Kepler is the historian of science's greatest friend. A professional astronomer, he had double vision and myopia. Vacillating wildly between servile depression and reckless mania, he felt that posterity would benefit from a candid confession of each of his blind alleyways, and spared posterity not a single detail. The father of celestial mechanics was also an inveterate Pythagorean who heard literal harmonies in the heavens and a professional astrologer who cast unflattering horoscopes portraying the characters of each of his curious relatives. His father left town under a cloud. His mother was tried for witchcraft. His marriage was a disaster begun under a "calamitous sky". In unhappy moments he cruelly described himself in the third person as a vicious dog that bites its benefactors. And all of it is laid open to the amused gaze of the historian.
Kepler's Pythagoreanism is beyond doubt:
The Sun in the middle of the moving starts, himself at rest and yet the source of motion, carries the image of God the Father and Creator.... He distributes his motive force through a medium which contains the moving bodies even as the Father creates through the Holy Ghost.
Why waste words? Geometry Existed before the Creation, is co-eternal with the mind of God, is God himself (what exists in God that is not god himself?); geometry provided God with a model for Creation and was implanted into man, together with God's own likeness--- and not merely conveyed to his mind through the eyes (cf. Koestler 59; pl 262).
This keen enthusiasm for the Sun led Kepler to make the Sun, rather than the center of Earth's orbit, the center of the universe.
Copernicus' starting premise was to execute the circular celestial mechanics of the ancients more faithfully. Galileo's theory of inertia was tied to Copernicus' conception of natural circular motion around the Earth.
Kepler's original idea, which occurred to him while drawing a geometrical figure in a lecture, was to explain the newly discovered Copernican plan of the universe. Recall that the layout of the universe was arbitrary for Ptolemy, but was uniquely triangulated within the Copernican theory. We might say that it is an accident of nature that the planets at precisely the distances from the sun that they are at now. Nothing about our present physics attaches any special significance to the planetary diameters. The laws take the orbital diameters as input and then determine where the planets will be later. If you ask for more, your physics teacher will tell you that you don't understand physics. That is to say, our current theories provide no explanation. But for Kepler that wasn't good enough. The plan was now known, so it ought to have an explanation. And he thought he could show that it was geometrically necessary.
There are five regular or Platonic solids, and Euclid could already show that there are at most five in three dimensional space. The Platonic solids are well known in the classical literaure as the shapes of Plato's geometrical atoms in the Platonic dialogueTimaeus.
There were also six planetary orbits around the sun: Mercury, Venus, Earth, Mars, Jupiter Saturn. Thus, the five Platonic solids could be nested between the orbs carrying these planets. The geometry of the solids would then determine the distances among the planetary orbits. Solids with more sides produce smaller distances because they hug the spheres more closely. But be this as it may, the small planetary orbits will be closer because the superscribed Platonic solids will be smaller as well. This is qualitatively the plan of the Copernican universe. The system was published in 1596 in Mystery of the Universe when Kepler was 25. Since there are just enough planets for the Platonic solids to separate, there could not be any more.
Kepler sold the idea of building a silver cup depicting the Platonic solid universe to the duke of Wuerttenberg. The idea was to have each hemisphere of the cup dispense a different, thematically appropriate beverage. Saturn, the largest orb, would contain stale beer, so that the noble's company could laugh at those who are ignorant of astrology. The sun would serve aquavit, Mercury brandy, Venus mead, the moon water, etc.
Kepler's entire career was devoted to defending this early hypothesis. In science, it would seem, prior commitment counts for a great deal. Without it, the tedious empirical work does not even get started.
Tycho was a Danish nobleman who took up astronomy as a full-time hobby. He had a silver nose, the result of a youthful duel. He was supported by the Danish king on an island called Hveen in the Oeresund between Denmark and Sweden. He was a hard partying autocratic jerk. He is still known today in Denmark as an autocratic jerk. When things look bad, people say "it's going to be a Tycho Brahe day".
His fame was made by observations placing the nova of 1572 above the moon. in 1577 he placed a coment in the heavens as well. Both observations caused a sensation, being the first documented parallax measurements of celestial changes.
Tycho got the idea that astronomy would profit from increased accuracy, since the curent theories were accurate only up to naked eye observation. But more is involved than the naked eye. One must use the eye to measure angles. Thus, the angle measurement device (a wooden protractor called a quadrant) could contribute to the error by vibration, inaccuracy of the scale, and simply by smallness of the scale, so that each mark covers many seconds of arc. By making the quadrant really, really big, these errors can be minimized without using a telescope. Tycho even went so far as to put his quadrants underground in holes to protect them from vibration from the wind. This sounds odd unless you have felt the wind in Denmark.
On Hveen he built an astronomical castle called Uraniborg, which was sort of the royal Disneyland of the age. It had murals of Tycho making observations. Here, he was the first to make systematic, successive, accurate observations of all the planets. Kepler wanted desperately to see the observations to check his Platonic solid theory.
Tycho also had his own theory of the universel. It was just like that of Copernicus, except that the sun moved around the Earth, carrying all the other planets around it. This preserves most of the harmonies, but does not require that the Earth move. In particular, it accounts for Galileo's observation of the phases of Venus.
1600 Tycho moved to a town near Prague and invited Kepler to be an assistant. Tycho assigned Kepler to work on the orbit of Mars. Mars is the most eccentric planet. Kepler worked under Tycho for 18 months, after which Tycho died from a bladder infection. Kepler inherited Tycho's position as Imperial mathematician to Rudolph II. He wrote New Astronomy during this time (1609).
Kepler tried 70 times to fit an epicycle to Mars and never succeeded. Then he tried equants, abandoning the Copernican program. This left an 8' of arc error, which was not within Tycho's margin of error.
Next, he tries non-circular orbits of various shapes.
He switched to the Earth to correct its orbit first.
Digression: force in the sun moves the planets, so there must be a natural speed law relating speed to distance from the sun: speed is proportional to distance. Checked only at two points. Kepler admitted it and then forgot the admission. This mistake cancelled with another mistake later.
Kepler's physics:
Second law: equal areas in equal times: result of three successive errors. No clear argument given.
First law: started with an oval ("cartful of dung"). Then an egg shape (six chapters). Then he found the path of an ellipse but could not recognize it as an ellipse. Numerical methods yielded a "chubby face".
1618 Harmony of the World:
Third law: T^2/R^3 = K.
Musical intervals of the planets (perihelion/aphelion ratio)
Platonic solids.