The Mysterium cosmographicum
The Mysterium cosmographicum (Cosmographical Mystery) boasts one of most celebrated illustrations in the history of science: the planetary spheres nested with the five Platonic solids. This picture graces nearly every history of astronomy. Who am I to break with tradition, here it is:
This depicts Kepler’s explanation of why there were six planets, plus the reason for their relative distances. The architecture of the universe, so to speak. (Historians call this the polyhedral hypothesis.)
Shades of the tightly nested spheres of the Planetary Hypotheses! Kepler and his contemporaries were not aware of this work, but they had read Peurbach’s Theoricae Novae Planetarum (see post 15).
In the preface to the Mysterium cosmographicum, Kepler said:
And there were three things above all for which I sought the causes as to why it was this way and not another—the number, the dimensions, and the motions of the orbs.
You can’t argue with the sheer elegance of Kepler’s explanation—but it proved a dead-end. At most, it speaks to Kepler’s drive to find patterns in the data, a drive that led to his third law. On the other hand, the noted physicist Steven Weinberg has defended Kepler’s scheme in its historical context:
No one today would take seriously a scheme like Kepler’s, even if it had worked better. This is not because we have gotten over the old Platonic fascination with short lists of mathematically possible objects, like regular polyhedrons. There are other such short lists that continue to intrigue physicists… What makes Kepler’s scheme so foreign to us today is not his attempt to find some fundamental physical significance for the regular polyhedrons, but that he did this in the context of planetary orbits, which are just historical accidents. Whatever the fundamental laws of nature may be, we can be pretty sure now that they do not refer to the radii of planetary orbits… In [Kepler’s] time no one knew (and Kepler did not believe) that the stars were suns with their own systems of planets, rather than just lights on a sphere somewhere outside the sphere of Saturn. The solar system was generally thought to be pretty much the whole universe, and to have been created at the beginning of time. It was perfectly natural then to suppose that the detailed structure of the solar system is as fundamental as anything else in nature.
—Weinberg (p.163–164)
From the beginning Kepler committed to Copernicanism. Only heliocentrism sets the relative Sun-planet distances without extra assumptions (recall scaling, post 2). Kepler noted that heliocentrism explains several mysterious features of the Ptolemaic approach (see post 6). He wrote, “Copernicus alone gives an explanation to those things that provoke astonishment among other astronomers, thus destroying the source of astonishment, which lies in the ignorance of the causes.”
Even in this first work, we find Kepler wrestling with celestial physics. I said in post 1 that Kepler’s physics, though wrong nearly point-for-point, nonetheless guided him past many pitfalls. How could this happen?
I’ll start with a one-sentence summary of what Kepler got right, physically speaking:
Forces emanating from the Sun guide or drive the planets in their orbits.
Let’s call this the motto. For the benefits listed in post 6, it matters not whether you use the mean Sun or the true Sun. Copernicus used the mean Sun throughout De revolutionibus. But our motto has a corollary. The mean Sun is a point in space, without physical meaning, and of no signficance for any planet except Earth. Hence:
Refer everything to the true Sun, and not the mean Sun. Nor should the Earth receive any special treatment.
Since the mean Sun’s very definition involves the Earth, the second sentence implies the first.
Gingerich1 proposed calling this corollary Kepler’s zeroth law. It looms large in the Astronomia nova, but already in the Mysterium cosmographicum, Kepler insisted on measuring distances from the true Sun.
The motto came from two observations. In the Copernican system, the farther a planet is from the Sun, the more slowly it moves. But also, a planet moves more slowly at aphelion than at perihelion. We know now that Kepler’s third law governs the “between planets” ratios, his second law the “aphelion vs. perihelion” ratios. And we know how Newtonian physics explains this: the conservation of angular momentum accounts for the second law, gravity’s inverse square law for the third.
To Kepler, these two regularities suggested that the “virtue” (virtus) moving the planets resides in the Sun. Perhaps the Sun’s virtue diminishes with distance as it spreads out? The aphelion-perihelion ratio pointed at a physical cause for Ptolemy’s equant.
Kepler took a stab or two at finding the rule for the “between planets” ratios. Not until much later, in the Epitome astronomiae Copernicanae, would Kepler find the right relation.
Diagonal Argument 