Kepler’s Physics
Let me repeat the motto, already implicit in the Mysterium cosmographicum, but come into full bloom in the Astronomia nova:
Forces emanating from the Sun guide or drive the planets in their orbits.
A word about the word ‘force’. F=ma this is not. Kepler’s forces are Aristotelian, satifying F∝v (force is proportional to speed). Not only that: we must be careful (as Stephenson writes (p.187)) not to “impute to Kepler a conceptual exactness which his physics—in contrast with his astronomy—did not possess …The word force, vis, did not yet have the clarity of an accepted technical term.”1
I wrote “forces” above. Kepler ends up with three forces in the Astronomia nova: (a) Gravity, which plays no role in determining the orbits. (b) A whirlpool-like force that sweeps the planets around the Sun. Kepler calls this the Sun’s species; I will call it the whirlpool force. (c) A force responsible for the elliptical shape of the orbit. Kepler calls this the magnetic virtue; I will call it the libration force, for reasons that will become apparent2.
Souls and Minds
Ptolemy in the Planetary Hypotheses endowed the planets with souls, the source of their motion. This seems odd to us. But remember that for the ancient Greeks, the planets were celestial beings, perhaps even gods. On Earth, what moves under its own power? Animals and people, of course. Add to this the authority of Aristotle. Here’s how Kepler recaps Aristotle’s Metaphysics (Book 12, part 8) in the Astronomia nova, Ch.2:
…having thus accumulated 49 orbs in all (or 53 or 55, following Callipus), he attributed to each its own mover … In this way, he introduced us to separate minds which, it turned out, were gods, as the perpetual administrators of the heavens’ motions. They also bestowed a moving soul [anima motrix], more closely attached to the orbs and giving them form, so that the mind would only have to give assistance … They therefore transferred this potentiality for creating motion to a soul …
Now this coupling of mind and soul is indeed quite in agreement with the detailed considerations of the astronomers, even though the philosophers’ mode of argument is chiefly metaphysical. For it is the same in humans: the moving faculty is one thing; that which makes use of the moving faculty according to the indications of the senses—the Will—is another … Similarly, if we should propose these Aristotelian orbs as objects of contemplation, two things will present themselves to us: (1) the motive force, from whose activity and constant strength the time of revolution arises; (2) the direction in which it acts. The former is more correctly ascribed to the animate faculty, and the latter to its intelligent or remembering nature.
More succinctly, Stephenson writes:
In these early chapters of the Astronomia nova, souls furnished the motion and minds the guidance.
—Stephenson (p.30)
From the first, Kepler preferred a different explanation for the planets’ motion. The decisive clue: the farther a planet is from the Sun, the slower it moves. In Kepler’s earliest extant astronomical writing (a disputation he wrote while still at Tübingen, six years before the Mysterium cosmographicum), he proposed that the motive cause resided in the Sun, “whence as if from the center and the certain heart of the world it would extend itself through its effect most equally to all surrounding orbs” (quoted in Voelkel, p.29). Five years later, in a letter to his old teacher Maestlin, Kepler repeated this idea:
…there is in the Sun a moving spirit [anima movens] and an infinite motion … that strength of motion (as light in optics), which is further from the source is that much weaker.
—quoted in Voelkel (p.36)
The next year, in the Mysterium cosmographicum, he wrote
… one of two conclusions must be reached: either the moving souls are weaker the further they are from the Sun; or, there is a single moving soul in the center of all the spheres, that is, in the Sun, and it impels each body more strongly in proportion to how near it is. In the more distant ones on account of their remoteness and the weakening of its power, it becomes faint, so to speak.
—quoted in Voelkel (p.54)
He immediately opts for the second conclusion. Notice that Kepler has not dispensed with souls, just relocated and united them all in the Sun. This line of thought led to the whirlpool force, culminating in the Second Law—as we will see.
Twenty-five years later Kepler published a second edition of the Mysterium cosmographicum with new notes. Here is the note for the phrase “there is a single moving soul”:
If for the word “soul” you substitute the word “force”, you have the very same principle on which the Celestial Physics is established in the Commentaries on Mars [i.e., Astronomia nova], and elaborated in Book IV of the Epitome of Astronomy. For once I believed that the cause which moves the planets was precisely a soul, as I was of course imbued with the doctrines of J.C. Scaliger on moving intelligences. But when I pondered that this moving cause grows weaker with distance, and that the Sun’s light also grows thinner with distance from the Sun, from that I concluded, that this force is something corporeal, that is, an emanation which a body emits, but an immaterial one.
The planets do not revolve in circular orbits concentric with the Sun. Here Kepler thought that planetary minds might come into play. Even with an eccentric circular orbit, the direction is sometimes partly towards the Sun, sometime away from it. As Stephenson puts it,
[W]hen Kepler spoke of a mind in the heavens he was considering the problem of controlling motion; more specifically, the problem of obtaining sufficient information to constrain motion into the regular path that was observed.
—Stephenson (p.30)
What computations would the mind have to make, what data would it need, and how would it obtain it? Even for a circular orbit, this perplexed him. The notion of the libration force, along with the possibility of an oval orbit, gradually took shape in Kepler’s thought. Although references to souls and minds occur throughout the Astronomia nova, physics began to displace planetary “psychology”. Stephenson again:
Kepler thus proposed two quite different theories in Chapter 57 to account for the planet’s [oval orbit]. One relied upon natural forces, magnetic or quasi-magnetic, while the other supposed some kind of primitive planetary mind.
—Stephenson (p.120)
By this time, in fact, Kepler was decidedly less enthusiastic than he had once been about planetary minds. Years of physical speculation had brought an increasingly confident belief that natural means alone could explain the patterns of motion for which he had, hesitantly, once invoked mental control. … The change in Kepler’s attitude was a gradual one, occurring over a period of years and never really completed. Celestial minds remained a part of Kepler’s universe; only from his astronomy can one see them discreetly withdrawing.
—Stephenson (p.132)
Souls, too, did not entirely disappear:
Kepler believed that a motive soul was necessary to account for the persistence of the solar rotation… He offered several reasons why it should be thought plausible that there was a soul in the body of the sun … Generally he thought that a soul was necessary to sustain the rotation, but that no mind or intelligence was needed, because the motion was constant in direction and speed.
—Stephenson (p.141)
[1] Kepler also employed the Latin virtus and species, sometimes translated ‘power’ and ‘image’, not with a clear distinction from vis. I will mostly steer clear of these subtleties. (For his translation of the Astronomia nova, Donahue (pp.107–108) wrote about species: “The translator, in the end, has thrown up his hands, admitted defeat, and has declined to translate it at all.”)
[2] In a previous version of the post, I called this the quasi-magnetic force, but I now feel that libration force is better. Stephenson calls it the libratory force.
Diagonal Argument 