Deciphering Johannes Kepler's Physics in His Astronomia Nova

Johannes Kepler first published his first two laws in 1609 in his Astronomia Nova¹ [New Astronomy]. The title of this book is completely appropriate, as it is really the first book to attempt to study astronomy as a part of physics.

In this post, I will examine certain aspects of the physics proposed by Kepler. It is important to remember that the publication date for the Astronomia Nova was 1609, a year before Galileo announced his first discoveries with the telescope in the Sidereus nuncius. To better situate this date, below are publication dates for documents pertaining to the discussion below:

• 1543: Nicolaus Copernicus (1473–1543), De revolutionibus orbium coelestium [On the Revolutions of the Heavenly Spheres]

• 1584: Giordano Bruno (1548-1600), De l'infinito, universo et mondi [On the Infinite, Universe and Worlds]

• 1600: William Gilbert (1544-1603), De magnete [On the Magnet]

• 1610: Galileo Galilei (1564-1642), Sidereus nuncius [Starry Messenger]

• 1632: Galileo, Dialogo sopra i due massimi sistemi del mondo [Dialogue Concerning the Two Chief World Systems]

• 1638: Galileo, Discorsi e dimostrazioni matematiche intorno a due nuove scienze [Two New Sciences]

Kepler was first and foremost a mathematician. Astronomia Nova is a serious treatise attempting to demonstrate with detailed mathematical arguments that a revised form of Copernicanism can explain, from a physical perspective, the workings of the solar system. Its presentational style is unique, as it takes the reader through a series of tentative hypotheses, detailed calculations, false leads, analogies with rivers and boats with oars, and more, starting with a comparison of the systems of Ptolemy, Tycho and Copernicus, and ultimately leading to a series of key theorems and laws at the end of the book, including, of course, his first two laws.

Here are some key principles that Kepler argued in favour of:

1. The sun is located at the center of the universe.

2. The orbit of each of the planets lies in a plane upon which lies the sun.

3. The motions of the planets are ultimately governed by the interactions between the sun and the planets.

4. The motion of a planet is greatest at the perihelion [at its closest approach to the sun] and least at the aphelion [at its furthest approach to the sun].

Point (1) is crucial. For Kepler, as for Bruno and Gilbert, the essence of the Copernican model was not the mathematics in Copernicus’s De revolutionibus, but the fact that the solar system is truly heliocentric, i.e., that the sun is at its center. In fact, the very page following the title page of the Astronomia nova consists of a quotation from the Scholae Mathematicae of Pierre de la Ramée (1515-1572) [Petrus Ramus], criticizing Copernicus, along with Kepler’s response. And it is here that we learn that the preface to De revolutionibus, in which it is claimed that Copernicus did not actually believe the solar system to be heliocentric, was not in fact written by Copernicus’s hand:

But would you like to know who originated this tale, at which you wax so wroth? “Andreas Osiander” is written in my copy [sc. of Copernicus’s De revolutionibus], in the hand of Hieronymus Schreiber of Nuremberg. This Andreas, when he was in charge of publishing Copernicus, thought this preface most prudent which you consider to be so absurd (as may be gathered from his letters to Copernicus), and placed it upon the frontispiece of the book, Copernicus himself being dead, or certainly unaware of this. Thus Copernicus does not mythologize, but seriously presents paradoxes; that is, he philosophizes. Which is what you wished of the astronomer. [p.4]

The data with which Kepler was working was the data from the late Tycho Brahe (1546-1601), the great Danish astronomer with whom Kepler worked in Prague the last few months of Brahe’s life. This was, at that time, the most detailed astronomical data ever produced in the Western world. However, Kepler could not just pick up the data and start doing calculations, as of all of that data had been acquired and processed—on earth, of course—using the knowledge of Tycho and his assistants, with Tycho believing in a system in which the moon and sun revolved around the earth, while the other planets revolved around the sun. If we consider point (2) above, for example, every datum had to be reassessed and recalibrated by Kepler: Exactly at what point in the earth’s revolution around the sun was the datum acquired? What was the exact angle of the plane of Mars’s orbit compared to that of the earth? And so on. And to do detailed calculations required accurate estimates of the distance from the earth to the sun at perihelion and aphelion.

All of these calculations were very difficult, especially as Kepler did not have at hand the tools of the infinitesimal calculus that would be developed later in the same century. Fortunately for him, the eccentricity of earth’s orbit is not great, which facilitated the calculations. This is not the case for the orbit of Mars, the main subject of his study in the Astronomia Nova. For a detailed discussion, chapter by chapter, of the development of the ideas in this text, I recommend Bruce Stephenson’s book, Kepler’s Physical Astronomy².

Before we examine Kepler’s physical explanations, it is important to understand that Kepler’s physics assumed the Aristotelean idea that an object only moves if it is pushed; should it no longer be pushed, it comes to a rest. It would not be until 1638, almost thirty years later, in the Two New Sciences, that Galileo would introduce inertia. See my previous post Galileo and Motion and Inertia. Ironically, it is Kepler himself who coined the word inertia in the Astronomia Nova, but with a different meaning.

Kepler came up with physical explanations for the discoveries that he made based on his understanding of magnetism. Gilbert had just published his De magnete when Kepler began his work on the Astronomia nova. And so Kepler enthusiastically turned to magnetism, coming up with some novel ideas, which all turned out to be erroneous.

The first problem to be addressed follows from point (3) above: How could the sun possibly affect the motion of the planets? Kepler discusses this problem in Chapter 32. He assumes that the sun rotates on its axis, and imagines magnetic fibers spinning around the sun at the same velocity as does the sun. The fibers close to a given planet push it along, and so the planet revolves around the sun. He estimates that the sun rotates on its axis every three days; the actual value is in the order of 27 days.

However, in my Mysterium Cosmographicum I pointed out that there is about the same ratio between the semidiameters of the sun’s body and the orb of Mercury as there is between the semidiameters of the body of the earth and the orb of the moon. Hence, you may plausibly conclude that the period of the orb of Mercury would have the same ratio to the period of the body of the sun as the period of the orb of the moon has to the period of the body of the earth. And the semidiameter of the orb of the moon is sixty times the semidiameter of the body of the earth, while the period of the orb of the moon (or the month) is a little less than thirty times the period of the body of the earth (or day), and thus the ratio of the distances is double the ratio of the periodic times. Therefore, if the doubted ratio also holds for the sun and Mercury, since the diameter of the sun’s body is about one sixtieth of the diameter of Mercury’s orb, the time of rotation of the solar globe will be one thirtieth of 88 days, which is the period of Mercury’s orb. Hence it is likely that the sun rotates in about three days.

[…]

The magnet, however, does not attract with all its parts, but has filaments (so to speak) or straight fibers (seat of the motor power) extended throughout its length, so that if a little strip of iron is placed in a middle position between the heads of the magnet at the side, the magnet does not attract it, but only directs it parallel to its own fibers. Thus it is credible that there is in the sun no force whatever attracting the planets, as there is in the magnet, (for then they would approach the sun until they were quite joined with it), but only a directing force and consequently that it has circular fibers set up in the same direction, which are indicated by the zodiac circle.

Therefore, as the sun forever turns itself, the motive force or the outflowing of the species from the sun’s magnetic fibers, diffused through all the distances of the planets, also rotates in an orb, and does so in the same time as the sun, just as when a magnet is moved about, the magnetic power is also moved, and the iron along with it, following the magnetic force.

The example of the magnet I have hit upon is a very pretty one, and entirely suited to the subject: indeed, it is little short of being the very truth. So why should I speak of the magnet as if it were an example? For, by the demonstration of the Englishman William Gilbert, the earth itself is a big magnet, and is said by the same author, a defender of Copernicus, to rotate once a day, just as I conjecture about the sun. And because of this very thing, that it has magnetic fibers intersecting the line of its motion at right angles, those fibers therefore lie in various circles about the poles of the earth parallel to its motion. I am therefore absolutely within my rights to state that the moon is carried along by the rotation of the earth and the motion of its magnetic power, only thirty times slower. [Chapter 34, pp.287-289, my emphasis]

The second question to be resolved follows from point (4): Why is the orbit of a planet not circular? Why does the distance between a planet and the sun vary? Kepler discusses this question in Chapter 57. The argumentation is quite elaborate and takes many pages. The basic idea is that the magnetism of a planet is not the same as the magnetism of the sun. A planet has two poles, like for the earth. The sun also has two poles, but differently arranged: one pole corresponds to the entire surface of the sun, and the other to the center of the sun. As the planet revolves around the sun, at different points the planet is attracted to the sun and at others it is repelled away from the sun, hence the variation of the orbit.

A clearer summary of this idea can be found in Book Four of Kepler’s Epitome Copernicae Astronomiae [Epitome of Copernican Astronomy³], published in 1620:

Whence comes this diversity of the opposite parts of the same body?

In loadstones the diversity comes from the situation of the parts in the whole. For if you break the loadstone AB at CD, then wheresoever the pieces are transposed to, parts A and CD of the two pieces are mutually repellent. In the whole loadstone these parts formerly looked towards the same region of the same region of the world. But if the pieces are put next to one another, so that the former relative situation of the parts occurs, as CAD, BCD, then the pieces attract one another.

In the heavens the thing is arranged somewhat differently. For the sun possesses this active and energetic faculty of attracting or repulsing or retaining the planet, not as a loadstone does, in one region, but in all the parts of its body. And so it is believable that the center of the solar body corresponds to one extremity or region of a loadstone, but the whole surface to the other region of the loadstone. Therefore in the bodies of the planets, that part or extremity which at the first commencement of things and at the first placing of the planet looked towards the sun is akin to the center of the sun and is attracted by the sun; but the part which stretched out away from the sun towards the fixed stars came to possess the nature of the surface of the sun; and if it is turned towards the sun, the sun repulses the planet. [Book Four, Part II, Section 3, p.58]

Now it is clear that Kepler’s ideas of magnetism were entirely erroneous. There are no magnetic fibers to push planets around, nor are there any magnets in the universe where the surface and the center are opposite poles.

Nevertheless, 23 years before Galileo published his Dialogue comparing the Ptolemaic and Copernican systems in a flamboyant rhetorical style, Kepler had derived equations describing in detail the elliptical orbits of the planets, and attempted to provide physical explanations for these phenomena. It was with Kepler’s Astronomia Nova that astronomy became a branch of physics.

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1. Johannes Kepler. Astronomia Nova. New Revised Edition. Translated by William H. Donahue. Foreword by Owen Gingerich. Santa Fe, NM: Green Lion Press, 2015.

2. Bruce Stephenson. Kepler’s Physical Astronomy. New York: Springer, 1987.

3. Johannes Kepler. Epitome of Copernican Astronomy & Harmonies of the World. Translated by Charles Glenn Wallis. Amherst, NY: Prometheus Books, 1995. Originally published by Annapolis: The St. John's Bookstore, 1939.