Christmas Trilogy 2018 Part 3: Johannes’ battle with Mars

It would be entirely plausible to claim the Johannes Kepler’s Astronomia Nova was more important to the eventual acceptance of a heliocentric view of the cosmos than either Copernicus’ De revolutionibus or Galileo’s Sidereus Nuncius. As with most things in Kepler’s life the story of the genesis of the Astronomia Nova ΑΙΤΙΟΛΟΓΗΤΟΣ seu physica coelestis, tradita commentariis de motibus stellae Martis ex observationibus G.V. Tychonis Brahe, to give it its full title, is anything but simple.


Astronomia Nova title page Source: Wikimedia Commons

From his studies at Tübingen University Kepler was sent, in 1594, by the Lutheran Church to Graz as mathematics teacher in the local Lutheran school and as district mathematicus, responsible for surveying, cartography and above all yearly astrological prognostica. His situation in Graz, a predominantly Catholic area, was anything but easy and as the Counter Reformation gained pace the Lutheran school was closed and the Protestants were given the choice of converting to Catholicism or leaving the area. Largely because of the success of his prognostica Kepler was granted an exemption. However, by 1600 things got very tight even for him and he was desperately seeking a way out. All of his efforts to obtain employment failed, including, somewhat surprisingly, an appeal to his teacher Michael Mästlin in Tübingen.

During his time in Graz he had published his first book, Mysterium Cosmographicum (The Cosmographic Mystery), in which he attempted to prove, the for us today bizarre hypothesis, that in a heliocentric cosmos there were and could only be six planets because their obits were separated by the ratios of the volumes of the five regular Platonic solids. He realized that regular polygons bound one inscribed and one circumscribed circle at definite ratios, which, he reasoned, might be the geometrical basis of the universe. However, when he actually did the maths he realised that although he had a good approximation, it wasn’t good enough; he blamed the failing accuracy on the poor quality of the data he had available. He needed to obtain better data.


Kepler’s Platonic solid model of the solar system, from Mysterium Cosmographicum (1596) Source: Wikimedia Commons

Kepler was well aware of the fact that, for the last thirty years or so, Tycho Brahe had been accumulating vast quantities of new, comparatively accurate data, so he decided to go visit the Danish aristocratic astronomer in Prague, maybe there was also a chance of employment. There was, however, a small problem with this plan. As a young, first time author, he had sent complimentary copies of his publication to all of the leading European astronomers. This had led to the first correspondence with Galileo, who had received his copy rather more by accident than by design but also to a very tricky situation with Tycho. Kepler had sent a copy to Nicolaus Reimers Baer (1551–1600), also called Ursus, at the time Tycho’s predecessor as Imperial Mathematicus to the Emperor Rudolph II; this was accompanied by the usual highly flattering Renaissance letter of introduction. Ursus was engaged in a very bitter priority dispute with Tycho about the so-called Tychonic system, Tycho had accused him of having stolen it during a visit to Hven, and Ursus printed Kepler’s flattering letter in a highly insulting answer to Tycho’s accusations. Kepler was very definitely not Tycho’s favourite astronomer, as a result. Despite all of this Tycho, also in desperate need of new assistants since moving to Prague, actually invited the young Kepler to come and visit him. By a strange twist of fate the letter of invitation arrived after Kepler had already left Graz for Prague.

Kepler duly arrived in Prague and one of the most fateful meetings in the history of astronomy took place. That first meeting was a monumental disaster. Kepler took umbrage and departed to sulk in a Prague hotel, convinced that his journey to Prague had been in vain. However, thanks to the diplomatic efforts of the Bohemian physician Johannes Jessenius (1566–1621) the two hot heads settled their differences and Tycho offered Kepler at least temporary employment. Having no better offers Kepler agreed, returned to Graz, packed up his home and together with his wife and children returned to Prague.

Unfortunately, there was no way that Tycho was going to trust a comparative stranger with the accumulated treasures of thirty years of observations and Kepler had to be satisfied with the tasks that Tycho gave him. First of all, maybe as a form of punishment, Tycho set him to work writing a vindication of Tycho’s claims against Ursus. Although Kepler did not produce the stinging condemnation of Ursus that Tycho wanted, he did produce a fascinating philosophical analysis of the role of hypothesis in the history of astronomy, A Defence of Tycho against Ursus, which was not published at the time but which historian Nicholas has described in the title of his scholarly edition of the work as ‘the birth of history and philosophy of science.[1]’ On the astronomical front, Tycho gave Kepler what would prove to be a task of immeasurable importance in the history of astronomy, the determination of the orbit of Mars.

When Kepler initially arrived in Prague to work with Tycho, Longomontanus, Tycho’s chief assistant, was working on the orbit of Mars. With Kepler’s arrival Tycho moved Longomontanus onto his model of the Moon’s orbit and put Kepler onto Mars. When first assigned Kepler famously claimed that he would knock it off in a couple of weeks, in the end he took the best part of six years to complete the task. This fact out of Kepler’s life often gets reported, oft with the false claim that he took ten years, but what the people almost never add is that in those six years the Astronomia Novawas not the only thing that occupied his time.

Not long after Kepler began his work Tycho died and he inherited the position of Imperial Mathematicus. This, however, had a major snag. Tycho’s data, the reason Kepler had come to Prague, was Tycho’s private property and that inherited his children including his daughter Elizabeth and her husband Frans Gansneb genaamd Tengnagel van de Camp. Being present when Tycho had died, Kepler secured the data for himself but was aware that it didn’t belong to him. There followed long and weary negotiations between Kepler and Frans Tengnagel, who claimed that he intended to continue Tycho’s life’s work. However, Tengnagel was a diplomat and not an astronomer, so in the end a compromise was achieved. Kepler could retain the data and utilise it but any publications that resulted from it would have Tengnagel named as co-author! In the end he contributed a preface to the Astronomia Nova. Kepler also spent a lot of time and effort haggling with the bureaucrats at Rudolph’s court, attempting to get his salary paid. Rudolph was good at appointing people and promising a salary but less good at paying up.

Apart from being distracted by bureaucratic and legal issues during this period Kepler also produced some other rather important scientific work. In 1604 he published his Astronomiae Pars Optica, written in 1603, which was the most important work in optics published since the Middle Ages and laid the foundations for the modern science. It included the first explanations of how lenses work to correct short and long sight and above all the first-ever correct explanation of how the image is formed in the eye. The latter was confirmed empirically by Christoph Scheiner.


Astronomiae Pars Optica title page

In 1604 a supernova appeared in the skies and Kepler systematically observed it, confirmed it was definitively supralunar (i.e. above the moon’s orbit) and wrote up and published his findings, De Stella nova in pede Serpentarii, in Prague in 1606.

The Astronomia Nova is almost unique amongst major scientific publications in that it appears to outline in detail the work Kepler undertook to arrive at his conclusions, including all of the false turnings he took, the mistaken hypotheses he used and then abandoned and the failures he made in his calculations. Normally scientific researchers leave these things in their notebooks, sketchpads and laboratory protocols; only presenting to their readers a sanitised version of their results and the calculations or experiments necessary to achieve them. Why did Kepler act differently with his Astronomia Nova going into great detail on his six-year battle with Mars? The answer is contained in my ‘it appears’ in the opening sentence of this paragraph. Kepler was to a large extent pulling the wool over his readers’ eyes.

Kepler was a convinced Copernicaner in a period where the majority of astronomers were either against heliocentricity, mostly with good scientific reasons, or at best sitting on the fence. Kepler was truly revolutionary in another sense, he believed firmly in a physical cause for the structure of the cosmos and the movement of the planets. This was something that he had already propagated in his Mysterium Cosmographicum and for which he had been strongly criticised by his teacher Mästlin. The vast majority of astronomers still believed they were creating mathematical models to save the phenomena, irrespective of the actually physical truth of those models. The true nature of the cosmos was a question to be answered by philosophers and not astronomers.

Kepler structured the rhetoric of the Astronomia Nova to make it appear that his conclusions were inevitable; he had apparently no other choice, the evidence led him inescapably to a heliocentric system with real physical cause. Of course, he couldn’t really prove this but he did his best to con his readers into thinking he could. He actually road tested his arguments for this literary tour de force in a long-year correspondence with the Frisian astronomer David Fabricius. Fabricius was a first class astronomer and a convinced Tychonic i.e. he accepted Tycho’s geo-heliocentric model of the cosmos. Over the period of their correspondence Kepler would present Fabricius with his arguments and Fabricius would criticise them to the best of his ability, which was excellent. In this way Kepler could slowly build up an impression of what he needed to do in order to convince people of his central arguments. This was the rhetoric that he then used to write the final version of Astronomia Nova[2].

To a large extent Kepler failed in both his main aims when the book was published in 1609. In fact it would not be an exaggeration to say that it was initially a flop. People weren’t buying either his heliocentricity or his physical cause arguments. But the book contains two gems that in the end would prove very decisive in the battle of the cosmological systems, his first and second laws of planetary motion:

1) That planets orbit the Sun on elliptical paths with the Sun situated at one focus of the ellipse

2) That a line connecting the planet to the Sun sweeps out equal areas in equal periods of time.

Kepler actually developed the second law first using it as his primary tool to determine the actually orbit of Mars. The formulation of this law went through an evolution, that he elucidates in the book, before it reached its final form. The first law was in fact the capstone of his entire endeavour. He had known for sometime that the orbit was oval and had even at one point considered an elliptical form but then rejected it. When he finally proved that the orbit was actually an ellipse he knew that his battle was over and he had won. Today school kids learn the first two laws together with the third one, discovered thirteen years later when Kepler was working on his opus magnum the Harmonice mundi, but they rarely learn of the years of toil that Kepler invested in their discovery during his battle with Mars.

[1]Nicholas Jardine, The Birth of History and Philosophy of Science: Kepler’s ‘A Defence of Tycho against Ursus’ with Essays on its Provenance and Significance, CUP, ppb. 2009

[2]For an excellent account of the writing of Astronomia Novaand in particular the Kepler-Fabricius correspondence read James R. Voelkel, The Composition of Kepler’s Astronomia Nova, Princeton University Press, 2001



Filed under Early Scientific Publishing, History of Astronomy, History of Mathematics, Renaissance Science

2 responses to “Christmas Trilogy 2018 Part 3: Johannes’ battle with Mars

  1. In addition to Voelkel’s book, the earlier book by Stephenson Kepler’s Physical Astronomy is a landmark in Kepler studies. Stephenson was the first to argue (based on internal evidence) that the Astronomia Nova was not in fact a record of Kepler’s progress–a dump of his lab notebooks, so to speak–but a carefully constructed argument. Stephenson remains the best place to learn the details of Kepler’s physics. (As for his physics, they probably lead to Descartes’ vortex theory.)

    Voelkel is an excellent companion treatise, with much more on the external circumstances, including the Kepler-Fabricius correspondence. From Voelkel comes the fascinating detail that late in the game, after Kepler had obtained his two laws, Fabricius devised a traditional deferent-epicycle-equant model for Mars that fit the Tychonic data just as well as Kepler’s laws! Kepler promptly broke off the correspondence.

    Voelkel also makes a strong argument that the structure of the Astronomia Nova was determined to a considerable degree by the legal aspects of Kepler’s agreement with Tengnagel.

    A final bit of curious trivia. In terms of predictive accuracy, Curtis Wilson once pointed out that Kepler’s first law wasn’t nearly as important (in purely numerical terms) as one of Kepler’s other innovations, one never mentioned in short summaries of Kepler’s work. In classical Ptolemaic astronomy, the sun, unlike all the other planets (and the sun was a planet for Ptolemy), traveled at a constant (linear) speed–no equant for the sun. Kepler from the start insisted on treating the earth just like all the other planets, and so gave it an equant. (Of course, the sun’s motion in a geocentric system turns into the earth’s motion heliocentrically.) Since the earth is our observing platform, this change affects the interpretation of the Martian data. Indeed, it makes a bigger difference than changing the Martian orbit from a circle to an ellipse.

  2. Ray

    Regarding Kepler, Scheiner and image formation: I take it from this and the linked post on Scheiner that Kepler’s idea of an inverted retinal image was controversial for some time, and without empirical proof. There is however, a very easy empirical observation which strongly suggests the image is in fact inverted. Press lightly on your eyeball just outside the place where your eyelids meet and you will see a dark spot appear on the opposite side of your visual field (When I do it the dark spot appears right on top of the part of my nose I can just barely see with my eye.) when you wiggle your finger the spot wiggles the opposite way. Do you know if this sort of thing featured at all in the early discussions of ocular image formation?

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