THE PICTURESQUE Swiss town of Schaffhausen, still retaining its medieval center, sits in a leaf-shaped salient largely surrounded by Germany. In fact, this geographic oddity itself completely envelops several pockets of German territory, as I had learned in trying to take shortcuts in the vicinity. I had purchased an export car at the VW factory in Wolfsburg, but my tax-free status in Germany had expired, so unintentionally crossing into Germany was a considerable nuisance. But being in a salient north of the Rhine was more than a nuisance for the citizens of Schaffhausen in World War II. It was a disaster. On 1 April, 1944, a thousand Allied bombs mistakenly rained down on the precariously situated town.
On that spring evening a score of B24 bombers had headed toward the German chemical works in Ludwigshafen, twenty miles farther east at the tip of Lake Constance, but clouds and winds over France confused the formation, which lost its way. When the lights of a town appeared through a clearing in the clouds, crews of thirteen of the planes assumed they were over Germany and mistakenly dropped their deadly loads onto Schaffhausen. The damage and civilian casualties in neutral Switzerland prompted a diplomatic crisis for the United States. An apology and a million dollars in reparations were immediately forthcoming, supplemented by three million more in October.
Among the losses were nine paintings by the sixteenth-century Swiss artist Tobias Stimmer. When Stimmer decorated the famous astronomical clock in the Strasbourg cathedral, he included a portrait of Copernicus (plate 2). As part of the painting he conspicuously inscribed the words vera efigies ex ipsius autographo depicta—"a true likeness from his own self-portrait." Stimmer's caption has led scholars to conjecture that the lovely and similar portrait of Copernicus now hanging in the city hall in Torun (his Polish birthplace) is, if not the actual self-portrait painted by Copernicus himself, at least a copy of a sketch made by the multitalented astronomer. There is as well a handsome woodcut by Stimmer, which, like the Strasbourg image, shows Copernicus holding a lily of the valley, a Renaissance symbol for a medical doctor.
Wood-block portrait of Copernicus attributed to Tobias Stimmer. The lily of the valley is the standard early Renaissance icon for a medical doctor.
Part of the American reparations went to establish the Tobias Stimmer Foundation, to help the museum in Schaffhausen acquire substitutes for their irreplaceable treasures. Among the pieces that survived the bombing is a curious sixteenth-century wooden instrument with a movable dial that can be used to calculate lunar phases. Some years ago the museum was able to purchase with the Stimmer Foundation funds the unique copy of the explanatory booklet that belongs with the instrument, and subsequently the foundation asked if I could provide a commentary to the book and instrument. I swiftly agreed, for there was a second reason I wished to visit Schaffhausen: The library next door to the museum (apparently undamaged in the raid) holds one of the most important copies of Copernicus' De revolutionibus. Thus, in a roundabout way, the American bombing of Schaffhausen in 1944 paid for my visit there in 1987.
The City Library sits in the charming medieval centrum of Schaffhausen. It is not large enough to support a rare book librarian. To see the Copernicus, I had to ask in the children's department, but I was allowed to take the book into the main reading room. There I opened it with some reverence. As an annotated copy, it is second only to the Reinhold volume that had precipitated the entire Copernicus chase, for it was thoroughly annotated by Michael Maestlin, a leading astronomer of the sixteenth and early seventeenth centuries, and Johannes Kepler's teacher. It was not the first time I had seen the book. I had examined and photographed it in 1972, and the library had provided a microfilm. The annotations were as fascinating as they were frustrating to read. The ink had partly faded, and still more troublesome, Maestlin wrote with an incredibly minuscule hand, so in many places, even using the microfilm, I could scarcely read what he had written. It required a firsthand examination to decipher some of the key marginalia.
Maestlin had been born in 1550, seven years after the publication of De revolutionibus, in Goppingen, a village about thirty miles east of Tubingen where he spent most of his professional career. As was the case with many young scholars including Kepler, his most famous student, he did his undergraduate studies at a preparatory school and came to the university to take his final exams and pick up his baccalaureate degree. Then he enrolled for the master's degree followed by the theological program, because Tubingen University's primary mission was to prepare young men for the Lutheran ministry. Thus educated, he was sent off in 1576 as an assistant pastor to Backnang, a post about twenty miles northwest of Goppingen. His time there was rather like that of young people today who serve in the Peace Corps before taking up their intended careers.
Michael Maestlin at age twenty-eight, from his Ephemerides novae (Tubingen, 1580), author's collection.
Maestlin's real talent lay in astronomy, and while a master's student he had invested in his copy of De revolutionibus. At age twenty-one, he had edited a new edition of Reinhold's Prutenic Tables, that set of numbers based on Copernicus to be used for computing planetary positions. While pastoring at Backnang, he published his observations of the Great Comet of 1577; like Tycho Brahe, he showed that the comet lay beyond the Moon, contrary to the accepted teachings of Aristotle. So it was only a matter of fulfilling his service appointment before he could move on, finally, at the age of thirty, to a mathematics professorship at Heidelberg, where he published the first of seven editions of his basic astronomy textbook. Four years later, in 1584, he received the call back to Tubingen.
As I sat with his De revolutionibus in the Schaffhausen library, I marveled at the multiple layers of annotations in the copy that demonstrated the lengthiest active use by a single owner. Inside the front cover was a hand-colored bookplate with a coat of arms, dating from 1584, when he had been recalled to Tubingen. But on the title page was an earlier inscription, "Ex libris M Michaelis Maestlini Goeppingensis Anno Domini 1570," and inside the back cover was a note saying that he had obtained the book from the widow of Victorin Strigel for one and a half florins. Strigel had been a student at Wittenberg, had founded the school that later became the University of Jena, and had gone on to become professor of theology at Leipzig, where he wrote an astronomy textbook. Elsewhere in the volume Maestlin's notes cite the third edition of De revolutionibus, which was published in 1617, and furthermore, the places censored or altered in 1620 by the Vatican Congregation of the Index were indicated with red emphasis marks. From 1570 to 1620—fifty years of annotating!
In the margins near the beginning of the book Maesdin penned a unique appreciation of what Copernicus had accomplished. No other copy of De revolutionibus contains anything comparable. Maestlin pointed out that "the arrangement presented in this book is the sort of structure in which all the sidereal motions and phenomena are explained very exactly. Therefore this hypothesis recommends itself to the intellect." Maestlin went on to comment that he thought many others would also agree with Copernicus' ideas if they hadn't been convinced long before that the Earth didn't move. Copernicus wasn't just playing a clever game, he wrote.
The heavenly motions were at the point of collapse, and so he concluded that appropriate hypotheses were needed to explain these motions. When he noticed that the common hypotheses were insufficient, he eventually accepted the idea of the Earth's mobility, since indeed, it not only satisfied the phenomena very well but it didn't lead to anything absurd.
In fact, if anyone would straighten out the common hypotheses so that they would agree with the phenomena and allow no inconsistencies, then I would gratefully trust him; clearly he would bring very many to his views. But I see that some, even very outstanding mathematicians, have labored on this, yet, in the end, without results. Therefore, I think that unless the common hypotheses are reformed (a task that I am not up to because of my inadequate abilities), I will accept the hypotheses and opinion of Copernicus—after Ptolemy, the prince of all Astronomers.
Because in his elementary astronomy textbook Maestlin presented only the geocentric arrangement, his complete commitment to the Copernican system has always seemed somewhat problematic. The statement near the beginning of his copy of Copernicus' book would dispel any doubts except for his repeated use of the word hypothesis. Today when the word hypothesis is used to describe a scientific concept (such as evolution), many people tend to mentally add the word mere, to make a pejorative mere hypothesis. Sixteenth-century astronomers, working in a very different intellectual framework, used the word in a very different way. They generally viewed astronomy as a geometric (rather than physical) science, and the hypotheses were the geometric devices or arrangements used to explain celestial motions. Later on Maestlin would scold his student Kepler for dragging physics into astronomy, which he believed was inappropriate. So Maestlin may well have harbored reservations about the physical reality of the Copernican arrangement even while accepting that it was the best explanation for the planetary phenomena.
Toward the back of the book long notes in Maestlin's microscopic hand revealed that he tried to pursue a fiercely technical question that Copernicus had left hanging and which could potentially serve as another convincing (but subtle) argument for the heliocentric arrangement. Copernicus had referred all of the planetary motions not to a fixed Sun but to the center of the Earth's orbit. This would have made little difference except that Copernicus had noticed that the distance between the Sun and the center of the Earth's orbit had diminished since Ptolemy's day. If the center of the Earth's orbit were the true center of the universe, then it wouldn't make any difference with the planets' orbits if the Sun bobbled back and forth with respect to Earth's orbit. On the other hand, if the Sun was the truly fixed reference point for the planets' orbits, then their own centerings would change over time as seen from the hobbling center of the Earth's orbit. So Maestlin set out to see if he could establish this effect. Had he been able to find it, there would have been one further connection between the Sun and the planets, a fine argument for the centrality of the Sun in understanding the planetary arrangement. But he failed, not for any shortcoming with his mathematical technique but because Ptolemy's observations were not accurate enough for the required comparison.
Maestlin's annotations, like Reinhold's, were thick in the technical, later sections of De revolutionibus. But unlike Reinhold, Maestlin also had some very cogent remarks about the front matter of the book; in fact, they are the most fascinating front-end comments in any extant copy. At the very beginning, above the anonymous introduction to the reader, the multiple layering of notes exhibits itself. Maestlin started off by saying, "This preface was added by someone, whoever its author may be, (for indeed, its weakness of style and choice of words reveal that it is not by Copernicus)."*
On the top margin of the facing page Maestlin added another note.
NB: Concerning this letter, I found the following words written somewhere among the books of Philipp Apian (which I bought from his widow); although no author was given I could recognize Apian's hand:
On account of this letter Georg Joachim Rheticus, the Leipzig professor and disciple of Copernicus, became involved in a very bitter wrangle with the printer, who asserted that it had been turned over to him with the rest of the work. Rheticus, however, suspected that Osiander [the proofreader of Copernicus' book] had prefaced it to the work. If he knew this for certain, he declared, he would handle that fellow so that in the future he would mind his own business and not slander astronomers any more. Nevertheless [Peter] Apian told me that Osiander had openly admitted to him that he had added this all by himself.
It took me some later detective work to sort out the origin of this confusing note—confusing because more than one Apian is mentioned. I realized that both Philipp Apian and his more famous father, Peter Apian, were involved in Maestlin's note after I discovered another copy of the quoted passage in Munich. The De revolutionibus in the Bavarian capital had been there since 1571, whereas the copy of the note that Maestlin had seen (not necessarily in a copy of Copernicus' book) was in his hands after 1589, when Philipp Apian had died. So here is how I reconstruct the story. Peter Apian, a well-known author and astronomy professor at Ingolstadt north of Munich, got the information about the anonymous introduction straight from Osiander himself and mentioned it to a colleague, who noted it in his copy of De revolutionibus. At some point the young Philipp Apian saw the note, probably after his father had died in 1552, and he made a verbatim copy of it. The original De revolutionibus containing the note was acquired by the banker Johann Jacob Fugger, who had it rebound (thereby trimming off part of the note). In 1571, when he was bankrupted by his passion for books, Fugger sold the De revolutionibus to Duke Albrecht V of Bavaria, founder of the library in Munich, where it has been ever since. Philipp Apian's copy has disappeared, but what is probably the original, as well as Maestlin's third-hand transcription, both survive.
This was not the end of the Osiander story, however, for Maestlin wrote a third, terse comment above the anonymous introduction: "NB: I know for sure that the author of this letter was Andreas Osiander (plate 7f)." What made him so sure? The answer revolves around Maestlin's most famous student, the primary reason that Maestlin himself is remembered today.
LIKE MAESTLIN, Johannes Kepler was born near Tubingen, studied in a preparatory school before going to the university to study for his master's degree, and then went into the theological program, fully expecting to become a Lutheran clergyman. When, instead, he was sent out to be a mathematics and astronomy teacher, he complained that nothing had indicated that he had a special talent for astronomy. In evidence, he was a straight A student except in astronomy, where he got an A-.* Nevertheless, astronomy was in his background. Kepler recalled that, when he was six years old, his mother had shown him the Comet of 1577. Also, he may very well have inherited his De revolutionibus through his family, possibly from a Nuremberg bookseller named Kepner, who may have been an ancestor.
I remember vividly the circumstances when I first saw Kepler's copy in Leipzig in 1972, the same field trip that had originally taken us to Schaffhausen. It was the first time Miriam and I had penetrated deep into East Germany beyond East Berlin. The country was a drab police state, but with scattered friendly though apprehensive persons cautiously willing to make contact with the outside world. Since we had got behind the iron curtain, I was keen to see the Wittenberg archives and to find any traces of Erasmus Reinhold, which was what made the trip particularly memorable. But first we had to attend to Leipzig.
Edition Leipzig was a major East German publishing house eager to bring in hard currency through splendidly printed art books and reproductions of library treasures. One of the great typographical triumphs of the sixteenth century, printed just three years before De revolutionibus, was Peter Apian's Astronomicum Caesareum—literally, "Astronomy for the Emperor," and the princely book Tycho had glowingly inscribed to Wittich. It was a giant folio with astronomical diagrams full of rotating parts, brilliantly hand colored. The most complex set of volvelles, seven layers deep, served as an analog computer to simulate the Ptolemaic epicyclic theory for finding the longitude of the planet Mercury. Edition Leipzig used a disassembled copy from the library in Gotha to make a spectacular facsimile. Unfortunately, while its facsimile was a typographical tour de force, the actual assembly of the moving parts was thoroughly botched, with some volvelles on the wrong pages and others pasted down so they wouldn't turn properly. On the pages of the Journal for the History of Astronomy I had called attention to this misassembly, and subsequently Edition Leipzig had invited me for a consultation.
I explained to my hosts that in addition to trying to figure out what to do about the faulty facsimile,* I hoped to explore the Wittenberg University archive. In response they broke the news that the famous old University of Wittenberg no longer existed. It had long since been combined with the university in Halle. And there was another problem. As the editors pointed out, our East German visa was good only for the Leipzig circle, and if we drove over to Halle, we would be dangerously conspicuous. They offered instead to send us over to Halle the following day by train with one of their assistants, thinking that no one would then notice.
The assistant was enormously pleased to accompany us to Halle. On that particular day the radical American activist Angela Davis was in Leipzig for a rally, and each company had a quota of employees obliged to turn out for the demonstration. The young assistant who accompanied us to Halle had been assigned as a "volunteer" to attend the rally, something she did not relish, so she was delighted to be escorting us instead. We were surprised at how freely she made her sentiments known, in English, on the train.
In Halle we got a warm welcome. The university library's copy of Copernicus' book had been missing for some time, but the librarian was eager to show us some of their other rarities. The crown jewel was the dean's book from sixteenth-century Wittenberg. I immediately recognized the clear, neat hand of Erasmus Reinhold. The deanship had been a bureaucratic office passed quickly around from one teacher to another, but because Reinhold's handwriting was so legible, some of the other deans asked him to do the honors. A pair of special lectures recorded in Reinhold's hand jumped out, one by Reinhold himself on astronomical hypotheses, and the other "Against the Anabaptists." Since I come from a long line of Anabaptists, this topic particularly resonated with me. I had brought along my Nikon, but I had only color film. This was the only time I've made a microfilm on Ektachrome.
Back in Leipzig I naturally went to see both the Astronomicum Caesareum and the first-edition De revolutionibus in the university library. I was especially thrilled to see Kepler's Copernicus, but in retrospect I missed several of the most important points. Since Edition Leipzig had already issued a facsimile of the book, I wasn't surprised to see on the flyleaf Kepler's Latin translation of a long Greek poem by the Leipzig humanist Joachim Camerarius, nor did I have a sudden burst of insight when I saw Osiander's name written above the anonymous introduction, the Ad lectorem. What Edition Leipzig had not included in its facsimile, quite rightly as it turned out, was an old inscription concerning the earliest copy of Copernicus' book acquired by the university. It had been clipped out of the original copy when it was sent out for auction as a duplicate, and hence it was an important document for the history of De revolutionibus in general, and so I was keen to see it even though it was totally irrelevant to Kepler's copy in particular.
What I failed to photograph were two annotations that attracted my attention only after I began to understand the layering of the annotations in the book. Most, but not all, of the marginal annotations are in Kepler's hand. Many small interlinear corrections are in the hand of its original owner, Jerome Schreiber, who had received the book as a gift from the printer, as he noted in a corner of the title page. Schreiber was from Nuremberg but studied at Wittenberg and was for a while a mathematics teacher there. He was an insider, so to say. That turned out to be quite important, because when I eventually examined those corrections more carefully in my copy of the facsimile, I discovered something curious. Where as the corrections in the first three-quarters of the book came directly from the printed errata leaf that accompanied some copies, the corrections continued to the very end, well beyond where the errata leaf left off. After I discovered this same extended errata set in a few more copies, I realized that the insiders had access to a more complete list than the printer Petreius had supplied to his customers.
After I saw the extended errata marked in several copies, I caught on that a marginal note on folio 96 was connected with these corrections, although it was simply a comment and not a correction. At that point in the text Copernicus was considering what was the true fixed center of the cosmos. Was it the Sun itself, or was it the center of the Earth's orbit? Because Copernicus believed that the stars were in a distant spherical shell, the question was whether the Earth's annual round, the "great orbit" as Copernicus put it, was neatly centered with respect to the stars (thereby putting the Sun slightly off-center), or whether the Sun itself was dead centered so that the Earth was closer to the starry shell in January than in June. If the Sun was the hub of the universe, Copernicus truly had a heliocentric system. If the hub was the center of the Earth's orbit, eccentrically offset from the nearby fixed Sun, it was a heliostatic system. This was an unresolved mystery in the book, for Copernicus hedged on the issue. However, the marginal note in a few of the copies indicated that Rheticus' Narratio prima said more. The one in Schreiber's hand reads (in Latin, of course), "These are in the Narratio of Joachim [Rheticus]. For in this work they are omitted." In fact, the Narratio prima did not discuss the question explicitly but simply assumed throughout that the Sun itself was the center of the universe.
What follows is an exercise in minutiae, but one that ultimately offers a most intriguing insight into Kepler's student-teacher relationship with Michael Maestlin. Below Schreiber's note is another, looking at first glance very much like Kepler's hand, yet clearly distinct from Kepler's annotations elsewhere in the book. In fact, I believe it matches Michael Maestlin's hand more closely than Kepler's.* It is not the minuscule writing that characterizes the notes in Maestlin's own De revolutionibus, but very much like the handwriting in his letters to Kepler. The note states, "What can be accepted about this question is that from Book V they make either the sun fixed or else the centers of all the planets slightly displaced with it." Maestlin not only wrote a very similar comment at the same place in his Schaffhausen copy but also marked places in Book V corresponding to his statement in Kepler's copy.
Why do I get excited about something as esoteric as this? Because the presence of this little note tells us that Kepler showed his copy to his teacher, and that's why Maestlin was so sure it was Osiander who had written the anonymous introduction to Copernicus' book. There it was in Kepler's copy, in black and white, coming straight from Schreiber, a Wittenberg insider. More than that, Maestlin's little annotation suggests that he and Kepler specifically discussed this point, what was the hub of the universe. And on the day when Kepler went to work for Tycho Brahe in 1600, his notebook shows that the very first task in his research program was to adjust the orbit of Mars so that it referred to the Sun rather than to the empty point that happened to be the center of the Earth's orbit. This became an essential part of Kepler's physical approach, and a fundamental principle that led to his successful reworking of the heliocentric details. It was presaged by that fateful student-teacher conversation at Tubingen.
Kepler is most famous for discovering the elliptical shape of the planetary orbits, and so another of the marginal comments
also seems highly relevant. On folio 143 there appears the single Greek word 
— that is, ellipse—together with the same sort of emphasis marks that Schreiber used to highlight the passage on folio 96.
Marginal annotations by Jerome Schreiber and Michael Maestlin (folio 96, left) and Johannes Kepler (folio 143, right).
When I first saw that book in Leipzig, I assumed that it was Kepler who had written 
in the margin, and I hadn't made a color slide of it. Later, when I had discovered more information about the double layer
of annotations and the evidence that it was likely Schreiber's handiwork, I had to worry about which one wrote it. Handwriting
comparison didn't help because it was in Greek letters, not Latin. I decided I had better go back to Leipzig for a close scrutiny
of the ink, only to learn that the book was away on exhibition. Eventually I obtained excellent color transparencies, which
left no doubt that it was indeed Schreiber's ink in the book Kepler had inherited.
Did this single, crucial word give Kepler the clue for his greatest discovery? And was Copernicus himself on the scent of the planetary ellipses? The fact that we can definitively answer the second question with a resounding "No!" comes as a considerable surprise to many of my colleagues.
I N 1985 A Louisville Seminary theologian named Harold Nebelsick published a fascinating but wrongheaded book entitled Circles of God. He made the provocative claim that the requirement of using circles and only circles to explain celestial motions was a theological invention of the ancient Greeks and a bad idea that had held astronomy in thrall for two millennia. Included in his contention was the insinuation that Copernicus had failed because he stuck with circles, not noticing that the orbits of the planets were really ellipses. But there was no way Copernicus could have found the ellipse, because the observations he had weren't nearly accurate enough.
That there is a problem becomes very clear if you draw an ellipse corresponding to the orbit of Mars. Take an ordinary piece of letter paper, put two tacks in about an inch and a half apart to represent the foci of the ellipse, then loop a string around them to guide the pencil using the page to its fullest, and you will get an ellipse. If you then draw the corresponding circle (with a radius of nearly four inches), you will be hard put to tell which is the ellipse and which is the circle, because the difference is about the width of the pencil line. Naturally astronomy textbooks don't show it this way, because they can't make the point about ellipses unless they enormously exaggerate the eccentricity of the ellipse. So for centuries, beginning with Kepler himself, a false impression has been created about the elliptical shape of planetary orbits. The eccentricity of planetary orbits (that is, their off-centeredness) is quite noticeable—even Ptolemy had to cope with that—but the ellipticity (the degree the figure bows in at the sides) is very subtle indeed. Observations of Mars must be accurate to a few minutes of arc for this tiny ellipticity to reveal itself. This is near to the limit of naked-eye acuity, and such observations simply weren't available to Copernicus or any of his predecessors. Not until Tycho Brahe's massive and precise observational campaign was the requisite data bank available, and within fifteen years of that availability, Kepler, with Tycho's record books in hand, found the elliptical compression of the orbit.
What about that passage in De revolutionibus, the place where Schreiber had written ellipsis in the margin? Could Copernicus have been on the trail of the ellipse? The Polish astronomer realized that when he replaced the Ptolemaic equant with a small epicyclet, the resulting path would not be exactly circular. In fact, though he never said so explicitly, the combination of deferent and epicyclet produced an ellipse. But it's a wrong ellipse, one that bowed out where the correct ellipse bows in. Copernicus' curve was an artifact of his model and had nothing to do with the true trajectory of the planet. Still, it's very romantic to speculate that the Greek word Schreiber penned in the margin had some subliminal power of suggestion on Kepler.
Copernicus, like Ptolemy centuries earlier, used very few observations to establish the parameters of the planet's orbit. He was no doubt blissfully unaware that for a brief period every seventeen years both his and Ptolemy's predictions for Mars went horribly wrong. For Ptolemy, Mars lagged behind the predictions by five degrees; for Copernicus, the ruddy planet went ahead by about four degrees. Apparently Kepler was the first person to comment on this, and he probably noticed it only after he had corrected the orbit of Mars for other reasons.
When I first became aware of this anomaly, I assumed it was caused by some erroneously chosen constant that entered into the calculations. Eventually I tried tweaking the numbers used in the model. The results proved very disconcerting. While I could make the error go away in one place, it always popped up somewhere else. Clearly there was a fundamental defect in the model itself, and it couldn't just be the lack of an ellipse.
Copernicus failed in this matter not because he hadn't caught on about the ellipse but because he wasn't Copernican enough. It was Kepler who remarked, in a slightly different context, that Copernicus was unaware of his own riches. If Copernicus had really believed that the Earth was just one of several planets, he should have treated them all the same. That would have been the "Copernican" thing to do. But Ptolemy hadn't used an equant for the Sun, and therefore Copernicus didn't use his equant substitute for the Earth. (The Earth and the Sun are the two celestial objects at opposite ends of the connecting line, and the mathematics works the same way regardless of which end of the stick is considered the stationary reference point.) The bottom line: In the Ptolemaic system the Sun moved around its circle at a constant speed—it just looked as if it moved at different speeds because that circle was eccentric to the earth. Likewise in the Copernican system the Earth moved around its circle at a constant speed—the Sun just looked as if it moved at different speeds because it wasn't at the center of the Earth's circle.
And this, Kepler believed, had to be wrong. If Mercury, the planet closest to the Sun, moved fastest, and Saturn, the most distant planet, moved slowest, then this was because Mercury, being closer, soaked up more of the Sun's motive power and thus naturally moved faster. But in winter the Earth was closer to the Sun than in summer, and Kepler reasoned that it should actually be going faster in its orbit in winter. That was physics, and Kepler, as the world's first astro-physicist, worked out the consequences. Maestlin rapped his student on the knuckles for that. He wrote to Kepler, "I think that one should leave physical causes out of the account, and should explain astronomical matters only according to the astronomical method with the aid of astronomical, not physical, causes and hypotheses. That is, the calculation demands astronomical bases in the field of geometry and arithmetic."
But Kepler persisted. He had to adjust the position of the Earth's orbit to make it work, and when he did, the periodic five-degree error in the Mars predictions just melted away. That was the biggest single correction that Kepler made in predicting the positions of the planets, and he doesn't get much credit for it because the astronomers who later selected three of Kepler's discoveries and numbered them as three laws (perhaps to match Newton's three laws) simply passed over this one as being too obvious.
Even before he made this discovery, Kepler found a tricky way to calculate, quite accurately, the longitude of Mars as it went in orbit around the Sun. But when he tried to locate Mars as seen from the Earth, he ran into trouble. The calculation that worked so well in tracking the east-west motion of Mars around the sky simply wouldn't work for Mars's north-south deviations in latitude. When he fixed that, he ended up with a maximum error of around half a degree. This was already ten times better than Ptolemy or Copernicus had achieved, but it wasn't good enough for Kepler because it didn't match Tycho's excellent observations. He could have used a jury-rigged, physically inconsistent scheme to get the longitudes almost five times better (or fifty times better than Copernicus' maximum error), but to Kepler that lacked reality because it didn't give correct latitudes, and unlike his teacher, he was a thoroughgoing realist. Kepler tried an ellipse, not quite the right one, as an approximating curve. And then came a moment of truth. "Oh ridiculous me!" he wrote. "I could not find out why the planet would rather go on an elliptical orbit. . . . With reasons agreeing with experience, there is no figure left for the orbit of the planet except a perfect ellipse."
Had he got the clue from that little marginal note in his De revolutionibus? I doubt it, but who knows what pathway triggered his imagination?
The ellipse would have been hard for Copernicus to accept because he was so thoroughly committed to the principle that celestial motions should be explained in terms of uniform, circular motion, but in the end he surely would have approved the quest for a physically real system.
* Ever since reading that, I've wished I could read Latin well enough to make such a judgment. Considering that its author misled a great many readers into supposing that the introduction was by Copernicus himself, I have to assume that it takes a particularly astute and perceptive critic to detect such nuances.
* In the Tubingen grade reports, a capital A was an A, and a lowercase a was an A.
* Edition Leipzig agreed to print a repair kit for the Astronomicum Caesareum, but abandoned the project when so few buyers caught on that something of this sort was needed. Since then I have used the color proofs of its aborted repair project to correct more than a dozen copies—typically requiring nearly eight hours of work on each one—and I have distributed repair kits to about a dozen other owners.
* ln fairness to full disclosure, I have to say that two of Germany's leading experts on Kepler's hand are fully convinced that I'm wrong, but their opinion does not come to terms with the fact that such a similar annotation also appears in Maestlin's De revolutionibus. Clearly there is a close connection between the two notes, which both begin with the identical words Quae de hac quaestione . . . possunf, it would be exceedingly odd if Kepler copied just part of the annotations and nothing else from his teacher's book. The most distinctive handwriting feature of the short nore is the way the tall s and t are joined in the word quaestione. I searched many pages of Kepler's manuscripts and found that he used such a combination only very occasionally. For Maestlin the conjoined letters are frequent, including in his own name, with a closely matching appearance.