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"Astronomical Scrapbook" from SKY AND TELESCOPE , August, 1982
DREYER AND TYCHO S WORLD SYSTEM by OWEN GINGERICH
Harvard- Smithsonian Center for Astrophysics

THERE is a Persian fairy tale in which the three princes of Serendip have such a marvelous propensity for making accidental diseoveries that, ever since the mid-18th century, the word serendipity has referred to the aptitude for, or process of, making happy, unexpected discoveries. Not only in science, but also in historical research, an unexpected answer can turn up to a question not even being asked! Last month I described my frustrated endeavor to find Henry Norris Russell's original version of his famous diagram, a search that led ultirnately to the 694th dinner of the Royal Astronomical Society Club in London on June 13, 1913, and to the after-dinner remarks by Russell and J. L. E. Dreyer.

J. L. E. Dreyer (1852- 1926). In addition to being a respected historian of science and compiler of the famous New General Catalogue, he was director of Armagh Observatory from 1882 to 1916. After graduating from Copenhagen University, he worked at Lord Rosse's observatory at Birr Cast1e where he observed with the great 6 - foot speculum mirror. This portrait is from the Mary Lea Shane Archives of Lick Observatory. All other illustrations with this article were supplied by the author.

Although Dreyer made his astronomical reputation by editing the New General Catalogue of Nebulae and Clusters, he repeatedly returned to the original texts and manuscripts of his illustrious Danish predecessor. In 1890 he published Tycho Brahe, a Picture of Scientific Life and Work in the Sixteenth Century, which remains to this day the standard biography of Tycho. One of the puzzles facing any Tycho scholar is to decide why Tycho rejected both the ancient Ptolemaic system and the radical new Copernican system, only to settle on a composite scheme.

In the Tychonic system the Earth remained safely at rest while the Sun, orbited by all the other planets, cycled around the Earth. Part of the reason for adopting this new arrangement was that Tycho, a self-assured egotist, wanted to promulgate a system of his very own. But Tycho was also an excellent scientist, and he sought some satisfactory observationa1 reasons as well. In the 16th century, there was no unambiguous observational way to decide between the Ptolemaic and Copernican systems. In these alternative models, predictions concerning the directions of planetary rnotion were essentially the same, but they differed a great deal with respect to the distances of the planets. For example, in the Ptolemaic arrangement Venus was always closer than the Sun and Mars farther than the Sun (see the diagram)

In each of the solar systern models depicted here, the directions (angles) to the Sun and Mars are identical, but the distances are quite different. In Ptolemy's epicyclic system, Earth is always closer to the Sun than to Mars; this is not the case according to Copernicus concept.

.Quite the contrary was true for the Copernican system. The problern was that no one had been able to rneasure the distances to the planets with any accuracy. Tycho realized that a good distanee measurement could distinguish between the two systems, and he set out to do this in an ingenious way, by measuring the positions of Mars both in the morning and in the evening.

According to the Copernican system, the Earth would rotate in those 12 hours, carrying the observer an Earthdiameter around and thereby giving a new position from which to sight Mars. Tycho set to work and soon claimed to find a measurable parallax for Mars, making it closer than the Sun, and hence ruling out the possibility of the Ptolemaic system.

To a rnodern reader who knows that the so called horizontal parallax of Mars can at most reach 23 arc seconds, Tycho's resu1t was, in Dreyer's words, "a surprising statement", because the quantity was much too srnall for Tycho to measure with his naked-eye instruments. The statement was equally puzzling to Johannes Kepler, who vainly sought to find the Martian parallax from Tycho's observational data. Kepler, in fact, proposed another and stronger geometrical configuration for finding the distance to Mars, but unfortunately Tycho had not provided any measurements under these circumstances.

Consequently, Kepler decided to attempt the observations himself: "This will treat you to a ridiculous spectacle", he wrote in describing his attempts. "In 1604, when I was considering the parallax, an occasion presented itself, which would have been rnore convenient in another climate".

Kepler said this because the February night was so cold that his bare hands stuck to the iron of the sextant, and with gloves it was impossible to get the clamps set securely. Furthermore, strong winds ruled out the use of lamps - the scales could be read only by the light of a glowing coal. " I would be insane to rely on these observations for anything so subt1e", Kepler admitted. "I hope that my readers, on account of their distaste for these uncertain things, will all the more seek out the surety of Tycho's observations".

However, neither Kepler's or Tycho's observations could settle such a delicate matter, and Kepler sought some explanation as to why Tycho had thought that his data had established Mars' distance. In searching through Tycho's record books, Kepler found that Tycho had assigned the calculations to his students. "But behold an unexpected thing!" wrote Kepler in Chapter 11 of his Astronomia nova. The student assistants, instead of computing the effect of the rotation of the Earth in establishing a baseline for a triangulation to Mars, had actually made an elaborate Copernican calculation and necessarily discovered that Mars at planetary opposition is closer than the Sun! "Thus Brahe had intended one thing, but his assistants carried out another. What was desired was for the morning and evening observations to be compared among themselves in order to investigate the parallax of Mars, but what they really investigated was how much parallax the Copernican diagram had. Whether it was just from trust in his assistants that Brahe made his pronouncement about the parallax, I do not know."

In his biography of Tycho, Dreyer paraphrased Kepler's remarks and let the matter rest. The obvious conclusion would be that Tycho rejected the Ptolemaic system for totally spurious reasons. However, by the time of the 1913 RAS Club dinner, Dreyer had examined Tycho's manuscripts more thoroughly and had found something overlooked by Kepler.

Dreyer discovered among the Tycho papers in the Austrian National Library in Vienna another copy of the Copernican calcu1ations, but they were in Tycho's own hand, not that of an assistant.

In other words, Tycho himself had also done the Copernican calculation, and contrary to Kepler's deduction, it was not an unwarranted trust io his assistants that had led Tycho to a rejection of the Ptolemaic system.

In his own personal copy of the Tycho biography, Dreyer wrote "Nonsense" alongside his citation of Kepler's opinion. Why, then, did Tycho reject the Ptolernaic systern? Popular accounts often credit the Comet of 1577, on the grounds that its movernent through the heavens would kave smashed the crystal spheres that held the Ptolemaic arrangement in place. The chronology of events suggests, however, that this was an afterthought, because Tycho himself indicates that he got the idea for his own planetary arrangement in 1583, at the time he was intensively studying the opposition of Mars.

In investigating the question, Dreyer concluded that the apparition of Mars was indeed the catalyst for Tycho's thinking, and he reasoned that the speed of Mars' retrogression provided the answer. The Sun moves across the sky at about one degree per day, Mars at about half a degree on the average. In the first few days of 1583, however, Mars was moving retrograde by nearly ha1f a degree per day.

Tycho's Copernican notes, which are labeled "Concerning the distance to Mars from the Earth around an opposition, according to Copernicus," and which derives the distance for January 17, 1583, showed Tycho that this motion would be possible only if Mars came closer than the Sun.

Dreyer also knew that the great Danish astronomer repeatedly rnentioned in his correspondence that he had tried hard to find the distance to Mars, and in a 1588 letter to the Wittenberg professor Caspar Peucer, he explicitly mentioned the daily motion of Mars as leading to the solution. Dreyer described his findings in the Latin prologue to his magnificent multivolume set of Tycho Brahe's "Complete Works."

The prologue was dated "Armagh, May, 1913," which rneans that he had just completed the first volurne of this Opera omnia when he spoke at the RAS Club. This explanation of the road to the Tychonic system still leaves one crucial point hanging.

In any model of the planetary system in which the orbit of Mars goes around the Sun - either the Copernican or Tychonic arrangement - the ratio of the average Sun - Mars and Sun - Earth distances must be about 1.5 2:1. Therefore, at opposition Mars will, on the average, approach the Earth to a proportional distance of 0.52, and thus be closer thao the Sun. But the Ptolemaic scheme, in which Mars moves on a large epicycle forever beyond the Sun, can also reproduce the observed positions, and none of Tycho's observations could disprove this model. Not until Galileo's telescopic examination of Venus, made about 30 years later, was there any direct observationa1 proof against the Pto1emaic arrangement.

Hence, despite Tycho's apparent belief that he had established his cosmologica1 system on observational grounds, he had actually taken a rnajor unproved intuitive leap in accepting a circumsolar orbit for Mars. Although Kepler erred in interpreting the Copernican diagram he found among Tycho's papers, he was correct in noticing that indeed Tycho had not been able to establish the distance to Mars empirically; hence, Tycho did not have a logica1 observational basis for rejecting the Ptolemaic system; but I would maintain that such intuitive leaps, often not strictly logical, are probably the most natural way in which creative science progresses.

As a bold and imaginative scientist, Tycho had dropped the Ptolemaic system in favor of a scheme more unified by its circumsolar orbits. And while his geo-heliocentric arrangement did not stand the test of time, it actually helped to bridge the way to the New Astronomy of Kepler.

Twelve volumes were published during his lifetime, and he left essentially complete manuscripts for the fina1 two volumes. His remarkable astronomical library was sold by the London bookseller Henry Sotheran (Catalogue 804), and Dreyer's annotated copy of his biography Tycho Brahe was item 231. The book passed into the hands of the English physicist E. N. da C. Andrade and subsequently into my own collection. Tycho Brahe was reprinted by Dover and, more recently, by Peter Smith; it will eventually be superseded by the forthcoming biography by Victor Thoren.