The Brahe System

The Worth Library holds two works by the Danish astronomer, Tycho Brahe, 1546-1601, and a number of other texts which display the influence of the Brahe or Tychonic system of cosmography.

 

 Tycho Brahe, Epistolarum Astronomicarum libri (Frankfurt, 1610),
Portrait of Brahe plate.

As Christianson (2000) points out, in this woodcut portrait of Tycho Brahe by Jacques de Gheyn the iconography is very much that of a Renaissance noble astronomer. Brahe was very conscious of his noble lineage and his royal connections. Here we see him wearing the Danish Order of the Elephant on a double chain and in the arch framing him are the coats of arms of his sixteen great-great-grandparents, including the Swedish royal Vasa ‘Stormvase’ coat of arms on the right hand column. On either side of a brief note on his accomplishments is his motto ‘Non haberi sed esse’ (Not to seem but to be). The sentiment reflected his life’s work: he was dedicated to observing the stars in a bid to understand their true nature, rather than construct mathematical constructs. The impetus to Tycho’s astronomical career was the new star of 1572. He immediately attempted to take parallax calculations and in so doing proved that the new entity was not a comet (since the position and therefore the parallax calculations did not change). Furthermore, it was quite clearly beyond the supra-lunary realm: change had come to the Aristotelian cosmos. Fired by his findings Brahe eschewed the normal career path of a Danish nobleman and concentrated instead of building-up a huge collections of astronomical observations with which he would challenge both Ptolemaic and Copernican cosmological assumptions. In doing so he eventually created his own deceptively simple Tychonic system.

The Tychonic System

Tycho Brahe De Mundi Aetherei Recentioribus Phaenomenis (Frankfurt, 1610), p. 189.

In this diagram from Brahe’s De Mundi Aetherei Recentioribus Phaenomenis, first published at Uraniborg in 1588 and printed here in Worth’s 1610 two-volume edition of Brahe’s works (Frankfurt, 1610), we see that while Brahe agreed with Copernicus that the inferior and superior planets of Mercury, Venus, Mars, Jupiter and Saturn revolved around the Sun, rather than the Earth, he was unable to let go of the Ptolemaic supremacy of the Earth. He therefore argued that Copernicus was only half right – the planets orbited the Sun, but the Sun in turn orbited the Earth. Brahe’s system was attractive for two reasons: first, because it seemed an acceptable moderate stance between the Ptolemaic and Copernican systems; and secondly, because it was seemingly supported by the huge collection of astronomical observations undertaken by Tycho and his assistants from 1572 onwards.
The replacement of the position of the Earth with that of the Sun might at first look like inspired guesswork but, as Thoren (1990) makes clear, it was the result of a complex and sometimes bafflingly contradictory trajectory of observational results which lead to the first publication of the system in his De Mundi Aetherei Recentioribus Phaenomenis of 1588. The first step along the road seems to have been taken in the mid 1570s when he accepted the Capellan motion for the inferior planets: he referred to the possibility of Mercury and Venus orbiting the Sun in his report to the Danish king on the 1577 comet but he said nothing of the superior planets of Mars, Jupiter and Saturn. It is clear though that he was intent on testing the orbiting pattern of the next planet, Mars, to see if an observation of planetary parallax would disprove Copernicus or Ptolemy.

Brahe and the Parallax View of Mars

Brahe’s attempt to calculate the planetary parallax of Mars was based on two assumptions. His first assumption was that he could measure Mars’s planetary parallax. In this he was misled because he was basing his calculations on Ptolemy’s unfortunately erroneous calculation of a solar parallax of 3′. Working from this measure, Brahe figured out that he might just be able to measure the parallax of Mars. In fact, the correct solar parallax is 9″, not 3′, and Mars’s correct diurnal parallax at 27″ was far too small for even Brahe’s massive instruments at Stjerneborg to cope with. His second assumption – and his principal reason in 1582-83 for attempting observation of the Mars parallax – was that, according to the Ptolemaic system, when Mars was in opposition, its distance from Earth was greater than the Sun’s maximum distance from Earth. Conversely, if the Copernican system was correct, the distance of Mars should be smaller since Mars at opposition would be much closer to Earth than was the Sun. As Gingerich and Voelkel (1998) explain, by looking at the diurnal parallax of Mars – i.e. looking at the apparent difference in position when Mars was at zenith and on the horizon – a larger parallax measurement would be a sign that the Copernican system was right. Tycho’s initial attempts in 1582-83 at trying to solve this problem led him to conclude that the Copernican system must be wrong since he could find no noticeable parallax for Mars.

According to Brahe’s correspondence, the big breakthrough came in 1584 when he suddenly glimpsed the rudiments of his Tychonic system. True, there were problems to iron out: as the above diagram of his system makes clear, if all the planets bar the Earth orbited the Sun then the orbit of Mars was due to intersect the orbit of the Sun twice. In the Ptolemaic/Aristotelian system of solid orbs an intersection of orbits was a physical impossibility but Tycho argued that, far from proving his system incorrect, his system disproved the solidity of the orbs. For Tycho a far more serious problem was his earlier calculation of negligible parallax for Mars: in 1582-83 he had blithely accepted it as disproving the Copernican theory of the centrality of the Sun but now that very centrality (at least as far as the non-terrestrial planets were concerned) was central to his new system.

Brahe’s understanding of the Mars parallax issue is complex. Writing to Heinrich Brucaeus in 1584 he reported that he had found that Mars’s parallax was very small, certainly much smaller than it should have been if Copernicus was correct. Yet by 1588, writing to Caspar Peucer, Brahe, citing the same observations of 1582, declared that his tests proved a much greater parallax was visible. Exactly what caused this seismic change in his perception of his own results between 1584 and 1588 we do not know: Gingerich and Voelkel (1998) suggest that his later observations of Mars at Stjerneborg in 1587 were unfortunately interpreted in the light of an outdated and erroneous solar refraction table; Schofield (1981) argues for a simple mistaken memory; Blair (1990) points out that a null parallax for Mars in opposition to Earth which might have been attractive in 1583 when he was trying to disprove Copernicus, was, by 1588, considerably less so when it undermined his own geoheliocentric model. In any case, by 1588, Tycho had managed to convince himself that he had amassed sufficient proof for his new system.

Despite a boulderised version of his new system being plagiarised by Nicolai Reymers Ursus in 1584, Tycho had been loath to publish until he had solved these problems and but now in 1588 he set forth a brief sketch of his Tychonic system at part of Chapter VIII of his De Mundi aetherei recentioribus phaenomenis. This work, which not only examined the new star in Cassiopeia of 1572 but also the famous 1577 comet, had been some years in the making. Brahe felt that his observational work on both the nova and the comet, work which had demonstrated beyond doubt the celestial, as opposed to terrestrial, origin of both phenomena, proved not only that there could be change in the celestial sphere but also, by implication of the comet’s movements, that the old theory of the solidity of the orbs was no longer tenable.

The Influence of the Tychonic System

Though the relatively short outline in De Mundi aetherei recentioribus phaenomenis had been a hasty addition to a work which was primarily devoted to the 1572 nova and 1577 comet, the appeal of the Tychonic system was immediately apparent – though as Hellman argues (1963), perhaps not so immediately accepted. Certainly Tycho did his best to spread news of his discovery far and wide, using his academic friendship circle of astronomers, one of whom was the Jesuit astronomer Christoph Clavius. It was, however, nearly twenty years after his death in 1601 that his system received quasi-institutional backing from the Jesuits but when they did take it on board they realised the unique potential of the scheme for preserving the centrality of the Earth. Observations had made clear that the Ptolemaic system was no longer tenable but there was little desire in the Jesuit order for a wholehearted acceptance of Copernicanism – especially not after the papal decree of condemnation in 1616. It should also be kept in mind that the Jesuit response to Copernicanism and their support for the Tychonic system was not based on papal prohibitions alone but was also a result of seemingly impossible aspects of the Copernican system: as Gaugroger (2006) argues, the fact that a stellar parallax had never been observed – but which was a concomitant of the annual motion of the Earth – was viewed by many as just one of a number of problems with Copernicus’s argument for a moving Earth. The Tychonic scheme therefore allowed them an empirically tested, commonsense response to the rise of Copernicanism.

Jesuits were not the only astronomers attracted to the seeming simplicity of the Tychonic system. Another work in the Worth Library, by the Utrecht professor Jan Luyts, amply displays that the Tychonic system was alive and well in 1692, just ten years before Edward Worth graduated with a doctorate in medicine from the University of Utrecht, having studied at the renowned medical faculty at Leiden:

 

Jan Luyts, Astronomica institutio (Utrecht, 1692), title page.

The Brahe System

As time went by, the empirical testing of the system became more important than the system itself. Ironically it was not the Tychonic System that lived on in the imagination but another ‘system’ which I call here the ‘Brahe System’ to distinguish it from the cosmographical one. The foremost exponent of the system is undoubtedly Christianson (2000) who investigates what Brahe was doing on the small island of Hven in the period 1576 to 1597. The building of Uraniborg (‘Urania’s Castle’) and later another observatory at Stjerneborg, was only the beginning of a complex research project which has fascinated scholars since the seventeenth century. It is fair to say that Brahe himself, with the publication of his Astronomia instaurata mechanica (Wandsbek, 1598), his Epistolae astronomicae (Uraniborg, 1596) and his Astronomia instauratae progymnasmata (Prague, 1602) was the first to draw attention to this aspect of the Brahe system. His Astronomia instaurata mechanica (Wandsbek, 1598) in particular sought to explain what exactly Brahe had doing during his sojourn on Hven. The message was simple: what had been achieved on Hven could be replicated elsewhere – an important message for Brahe following his fall from royal favour in 1597 and his subsequent exile and search for a patron. It is one of the most skilfully presented astronomical works of the seventeenth century and as an appeal to the Emperor Rudolf II for patronage it was ultimately successful. Unfortunately for both Rudolf II and Brahe, the latter died too soon to replicate the glory that had been Uraniborg but his presence in Prague and the subsequent use of the fruits of Uraniborg, his observations, by Johannes Kepler, would form the bedrock of the Keplerian Revolution.

Uraniborg

Brahe had already taken massive amounts of observational data before the construction of Uraniborg but it was the ambitious scale of the latter which marked him out from other would be astronomers. In 1586 King Frederic II of Denmark granted him the small island of Hven in the Öresund Sound, on which to build an astronomical observatory. The following picture of Hven, taken from Jean Picard’s description of the island in 1680, makes plain the lack of habitation on the island which boasted only one church, St. Ibb’s, and the small village of Tuna.

Picard, Jean, Voyage d'Uranibourg, ou, Observations 
astronomiques faites en Dannemarck (Paris, 1680), 
plate of Hven.

What made Uraniborg and the underground observatory at Stjerneborg so important to modern astronomy was the total dedication of Brahe. Everything was geared towards astronomical research. In the literary advertisement for both himself and his research institute that he wrote in 1598, the Astronomia Instaurata Mechanica, (of which Worth had the second edition published at Nuremberg in 1602), Brahe was at pains to draw attention to the significance of his project. In a sense, there were two Brahe or Tychonic systems: one, his astronomical cosmography; the other the research structure underpinning it. What made Tycho’s cosmography all the more believable was that it was a product of Uraniborg, the astronomical institute par excellence in early modern Europe. It was here that mathematicians and astronomers across Europe congregated to discuss new sightings and it was here that Tycho established not only new methods of observations but also, crucially, new instruments with which to observe. It was here also that Tycho established a construction unit for his new instruments and a printing press with which to promulgate both the new methodology and the new findings. It was from Uraniborg that an expedition to Frombork (Copernicus’s Frauenburg) was sent to check on the latitude of Copernicus’s observations. No stone was left unturned by Brahe in his search of observational excellence.

Brahe’s 1602 map of Uraniborg
Brahe, Tycho, Astronomicae instaurata mechanica 
(Nurnberg, 1602) Sig H6r.

The illustration of Uraniborg’s many roofs reflects not only Tycho’s architectural extravangances but the very practical possibilities of his design: the wooden shutters of the towers could be easily uncovered so that observations from all angles could take place.

Brahe, Astronomicae instaurata mechanica (Nurnberg, 1602), Sig A6v.

The iconic image of the mural quadrant not only draws attention to Brahe and his huge wall quadrant but also to other aspects of Uraniborg: the alchemical experiments in the basement, the team work explored by Christianson (2000), so evident in the grouping of figures both in the ground floor depictions but also in the foreground, remind us that Brahe was not alone. Uraniborg was not just a day’s excursion for visiting royals and nobles in Copenhagen. Far more importantly it acted as a state funded research centre where Brahe was assisted by men such as Elias Olsen Morsing who had gone on the Frombork expedition.

When Brahe realised that his instruments, though certainly more accurate than others used elsewhere, were of insufficient magnitude he simply built Stjerneborg, thus allowing him yet greater possibilities.

Brahe 1602 map of Stjerneborg
Brahe, Tycho, Astronomicae instaurata mechanica (Nurnberg, 1602) I1r

It was following the building of the underground observatory at Stjerneborg that Brahe once again attempted his observation of the diurnal parallax of Mars which was so crucial for his system.

The continuing appeal of Uraniborg and Stjerneborg in the later seventeenth century may be seen in Worth’s edition of Jean Picard’s Voyage d’Uranibourg, ou, Observations astronomiques faites en Dannemarck (Paris, 1680). Picard, 1620-1682, had been a founding member of the Académie Royale des Sciences and in 1669 had proposed to the Académie that an expedition should be sent to Hven to check the coordinates so that Brahe’s observations between 1576 and 1597 could be compared with those of the Paris observatory. Picard was put in charge of the expedition which left in 1671. The decision of the Parisian observatory – at that point the leading astronomical observatory in Europe – to attempt in effect to re-connect with Brahe’s Hven is just one testimony among many to the abiding fascination for what Brahe had accomplished on that small island off the coast of Denmark. In England the Royal Greenwich Observatory, founded in 1675, followed a similar model while Chinese Jesuits exported the idea as far away as Beijing.

Selected Reading

Blair, A. (1990). ‘Tycho Brahe’s Critique of Copernicus and the Copernican System’, Journal of the History of Ideas, 51. no. 3, 355-377.
Christianson, J. R. (1979). ‘Tycho Brahe’s German Treatise on the Comet of 1577: A Study in Science and Politics’, Isis 70, no. 1, 110-140.
Christianson, J. R. (2000). On Tycho’s Island. Tycho Brahe and his assistants 1570-1601. Cambridge: Cambridge University Press.
Gaukroger, S. (2006). The Emergence of a Scientific Culture. Science and the Shaping of Modernity 1210-1685. Oxford: Oxford University Press.
Gingerich, O. And Voelkel, J. R. (1998). ‘Tycho Brahe’s Copernican Campaign’, Journal for the History of Astronomy, XXIX, 1-34.
Hellman, C. D. (1963). ‘Was Tycho Brahe as influential as he thought?’, The British Journal for the History of Science, 1 no. 4, 295-324.
Mosley, A. (2007). Bearing the Heavens. Tycho Brahe and the Astronomical Community of the late Sixteenth Century. Cambridge: Cambridge University Press.
Schofield, C. J. (1965). ‘The Geoheliocentric Mathematical Hypothesis in Sixteenth-Century Planetary Theory’, The British Journal for the History of Science 2 no. 8, 291-96.
Schofield, C. J. (1981). Tychonic and Semi-Tychonic World Systems. New York.
Taton, J. And Taton, R. (1974). ‘Picard, Jean (b. La Flèche, France, 21 July 1620; d. Paris, France, 12 October 1682), astronomy, geodesy’ in C. C. Gillespie (ed.) Dictionary of Scientific Biography. New York: Charles Scribner’s Sons.
Taton, R. And Wilson, C. (eds) (2003). Planetary astronomy from the Renaissance to the rise of astrophysics. Part A: Tycho Brahe to Newton. Cambridge: Cambridge University Press. The General History of Astronomy Series.
Thoren, V. E. (1990). The Lord of Uraniborg. A biography of Tycho Brahe. Cambridge: Cambridge University Press.