Tycho Brahe

Brahe was a Danish nobleman who carried out observations from 1576 to 1597 at his castle observatory Uraniborg on the island of Hveen between Denmark and Sweden. As a result of a dispute with the King of Denmark, he moved, at the end of 1597, to Prague to become court astrologer to the Emperor Rudolph II. He was assisted in the last years of his life by the young astronomer Johannes Kepler, who took possession of Tycho's treasure of observations when the latter died unexpectedly of a bladder infection in 1601.

In November of 1572 a new star appeared in the constellation Cassiopeia in the northern night sky. The star shone brightly for a month and then began to fade, disappearing from view altogether by March. The appearance of the star created a sensation in Europe, where it was regarded as an omen of great import for the affairs of man. Although the new star partook of the daily motion of the heavens, it was not clear whether it was an atmospheric phenomenon located in the sublunary sphere relatively close to the Earth or whether it was indeed a genuine celestial object. According to Aristotelian doctrine, the world beyond the Moon was eternal and changeless, a point of view that implied comets must be atmospheric. Tycho made a careful series of observations of the position of the new star throughout the night in order to determine whether it exhibited any diurnal parallax. The latter is a small shift in the apparent position of an object that occurs within a 24-hour period. (For an explanation of diurnal parallax, see chapter 2. Diurnal parallax is an effect that occurs in both a geocentric and heliocentric system.) The size of diurnal parallax decreases with distance from the Earth; it has the value of about one degree for the Moon and is indiscernible to the naked eye for the planets and Sun. In the case of the star of 1572 Tycho could detect no diurnal parallax nor indeed any change in position whatsoever of the new star with respect to the surrounding stars of Cassiopeia. It followed that the new star was located in the heavens some substantial distance beyond the Moon, an intruder in the celestial realm more like a star than a planet.

Tycho's new star was what became known in later astronomy as a nova, a star that undergoes a large change in brightness over a fairly short time period as a result of internal instability. Tycho suggested that the new star was something that had condensed from the surrounding matter of the Milky Way and even identified a dark spot nearby as its place of origin. Although this explanation was only speculative, the identification of the celestial character of the star was the first step in arriving at a scientific understanding of this class of objects.

Tycho applied the same technique of close observation four years later to a bright comet that blazed across the night sky. Tycho observed the comet during the three months it was visible and concluded that it showed no detectible parallax. This was a more difficult finding than the one for the 1572 nova because the comet actually moved across the celestial sphere, and it was necessary to show that any shift in position was due to this motion alone and not to parallax. Having established the superlunary character of the comet, Tycho charted its position on the celestial sphere and concluded that it was in orbit about the Sun. Over the next decade Tycho pondered the subject of the comet of 1777 and another comet of 1780. He consulted the writings on this subject of other astronomers, most notably Michael Maestlin, who had also derived a heliocentric orbit for the 1777 comet. The results of Tycho's investigation were published in 1588 in the book Recent Phenomena of the Celestial World.

In addition to his studies of new stars and comets, Tycho made several other fundamental contributions to observational astronomy. The large instruments that he had built for his observatory at Hveen and his skill in their use permitted a level of accuracy of observation hitherto unknown in astronomy. He showed that precession takes place at a constant rate, revealing the unsoundness of the doctrine of trepidation that had caused so much trouble for earlier astronomers. In his study of the motion of the Moon he identified the irregularity in its motion that is called the variation. He prepared a new star catalog with coordinates of the stars accurate to within three minutes of arc. His detailed observations of the positions of the planets would provide crucial data for Kepler's subsequent research and became the basis for Kepler's Rudolphine tables, published in 1627.

Tycho had used the Prutenic tables at a fairly early stage in his study of astronomy and lectured on Copernican astronomy in 1574 at the University of Copenhagen. Although he praised Copernicus as an astronomer, he could not accept the Copernican system. His opposition to the heliocentric idea was expressed in his correspondence with the German astronomer Christoph Rothmann, the latter himself a firm believer in the Copernican system. Tycho gave the usual common-sense physical objections to a moving Earth such as the change that should occur but is not observed in the range of a canon depending on whether it is fired to the west or to the east on a rotating Earth. He also cited astronomical, cosmological, and religious reasons. If in fact the Earth revolved about the Sun, then one would expect to observe what is known as annual parallax: at two times six months apart, when the Earth is at opposite ends of a line through the Sun, there will be a shift in the apparent direction of the stars. The size of this shift will depend on the distance of the stars relative to the distance of the Earth from the Sun. Tycho, following Ptolemy, placed the fixed stars just beyond the orbit of Saturn, not unreasonably believing that some parallax should be observed. Indeed, speculation since the time of Ptolemy accorded substantial values to the diameters of the stars, a line of thinking in keeping with a belief in their proximity to the planetary system. The observed absence of stellar parallax meant that in a Copernican universe, there must be a very large space between the orbit of Saturn and the celestial sphere. Such a wastage of space was scarcely in keeping with the handicraft of a divine creator, in Tycho's opinion. Finally, Tycho was convinced that the Copernican system was plainly contrary to the teachings of the Bible, a source from which he could cite multiple passages to support his position.

It should be noted that Tycho found much to admire in Copernicus's writings on technical astronomy. His admiration was influenced by what he regarded as the appropriate mathematical methods to be used in astronomy. He objected strongly to Ptolemy's use of the equant, the device in which the angular speed of the planetary epicycle is taken as constant with respect to a point slightly offset from the center of the deferent. He approved of Copernicus's move to eliminate the equant and replace it by alternate mechanisms, which mainly consisted of the introduction of secondary epicycles.

Having decided against Copernican cosmology, Tycho was also unable to uphold the traditional Ptolemaic system. Historians have suggested that his opposition to Ptolemy resulted from a desire to eliminate the equant from technical astronomy and that Tycho was led to his own system as a result of trying to adapt Copernican equant-less models to a geocentric theory. It has been conjectured (Westman 1975, 338) that such a goal motivated a whole generation of astronomers in the years following the publication of the Revolutions. A difficulty with this explanation is that Islamic astronomers had shown that it was possible to stay within the confines of Ptolemaic astronomy and do without the equant. There was no necessary connection between the technical goal of eliminating the equant and Tycho's decision to depart from Ptolemy and develop his own heliogeocentric system.

Tycho's comet studies gave him reason to find fault with Ptolemaic physical cosmology. In both the Almagest and the Planetary Hypotheses Ptolemy adhered in a fundamental way to a principle of planetary order, according to which each planet and that planet alone moved within a definite shell formed by two concentric spheres about the Earth. Ptolemy took Mars to be beyond the Sun in the planetary order, and so it followed that the distance from the Earth to the Sun was always less than the distance from the Earth to Mars. Furthermore, Ptolemy took the planetary spheres to be nested in such a way that there was no space between the spherical shells within which the planets moved. The most plausible explanation for Ptolemy's conception was that he believed the planetary spheres to be physical as well as mathematical objects. Tycho's demonstration that comets showed no diurnal parallax revealed that they were located beyond the sphere of the moon, and his study of their trajectories indicated that they were well within the orbit of Saturn. Evidently, comets must move across the zone of motion of the Sun, Moon, or one of the planets. It was impossible to avoid the conclusion that the material spheres of traditional astronomy did not in fact exist.

Tycho's ostensible reason for rejecting Ptolemy was based on difficulties he believed he had found with the relative distances of the Sun and planets in the Ptolemaic system. In both the Ptolemaic and Copernican systems the planet Mars is closest to the Earth when it is in opposition, 180 degrees opposite from the Sun in the sky. In the Ptolemaic system the sphere of Mars lies above the sphere of the Sun so that Mars is always more distant from the Earth than the Sun. Tycho accepted the traditional value for the solar parallax of three minutes, a value that indicated that the Sun was a fairly distant object from the Earth compared to the Moon. (Tycho was, of course, correct, even as he underestimated the size of the solar parallax by a good order of magnitude.) Through his observations in 1582—1583 of Mars while in opposition Tycho concluded that the parallax of Mars was larger than the Sun's, thus establishing that Mars at this time was definitely closer to the Earth than the Sun was. This finding was in plain contradiction with Ptolemy's ordering of the planets.

Brahe began to think about a third system of the world in the late 1570s and continued to work on the idea into the 1580s. He seems to have begun with the Ptolemaic system and then modified it in a series of steps in order to recover within a geocentric cosmology the advantages enjoyed by the Copernican system. He published the result of this investigation in his book of 1588. Like Ptolemy, he placed a stationary Earth at the center of the universe, around which revolve the Moon and the Sun. However, he followed Copernicus in assuming that the five planets revolve about the Sun as center so that each planet goes around the Sun as the Sun goes around the Earth (see figure 5.1). In the resulting geoheliocentric system the analysis of planetary motions is carried out along essentially Copernican lines but within a physical system predicated on a stationary Earth at the center.

In the Tychonic system the orbits of Mars and the Sun intersect, something that could not happen if they moved through the action of actual material spheres. Because Tycho had shown by his comet studies that the spheres do not exist, he was free to ignore this difficulty.

In upholding the tradition of an Earth-centered cosmos Tycho seemed to believe that evidence would be found in the class of new celestial objects that his observations had revealed comets to be. Certainly, the discovery of a sizeable number of Moon-like objects with geocentric orbits would strengthen the case for a geocentric cosmology. The difficulty here was that it was not a straightforward task to determine the orbit of a comet from a series of observations. In cases where Tycho succeeded in doing so, such as the comet of 1577, it was found that the comet's orbit was heliocentric. Tycho suggested that the absence of retrograde motion when the comets are in opposition was consistent with a geocentric orbit, but in the absence of detailed information about the nature of their orbits, such a consideration was hardly conclusive.

Tycho had shown that the motion of the planets cannot take place by means of the rotation of material and impenetrable spheres. Although this was surely his most important contribution to cosmology, he was not altogether consistent in his thinking on the subject. The primary objection to the equant was the fact that it was inconsistent with how a rigid sphere would rotate as it carries the epicycle around the deferent. Because Tycho had shown that such spheres apparently do not exist, this objection was no longer valid, and his own unwavering criticism of the equant seemed to lose much of its force.

The crucial event in Tycho's intellectual journey to the new cosmology was his putative discovery that the parallax of Mars at opposition is smaller than the parallax of the Sun. In fact, both values are an order of magnitude smaller than he believed them to be and are undetectable by even the most sophisticated instruments of naked-eye astronomy. It seems probable that Tycho, in

Figure 5.1: The Tychonic system.

a rather unconscious way, had come to see the plausibility of the Copernican system. For the purposes of positional astronomy the Tychonic system is simply the Copernican system as viewed from an observer on Earth. (When Kepler, a committed heliocentrist, carried out his analysis of the motion of Mars, he used a Tychonic reference system; the observations, after all, were made from the Earth, and the two systems, in this sense, are indistinguishable.) A number of writers of the period pointedly observed that Tycho's scheme was simply an "inverted Copernican" system. The heliocentrist Philip Landsberg suggested in 1632 that Tycho's scheme was "taken more from the diagram of Nicolaus Copernicus than from the heavens themselves" (Schofield 1981, 183). It is not surprising that the geoheliocentric idea occurred independently to several different authors following the publication of Revolutions in 1543. Tycho attributed physical meaning to his system and certainly believed in a geostatic cosmology, but this does not diminish the fact that the essential idea was taken from Copernicus.

The derivative character of the Tychonic system is illustrated by a diagram made by the young English astronomer Jeremiah Horrox (1619—1641) (see figure 5. 2). If one takes a diagram of the Copernican system and draws a circle with the Earth as center and the line from the Earth to the Sun as a radius, one is led to a diagram of the Tychonic system (figure 5.2). Another writer of the period, Otto von Guerricke (1602-1686), pointed out that one could take any of the planets as center, thus obtaining a Tychonic-type system corresponding to each planet (Schofield 1981, 408). Considerations of this sort revealed the inherent artificiality of the Tychonic system and its logical status as a frame-of-reference transformation of the Copernican system. Although Tycho believed that the Earth really was at rest at the center of the universe, it remained the case that any advantages his scheme enjoyed over Ptolemy's derived from its exact equivalence to the Copernican system.

During the last years of his life Tycho became embroiled in a priority dispute with one Nicholas Reymers Baer (d. 1600), better known by his Latin name, Ursus ("bear"). To the end of his life, Tycho believed that his geo-heliocentric cosmology was the most important thing he had done in science. Ursus published a book in which he developed a system very similar to Tycho's, with the exception that the Earth was allowed to rotate, and the orbit of Mars was placed outside the orbit of the Sun.

Figure 5.2: Tychonic and Semi-Tychonic World Systems. Figure from Schofield (1981, plate 16).

Ursus's book also contained some intemperate criticism of Tycho and other astronomers of the period. A bitter public dispute between Tycho and Ursus was ended only by the death of the latter in 1600. This episode has to be seen as a fairly odd quarrel given that the essential issue of priority concerned an idea which itself was derived from Copernicus.

Tycho's identification of the celestial character of novae and comets, his discovery of the lunar variation, his analysis of precession, the star catalog he compiled, and his detailed observations of planetary positions established him as one of the greatest observational astronomers of all time. His scientific career shows that it is possible to be a profound observationalist and an indifferent cosmologist. Despite its lack of originality, the Tychonic system was important in the history of cosmology for two reasons. First, Tycho freed cosmological theorizing from a belief in material spheres and the constraints imposed by the associated conception of simple clockwork-like production of planetary motion. Second, the Tychonic system allowed a form of disguised Copernicanism to flourish in an often hostile intellectual environment, allowing for a formal commitment to geocentric astronomy with the adoption of all the system-like advantages of the heliocentric theory.

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