Dec 142018

Today is the birthday (1546) of Tyge Ottesen Brahe, known in the English-speaking world as Tycho Brahe, a Danish nobleman, astronomer, and writer known for his accurate and comprehensive astronomical and planetary observations. He was born in the then-Danish (now Swedish) peninsula of Scania. His observations, done only with the naked eye before telescopes were available, were about five times more accurate than the best available observations at the time.

Tycho aspired to a level of accuracy in his estimated positions of celestial bodies of being consistently within a arcminute of their real celestial locations, and also claimed to have achieved this level. But, in fact, many of the stellar positions in his star catalogues were less accurate than that. To perform the huge number of multiplications needed to produce much of his astronomical data, Tycho relied heavily on a new technique called prosthaphaeresis, an algorithm for approximating products based on trigonometric identities that predated logarithms.

Although Tycho admired Copernicus and was the first to teach his theory in Denmark, he was unable to reconcile Copernican theory with the basic laws of Aristotelian physics, that he considered to be foundational. He was also critical of the observational data that Copernicus built his theory on, which he correctly considered to have a high margin of error. Instead, Tycho proposed a “geo-heliocentric” system in which the Sun and Moon orbited the Earth, while the other planets orbited the Sun. Tycho’s system had many of the same observational and computational advantages that Copernicus’ system had, and both systems could also accommodate the phases of Venus, although Galileo had yet to discover them. Tycho’s system provided a safe position for astronomers who were dissatisfied with older models but were reluctant to accept heliocentrism and the Earth’s motion. It gained a considerable following after 1616 when Rome declared that the heliocentric model was contrary to both philosophy and Scripture, and could be discussed only as a computational convenience that had no connection to fact. Tycho’s system also offered a major innovation: while both the purely geocentric model and the heliocentric model as set forth by Copernicus relied on the idea of transparent rotating crystalline spheres to carry the planets in their orbits, Tycho eliminated the spheres entirely. Kepler, as well as other Copernican astronomers, tried to persuade Tycho to adopt the heliocentric model of the solar system, but he was not persuaded. According to Tycho, the idea of a rotating and revolving Earth would be “in violation not only of all physical truth but also of the authority of Holy Scripture, which ought to be paramount.”

With respect to physics, Tycho held that the Earth was just too sluggish and heavy to be continuously in motion. According to the accepted Aristotelian physics of the time, the heavens (whose motions and cycles were continuous and unending) were made of “Aether” or “Quintessence.” This substance, not found on Earth, was light, strong, unchanging, and its natural state was circular motion. By contrast, the Earth (where objects seem to have motion only when moved) and things on it were composed of substances that were heavy and whose natural state was rest. Accordingly, Tycho said the Earth was a “lazy” body that was not readily moved. Thus while Tycho acknowledged that the daily rising and setting of the sun and stars could be explained by the Earth’s rotation, as Copernicus had said, he, nonetheless believed that, “such a fast motion could not belong to the earth, a body very heavy and dense and opaque, but rather belongs to the sky itself whose form and subtle and constant matter are better suited to a perpetual motion, however fast.”

With respect to the stars, Tycho also believed that, if the Earth orbited the Sun annually, there should be an observable stellar parallax over any period of six months, during which the angular orientation of a given star would change thanks to Earth’s changing position. (This parallax does exist, but is so small it was not detected until 1838, when Friedrich Bessel discovered a parallax of 0.314 arcseconds of the star 61 Cygni.) The Copernican explanation for this lack of parallax was that the stars were such a great distance from Earth that Earth’s orbit was almost insignificant by comparison. However, Tycho noted that this explanation introduced another problem: Stars as seen by the naked eye appear small, but of some size, with more prominent stars such as Vega appearing larger than lesser stars such as Polaris, which in turn appear larger than many others. Tycho had determined that a typical star measured approximately a minute of arc in size, with more prominent ones being two or three times as large. In writing to Christoph Rothmann, a Copernican astronomer, Tycho used basic geometry to show that, assuming a small parallax that just escaped detection, the distance to the stars in the Copernican system would have to be 700 times greater than the distance from the sun to Saturn. Moreover, the only way the stars could be so distant and still appear the sizes they do in the sky would be if even average stars were gigantic — at least as big as the orbit of the Earth, and of course vastly larger than the sun. And, Tycho said, the more prominent stars would have to be even larger still. And what if the parallax was even smaller than anyone thought, so the stars were yet more distant? Then they would all have to be even larger still. . . which, in fact, they are.

Kepler used Tycho’s records of the motion of Mars to deduce laws of planetary motion, enabling calculation of astronomical tables with unprecedented accuracy (the Rudolphine Tables) and providing powerful support for a heliocentric model of the solar system. Galileo’s 1610 telescopic discovery that Venus shows a full set of phases refuted the pure geocentric Ptolemaic model. After that it seems 17th-century astronomy mostly converted to geo-heliocentric planetary models that could explain these phases just as well as the heliocentric model could, but without the latter’s disadvantage of the failure to detect any annual stellar parallax that Tycho and others regarded as refuting it.

The three main geo-heliocentric models were the Tychonic, the Capellan with just Mercury and Venus orbiting the Sun such as favored by Francis Bacon, for example, and the extended Capellan model of Riccioli with Mars also orbiting the Sun whilst Saturn and Jupiter orbit the fixed Earth. But the Tychonic model was probably the most popular, albeit probably in what was known as ‘the semi-Tychonic’ version with a daily rotating Earth. This model was advocated by Tycho’s ex-assistant and disciple Longomontanus in his 1622 Astronomia Danica that was the intended completion of Tycho’s planetary model with his observational data, and which was regarded as the canonical statement of the complete Tychonic planetary system.

The ardent anti-heliocentric French astronomer Jean-Baptiste Morin devised a Tychonic planetary model with elliptical orbits published in 1650 in a simplified, Tychonic version of the Rudolphine Tables. Some acceptance of the Tychonic system persisted through the 17th century and in places until the early 18th century; it was supported (after a 1633 decree about the Copernican controversy) by “a flood of pro-Tycho literature” of Jesuit origin. Among pro-Tycho Jesuits, Ignace Pardies declared in 1691 that it was still the commonly accepted system, and Francesco Blanchinus reiterated that as late as 1728. Persistence of the Tychonic system, especially in Catholic countries, has been attributed to its satisfaction of a need (relative to Catholic doctrine) for “a safe synthesis of ancient and modern”. After 1670, even many Jesuit writers only thinly disguised their Copernicanism. But in Germany, the Netherlands, and England, the Tychonic system vanished from scientific literature much earlier.

No dish better suits the celebration of Tycho Brahe than spettekaka or spettkaka (spiddekaga in native Scanian) a dessert that originates in the province of Scania (Skåne) where he was born.  The name means “cake on a spit” which, as you will see from the video, exactly describes its production. A mixture consisting mainly of eggs, potato starch flour and sugar is squirted slowly on to a conical spit which is being rotated over an open fire or other heat source. So, a spinning dessert for an advocate of spinning bodies in space. Spettekaka can range in size anywhere from a few inches to several feet in height and over a foot in diameter. The very large cakes are served by sawing cuboids from the cake, leaving as much standing as possible. Spettekaka is frequently served accompanied by dark coffee, vanilla ice cream and port wine.

This video shows how spettekaka is made. Sorry it is in Swedish, but you’ll get the gist: