COPERNICUS DAY 27 TYCHO BRAHE S SEMI-HELIOCENTRIC MODEL

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1 COPERNICUS DAY 27 TYCHO BRAHE S SEMI-HELIOCENTRIC MODEL We are now transitioning to the thought of Copernicus. Oddly, however, a very good way to transition to the heliocentric vision of Copernicus is by way of the semi-heliocentric model of Tycho Brahe, who came after Copernicus. Although this is a bit out of historical order, Brahe s model really is a halfway house from full-blown Ptolemaic geocentrism to full-blown Copernican heliocentrism. So here in Day 27, we will spend a little bit of time on this transitional figure. THE FASCINATING AND STRANGE TYCHO BRAHE Tycho Brahe was a Danish astronomer who lived from 1546 to Though that may make him sound boring, he was really anything but. He was born the only son to a pair of high-ranking Danish aristocrats who for some reason (possibly drunkenness) promised to hand him over to the husband s childless brother. When Tycho was born, however, his parents showed no intention of handing him over, and the brother said nothing, so they just kept him until he turned two, that is, and the brother swooped in and claimed him. Strangely, the parents did not put up a fight, but handed the boy over. It doesn t do for aristocrats to go back on their word, apparently. And so Tycho was moved from one castle to another. Tycho s uncle (and foster father) Jørgen Brahe intended for Tycho to study law and philosophy, but a solar eclipse in 1560 inspired him to become an astronomer instead. While he was at the universities of Copenhagen and Leipzig, whenever his tutor dozed off, he would put down his law books and observe the stars. In those early days he had no more equipment than a globe and a pair of compasses, but that was sufficient to enable him to detect significant errors in the Alfonsine and Prutenic tables then used for developing the calendar, and to correct them. When he was 20 years old, Brahe got into a mathematical disagreement with another Danish aristocrat by the name of Manderup Parsbjerg. Naturally, this led to a duel in which Brahe lost a good chunk of his nose. For the remainder of his life he wore a prosthetic one made of metal. It was for a long time thought to be gold, and possibly he did have a golden fake nose, but apparently when his body was exhumed in the 20 th century the nose with which he had been buried turned out to be copper. That is odd, since he was certainly wealthy enough to have a gold nose (as we shall see). Some have speculated that a copper nose would be much lighter, and therefore more comfortable than a golden one. Or did someone steal his gold nose just prior to his burial? No one knows. 1

2 Tycho Brahe discovered a new star, as we read in Arthur Koestler s Sleepwalkers: On the evening of 11 November, 1572, Tycho was walking from Steen s alchemist laboratory back to supper when, glancing at the sky, he saw a star brighter than Venus at her brightest, in a place where no star had been before. The place was a little to the north-west of the familiar W the constellation of Cassiopeia, which then stood near the Zenith. The sight was so incredible that he literally did not believe his eyes; he called at first some servants, and then several peasants to confirm the fact there really was a star where no star had any business to be. It was there all right, and so bright that later on people with sharp eyes could see it even in the middle of the day. And it remained in the same spot for 18 months. It was, in fact, a supernova. Unlike a comet, it stayed in the same spot every night among the stars. Publishing and lecturing on this new star won Tycho immediate fame as an astronomer, and he was in high demand everywhere. The King of Denmark and Norway, Frederick II, wanted to keep this prize at home, however, and managed to do so basically by giving Brahe an enormous bribe. In return for serving as the court astrologer, Brahe would have the island of Hven for his own on which to build an observatory and a castle, and he would also have money enough to equip these as he saw fit. The total amount of money going his way is estimated to have been about 5% of Denmark s GNP at the time Not bad. Brahe accepted this arrangement, and in 1576 built the castle of Uraniborg ( fortress of the heavens ). The place had a large number of furnaces for conducting other kinds of experiments, too, chemical and medical. It was something of a prototype for European research centers. As the telescope had not yet been invented, Tycho was still conducting naked-eye astronomy, but taken to the limit. He spared no expense in having made gigantic and very finely made instruments to assist in his observations of the heavens. For twenty years Brahe made his observations there. When King Frederick II died, however, his 19-year-old son, Christian, took the throne, and for some reason Brahe fell entirely out of favor. Some people believe that Brahe had had an affair with Frederick s wife, Christian s mother, and that this was known to Christian. Some people even suspect that Brahe was murdered. He died at a banquet, supposedly of a bladder problem, but when his body was exhumed traces of mercury were found on the body. Was the mercury something he had been medicating himself with for a long time? Or something he inhaled during his chemical experiments? Or was it put into his cup at his last supper? No one knows for certain. Some have speculated that Brahe was part of the inspiration for Shakespeare s Hamlet. A Danish adulterer with the queen, a young and vengeful heir to the throne, and mercury poisoning. Whatever the cause, when his first patron died in 1588, Tycho fell out of favor, and all his former privileges were revoked. Christian IV even withdrew the precious observatory from Brahe, although it could hardly have been put to better use in anyone else s hands (except perhaps Kepler s). But the Holy Roman Emperor invited Brahe in 1597 to build a new Uraniborg (and to live on a pension of 3000 ducats) upon an estate near Prague, in Benatky nad Jizerou. Brahe died before it was completed. Brahe himself was married to a commoner, by whom he had eight children. He kept an elk as a pet. Once, while it was away paying some sort of visit to another aristocrat, it got drunk on beer, fell down a set of stairs, and died. Brahe also had a little person as a court jester whose name was Jepp, whom Brahe believed to be clairvoyant. 2

3 Brahe s moustache was apparently quite long and eccentric. The odd details of his life seem to be endless. Interesting as these are, we are more interested in his work. Some of Brahe s writings are De Nova Stella ( Concerning the New Star, 1573), Epistolae Astronomicae ( Astronomical Epistles, 1596), and Astronomiae Instauratae Mechanica (a work in which Brahe describes his equipment, 1598). Johannes Kepler served as Brahe s assistant in the years 1600 and When Brahe died, Kepler took full advantage of the confusion and more or less stole Brahe s records of astronomical data. In life, Brahe had been extremely possessive of this data, and did not even permit Kepler to look through it freely. (Some people have speculated that Kepler murdered Brahe for the data but there is no real evidence of that.) Kepler thus came into possession of many tables of extremely precise data with which to compute the true orbit of Mars, and with which he would discover that the planets move on elliptical paths. Brahe s obsession with precise observations, and the later fruit of this arduous labor in the discoveries of Kepler, ushered in the age of precision in astronomical measurement. Brahe took this as far as naked eye astronomy could go. He determined the length of the solar period to within less than a second, which led to the abandonment of the Julian calendar in favor of the Gregorian. Kepler was familiar with Brahe s precision and accuracy, and took Tycho s observations as infallible and unquestionable. If Brahe s observations disagreed with the Ptolemaic hypothesis by one arc-second, that meant the Ptolemaic hypothesis was simply wrong. For now, however, we are mainly interested in Brahe s own model of the planetary motions. Tycho Brahe never accepted the Copernican model, in which the planets, including Earth, all go round the sun. Brahe instead supposed that the planets all revolve around the mean sun, while the mean sun orbits an immobile Earth. This theory was made possible by supposing that the mean sun was inside the epicycles of the inner planets (Venus and Mercury) and also inside the moving eccentrics of the outer planets (Mars, Jupiter, and Saturn). 3

4 FIXED STARS SATURN JUPITER MARS V E N U S SUN M E RCURY M O O N EARTH THE SEMI- HELIOCENTRIC HYPOTHESIS Note the following in this diagram of Brahe s Semi-Heliocentric Hypothesis: The moon goes around the Earth. The planets all move on epicycles which go around the mean sun at their common center. The inner planets are on same-direction epicycles which are smaller than the deferent, i.e. than the sun s orbit around the Earth. The outer planets are on opposite-direction epicycles which are larger than the deferent, i.e. than the sun s orbit around the Earth hence they can also be thought of as moving eccentrics spinning about the Earth. The Earth is inside the epicycles of Mars, Jupiter, and Saturn, and so these are really moving eccentrics for us, and so the stars must move on these in the opposite direction of the eccentrics themselves. Earth remains immobile and at the center of the universe. The planetary orbits are drawn roughly to scale (but the sphere of fixed stars is drastically diminished to fit it onto the page). 4

5 How do the speeds S, L, A enter in? The epicycles of Venus & Mercury move with longitudinal speed L = S, and each moves on its epicycle with speed A. The eccentrics of Mars, Jupiter, Saturn move with speed S = L + A, and each moves backward on its eccentric with speed A. COMPARISON TO PTOLEMY. What is new in the diagram? How does it differ from Ptolemy? Really there is only one feature distinguishing this model from the Ptolemaic system: The sun (i.e. the mean sun) is inside all the epicycles, i.e. the sun is at the center of all planetary orbits. Perhaps there is also this: Ptolemy never really presented us with a single diagram of the universe as he understood it. This is partly because he saw that there were equivalent models for each of the motions, and partly because he did not know for sure where to place the sun in the order of the spheres. But surely it is desirable to have a picture of the universe! Brahe is providing us with one here. ADVANTAGES. Unlike the Ptolemaic universe, the Brahean is unified. All the planets (except Earth, which to them was not a planet) are orbiting the sun, rather than making epicycles at unspecified distances from Earth. And since the sun orbits Earth, the Earth-Sun distance becomes a common element in every planetary model, enabling us to compare all the distances to one another. DISADVANTAGES. Brahe still has everything orbiting the Mean sun, a mathematical fiction. It is not easy to conceive of a physics that would account for these motions: Why are so many things going around the sun? Is it because it is so big and influential? Then why isn t the Earth going around it? 5

6 If we make one slight change, and say the Earth is orbiting the sun, and it is the sun that is sitting still, then we get the diagram below, i.e. the full-blown heliocentric and Copernican model, where everything orbits the sun in concentric circles and in the same direction! And the epicycles of Venus & Mercury become mere orbits. As to the appearances, these two models can be made perfectly equivalent. The diagrams themselves seem to have already made a powerful argument in favor of Copernicus already. FIXED STARS SATURN JUPITER MARS A E R T H V E N US & M E RCUR Y M O O N SUN THE HELIOCENTRIC HYPOTHESIS 6