"Monk", Master and Mystic - Setting the Stage for a Revolution

For fifteen hundred years the Ptolemaic Model of the heavens, as expressed in the Almagest was the dominant authority on matters astronomical. This is remarkable. But the revision of the Ptolemaic Model under Alfonso X and the recognition that accumulating error was a serious problem for the accuracy of the Ptolemaic model set the stage for a profound revolution in science. The "circle dogma" and geocentricism of Plato, Aristotle and others inevitably began to crumble. Part of the impetus for this came from three of the most peculiar and dissimilar characters in the history of science. One was an obscure though mathematically talented church cleric, one was born of nobility and power but turned his back on all this to study astronomy and one was a mystic of exquisite mathematical genius.

The "Monk": Nicholas Copernicus (1473-1543)

First - Copernicus was not a monk but a canon and from the age of 24 worked as a church administrator. As a youth Copernicus studied the Almagest and was well acquainted with the Ptolemaic Model. Despite its ingenious use of geometrical contrivances and ability to accurately predict planetary positions, the Ptolemaic Model had a serious defect - it required periodic "tinkering" to reset the planetary positions and once again - for a while - provide accurate predictions. Using Ptolemy's and Hipparchus' tables Copernicus "resurrected" the heliocentric cosmology. He progressed back 2000 years to Aristarchus! Actually, the heliocentric model was never forgotten - it was merely disbelieved and to promote it as the truth could be construed as an attach on the authority of Scripture. Copernicus did not make a "clean" break with Ptolemy - he still retained the use of deferents and epicycles and fundamentally the idea that motion in the heavens was circular (the "circle dogma"). For this reason, his model was no more accurate than the Ptolemaic Model nor was it simpler.

Figure 4.11a Nicholas Copernicus

Figure 4.11b Nicholas Copernicus statue in old-square Warsaw (with rowdy tourist!)	Figure 4.11c Nicholas Copernicus statue at the Jagolinian University, Krackow

As early as 1514 Copernicus had written on the possibility of the heliocentric model. In 1517 the start of the Reformation made expressing any opinion that could be construed as a challenge to church authority dangerous. This extended to astronomy since the official church position was that of Aristotle and Ptolemy in this matter. It was not until the spring of 1543 and on his death bed that Copernicus published his most famous work - De Revolutionibus Orbium Coelestrium (The Revolutions of the Celestial Spheres).

This is the first European publication of the heliocentric model. However, Copernicus' failure to relinquish the idea that the planets and the moon must move in circular paths meant that his model was no more accurate than the Ptolemaic model. The real significance of Copernicus' model only makes sense when put in the context of who follows him.  
 

Tycho Brahe was born into the Danish nobility. He descended from rulers, diplomats and persons of wealth and power and is one of the most "quixotic" characters in all of science. Despite this, he turned his back on all this to pursue his passion for astronomy. Here is a brief summary of his astronomical life He was the last and perhaps greatest of the "naked-eye" astronomers. All of his work was done prior to the invention of the telescope. Using what are essential huge protractors, he produced the most precise tables of stellar and planetary motion and especially that of the planet Mars in his time.. In 1572 a supernova appeared in Cassiopeia.- a propitious event at a crucial time and his detailed and accurate charting of its position have helped modern astronomers locate the remnants of this object. In1576 Tycho Brahe received the island Hven from king Fredrik II and established Uranienborg - an astronomical "community" and the most sophisticated observatory in the world at that time.

Figure 4.12 Tycho Brahe

• This was a time of great political instability in Europe and, in 1597, Brahe loses royal support and leaves the island. Tycho goes to Wandsbech (near Hamburg) and then to Prague. Eventually, Emperor Rudolf II gives him the castle Benatky 30 km from Prague, but he later moves to a house in Prague from which he continues his observations.
• In 1600 Brahe makes a fateful decision - he hires a young German mathematician, Johannes Kepler, to assist him in analyzing his observations of the position of the planet Mars.
• In 1601 Brahe dies and Kepler, legend holds, writes down his last words: "Ne frustra vixisse videar" (May I not seemed to have lived in vain)

The Mystic: Johannes Kepler (1571-1630)

Who was Johannes Kepler? Consider these points: He was the most gifted mathematician of his time was also an active astrologer! (Its a living!). His mother was a "witch"! He was probably the only person capable of using Brahe's observations to their full potential. Eventually he broke free from the Platonic "circular dogma". Kepler's work as an "astrologer" and the accusation that his mother "was a witch" should tell you something about the time in which he lived. This was still a "pre-scientific" society and belief in witchcraft and astrology was still common. Casting horoscopes was a form of income for Kepler. The accusation of witchcraft could be brought against people for the flimsiest of reasons. In Kepler's own account, his mother's quarrelsome disposition, her knowledge of herbs and belief in magical potions was probably sufficient!

Figure 4.13 Johannes Kepler

  Kepler is an odd figure - a blend of "hopeless mystic" and profound mathematical genius. His two greatest works Mysterium Cosmographicum (Mystery of the Universe) and Harmonice Mundi (Harmony of the World) are blends of mystic ramblings occasionally punctuated by deep mathematical insights into the nature of planetary motion. In the next section we will explore his discoveries in more detail. For the moment, however, by carefully cobbling together his discoveries on the nature of planetary motion we can attribute 3 fundamental laws that now are associated with Kepler's name:
 

1. Planets move in ellipses, the sun at one focal point: This finally broke the "spell" of the circle dogma. By understanding that planets could move in elliptical orbits Kepler was able to predict planetary positions with unprecedented accuracy.
2. Planets sweep out equal areas in equal times: In this law Kepler is providing a way of quantifying the change in speed of a planet as it sweeps around the sun. This was also a break from a previously held belief that planets moved with a constant speed.
3. The period of an orbit squared is proportional to the radius of the orbit cubed: This is one of the first examples of a precise mathematical statement of a "physical" law.

Kepler's last and perhaps greatest work was the 1627 publication of the Rudolphine Tables. In these tables Kepler presented predicted positions of the known planets with a precision 10 to 100 greater than any previous table. This was a clear demonstration of his remarkable discoveries concerning the nature of planetary motion.