As stated earlier the predominant medieval view of the cosmos was an uneasy bundle of Aristotle’s cosmology, Ptolemaic astronomy, Aristotelian terrestrial mechanics, which was not Aristotle’s but had evolved out of it, and Aristotle’s celestial mechanics, which we will look at in a moment. As also pointed out earlier this was not a static view but one that was constantly being challenged from various other models. In the early seventeenth century the central problem was, having demolished nearly all of Aristotle’s cosmology and shown Ptolemaic astronomy to be defective, without however yet having found a totally convincing successor, to now find replacements for the terrestrial and celestial mechanics. We have looked at the development of the foundations for a new terrestrial mechanics and it is now time to turn to the problem of a new celestial mechanics. The first question we need to answer is what did Aristotle’s celestial mechanics look like and why was it no longer viable?
The homocentric astronomy in which everything in the heavens revolve around a single central point, the earth, in spheres was created by the mathematician and astronomer Eudoxus of Cnidus (c. 390–c. 337 BCE), a contemporary and student of Plato (c. 428/27–348/47 BCE), who assigned a total of twenty-seven spheres to his system. Callippus (c. 370–c. 300 BCE) a student of Eudoxus added another seven spheres. Aristotle (384–322 BCE) took this model and added another twenty-two spheres. Whereas Eudoxus and Callippus both probably viewed this model as a purely mathematical construction to help determine planetary position, Aristotle seems to have viewed it as reality. To explain the movement of the planets Aristotle thought of his system being driven by friction. The outermost sphere, that of the fixed stars drove the outer most sphere of Saturn, which in turn drove the next sphere down in the system and so on all the way down to the Moon. According to Aristotle the outermost sphere was set in motion by the unmoved mover. This last aspect was what most appealed to the churchmen of the medieval universities, who identified the unmoved mover with the Christian God.
During the Middle Ages an aspect of vitalism was added to this model, with some believing that the planets had souls, which animated them. Another theory claimed that each planet had its own angel, who pushed it round its orbit. Not exactly my idea of heaven, pushing a planet around its orbit for all of eternity. Aristotelian cosmology said that the spheres were real and made of crystal. When, in the sixteenth century astronomers came to accept that comets were supralunar celestial phenomena, and not as Aristotle had thought sublunar meteorological ones, it effectively killed off Aristotle’s crystalline spheres, as a supralunar comet would crash right through them. If fact, the existence or non-existence of the crystalline spheres was a major cosmological debate in the sixteenth century. By the early seventeenth century almost nobody still believed in them.
An alternative theory that had its origins in the Middle Ages but, which was revived in the sixteenth century was that the heavens were fluid and the planets swam through them like a fish or flew threw them like a bird. This theory, of course, has again a strong element of vitalism. However, with the definitive collapse of the crystalline spheres it became quite popular and was subscribed to be some important and influential thinkers at the end of the sixteenth beginning of the seventeenth centuries, for example Roberto Bellarmino (1542–1621) the most important Jesuit theologian, who had lectured on astronomy at the University of Leuven in his younger days.
Robert Bellarmine artist unknown Source: Wikimedia Commons
It should come as no surprise that the first astronomer to suggest a halfway scientific explanation for the motion of the planets was Johannes Kepler. In fact he devoted quite a lot of space to his theories in his Astronomia nova (1609).
Astronomia Nova title page Source: Wikimedia Commons
That the periods between the equinoxes and the solstices were of unequal length had been known to astronomers since at least the time of Hipparchus in the second century BCE. This seemed to imply that the speed of either the Sun orbiting the Earth, in a geocentric model, or the Earth orbiting the Sun, in a heliocentric model, varied through out the year. Kepler calculated a table for his elliptical, heliocentric model of the distances of the Sun from the Earth and deduced from this that the Earth moved fastest when it was closest to the Sun and slowest when it was furthest away. From this he deduced or rather speculated that the Sun controlled the motion of the Earth and by analogy of all the planets. The thirty-third chapter of Astronomia nova is headed, The power that moves the planets resides in the body of the sun.
His next question is, of course, what is this power and how does it operate? He found his answer in William Gilbert’s (1544–1603) De Magnete, which had been published in 1600.
William Gilbert Source: Wikimedia Commons
Kepler speculated that the Sun was in fact a magnet, as Gilbert had demonstrated the Earth to be, and that it rotated on its axis in the same way that Gilbert believed, falsely, that a freely suspended terrella (a globe shaped magnet) did. Gilbert had used this false belief to explain the Earth’s diurnal rotation.
It should be pointed out that Kepler was hypothesising a diurnal rotation for the Sun in 1609 that is a couple of years before Galileo had demonstrated the Sun’s rotation in his dispute over the nature of sunspots with Christoph Scheiner (c. 1574–1650). He then argues that there is power that goes out from the rotating Sun that drives the planets around there orbits. This power diminishes with its distance from the Sun, which explains why the speed of the planetary orbits also diminishes the further the respective planets are from the Sun. In different sections of the Astronomia nova Kepler argues both for and against this power being magnetic in nature. It should also be noted that although Kepler is moving in the right direction with his convoluted and at times opaque ideas on planetary motion there is still an element of vitalism present in his thoughts.
Kepler conceived the relationship between his planetary motive force and distance as a simple inverse ratio but it inspired the idea of an inverse squared force. The French mathematician and astronomer Ismaël Boulliau (1605–1694) was a convinced Keplerian and played a central roll in spreading Kepler’s ideas throughout Europe.
Ismaël Boulliau portrait by Pieter van Schuppen Source: Wikimedia Commons
His most important and influential work was his Astronomia philolaica (1645). In this work Boulliau hypothesised by analogy to Kepler’s own law on the propagation of light that if a force existed going out from the Sun driving the planets then it would decrease in inverse squared ratio and not a simple one as hypothesised by Kepler. Interestingly Boulliau himself did not believe that such a motive force for the planet existed.
Another mathematician and astronomer, who looked for a scientific explanation of planetary motion was the Italian, Giovanni Alfonso Borelli (1608–1697) a student of Benedetto Castelli (1578–1643) and thus a second-generation student of Galileo.
Giovanni Alfonso Borelli Source: Wikimedia Commons
Borelli developed a force-based theory of planetary motion in his Theoricae Mediceorum Planatarum ex Causius Physicis Deductae (Theory [of the motion] of the Medicean planets [i.e. moons of Jupiter] deduced from physical causes) published in 1666. He hypothesised three forces that acted on a planet. Firstly a natural attraction of the planet towards the sun, secondly a force emanating from the rotating Sun that swept the planet sideway and kept it in its orbit and thirdly the same force emanating from the sun pushed the planet outwards balancing the inwards attraction.
The ideas of both Kepler and Borelli laid the foundations for a celestial mechanics that would eventually in the work of Isaac Newton, who knew of both theories, produced a purely force-based mathematical explanation of planetary motion.
The Renaissance Mathematicus 
Regarding Kepler’s vitalism, I feel like he considers vitalism in Astronomia Nova but ultimately rejects it. He talks about how hard it would be for the intelligence that moves a planet to keep the planet in an eccentric orbit around the Sun. A Sun-centered orbit is easy – just maintain a fixed distance from the Sun which could be done by keeping the Sun’s angular size fixed. But an eccentric orbit would be amazingly difficult and so, as I read it, Kepler abandons vitalism and instead seeks for a physical power to move the planets.
I think “This seemed to imply that the speed of either the Sun orbiting the Earth, in a geocentric model, or the Earth orbiting the Sun, in a heliocentric model, varied through out the year.” undersells Kepler’s accomplishment in that area. Nobody had given the Sun/Earth an equant before. The differences in the seasons were accomplished entirely with an eccentric. And my impression from the Mysterium is that Kepler believes the Earth should have an equant on philosophical grounds (because Earth is a planet and the other planets have equants) rather than because the data suggest it. Of course, when he actually tries it out in the Astronomia Nova he finds that it works extremely well to match Tycho’s data.
Yesterday I taught my class about Eudoxus’ model and gave them a brief introduction to Aristotle’s cosmology. It struck me bit then, and even more so on reading this post, that that was the last time physics and astronomy were truly unified until Newton. I wonder how much of the divorce between physics and astronomy (that the purpose of astronomy was only to “save the appearances” not to discern the true nature of the heavens) was motivated by the fact that they just couldn’t get the Eudoxan model to work very well. Then the Apollonian (and eventually Ptolemaic) model comes along and works very well, but really doesn’t fit with Aristotle’s physics.
Reblogged this on Die Goldene Landschaft.