Leonard Kelley holds a bachelor's in physics with a minor in mathematics. He loves the academic world and strives to constantly explore it.
Aristotelian Greek Viewpoints
Plato’s Phaedo offers one of the first recorded theories on how our solar system is organized, though the details are sparse. He credits Anaxagoras with the original theory which describes the Earth as an object in a huge celestial vortex. Sadly, this is all he mentions and no other work on the subject seems to have survived (Jaki 5-6).
Anaximander is the next known record, and he doesn’t mention vortices but instead refers to the distinction between hot and cold. Earth and the air around it are in a cold sphere which is surrounded by a hot “sphere of flame” which as initially closer to the Earth but slowly spread out and formed holes in the sphere where the sun, moon, and stars exist. Nowhere are planets even mentioned (6).
But Plato decided neither of these was right and instead turned to geometry to find some order that would provide insight into the Universe. He imagined the Universe as split by the sequence 1,2,3,4,8,9, and 27, where each was used as a length. Why these numbers? Note that 12 = 13 = 1, 22 = 4, 32 = 9, 23 = 8 and 33 = 27. Plato then set the Sun, moon, and planets at different lengths from us using these numbers. But what about the geometry? Plato argued that 4 of the perfect solids (the tetrahedron, the cube, the octahedron, and the icosahedron) were responsible for the elements of fire, earth, air, and water while the 5th perfect solid (a dodecahedron) was responsible for whatever the heavens were made of (7).
Quite the creative guy, but he didn’t stop there. In his Republic, he mentions the “Pythagorean doctrine of the harmonies of the spheres” where if one finds musical ratios by comparing different sphere ratios, then maybe planetary periods exhibit these ratios. Plato felt this further demonstrated the perfection of the heavens (Ibid).
Post-Aristotelian Greek Viewpoints
Epicurus did not continue the geometrical arguments developed by Plato but instead gets into some deeper questions. Because temperature differences between hot and cold fluctuate, Epicurus argues that the growth and decay between them result in a finite world existing in an infinite Universe. He was aware of the vortex theory and did not care for it, for if true then the world would spiral outward and no longer be finite. Instead, he argues that those changes in temperature lead to an overall stability that prevents a vortex from forming. On top of that, the stars themselves provided a force that keeps us in our current location and not moving in any general direction. He doesn’t deny that other worlds could exist and in fact says they did but were lumped together into their current configuration because of that star force. Lucretius mentions this in his book De rerium natura (8-10).
Eudoxas’ model is the standard geocentric model with the Earth in the center of the Universe and everything else orbiting it in nice neat little circles, for they are a perfect shape reflecting the perfect cosmos. Not too long after this, Aristarchus of Samos presented his heliocentric model which instead fixed the sun as the center instead of the Earth. However, the ancients decided that this was not feasible, for if so then the Earth would have to be in motion and everything would fly off its surface. Besides, the stars didn’t exhibit parallax like thy should if we moved to opposite ends of the sun’s orbit. And the Earth as the center of the Universe reveals our uniqueness in the Universe (Fitzpatrick).
Now we get to a heavy hitter, whose impact on astronomy would be felt for over a millennium. In his book Tetrabibles, Ptolemy tried to tie astronomy and astrology together and show their interrelations. But this didn’t fully satisfy him. He wanted predictive power as to where the planets would go, and none of the prior work even addressed this. Using geometry, he felt like Plato that the heavens would reveal their secrets (Jaki 11).
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And so his most famous work Almagest came into being. Building upon the work of previous Greek mathematicians, Ptolemy mad use of the epicycle (the circle on a circle method of motion) and excentric (we moving about an imaginary deferent point as the deferent carried the epicycle) models to explain away the motions of the planets in geocentric model. And it was powerful, for it did predict their orbits incredibly well. But he realized that it did not necessarily reflect the reality of their orbits, so he examined this and wrote Planetary Hypotheses. In it, he explains how the Earth is at the center of the Universe. Ironically, he is critical of Aristarchus of Samos, who placed the Earth with the rest of the planets. Too bad for Samos, poor guy. Ptolemy kept going on after this critique by imaging spherical shells that contained a planets greatest distance from the Earth and the furthest. When fully imagined, it would be like a Russian nestling egg doll with Saturn’s shell touching the celestial sphere. However, Ptolemy had some problems with this model that he conveniently ignored. For example, Venus’ greatest distance from Earth was smaller than the smallest distance from the Sun to the Earth, violating the placement of both objects. Also, Mars’ greatest distance was seven times as large as its smallest, making it an oddly placed sphere (Jaki 11-12, Fitzpatrick).
Medieval and Renaissance Period Viewpoints
Oresine was one of the next to offer a new theory a couple of hundred years after Ptolemy. He envisioned a Universe which was brought out from nothing in a “perfect state” that acts like “clockwork.” The planets operate according to “mechanical laws” that were set by God, and throughout his work Oresine actually hinted that the then unknown conservation of momentum and also the changing nature of the Universe! (Jaki 13)
Nicholas of Cusa wrote his idea in De docta ignorantia, written in 1440. It would end up being the next big book of cosmology until the 17th century. In it, Cusa puts the Earth, planets, and stars on equal footing in an infinite spherical Universe representing an infinite God with a “circumference of which was nowhere and the center everywhere.” That is huge, for it actually hints at the relative nature of distance and time that we know Einstein formally discussed plus the homogentiality of the overall Universe. As for other celestial objects, Cusa claims they have solid cores which are surrounded by air (Ibid).
Giordano Bruno continued many of Cusa’s ideas but without much geometry in La cena de le coneu (1584). It too references an infinite Universe with stars that are “divine and eternal entities.” The Earth, however, rotates, orbits, pitches, yaws, and rolls just like a 3-D object. Though Bruno didn’t have any evidence for these claims, he ended up being right but at the time it was a huge heresy and he was burned at the stake for it (14).
Copernicus and the Heliocentric Model
We can see that the viewpoints on the Universe were slowly starting to drift from Ptolemaic ideals as the 16th century progressed. But the man who hit it home was Nicholas Copernicus, for he took a critical look at Ptolemy’s epicycles and pointed out their geometric flaws. Instead, Copernicus made a seemingly minor edit that rocked the world. Simply move the Sun to the center of the Universe and have the planets, including Earth, orbit it. This heliocentric Universe model gave better results than the geocentric Universe model, but we must note that it placed the Sun as the center of the Universe and therefore the theory itself had a flaw. But its impact was immediate. The church fought it for a brief time, but as more and more evidence piled up especially from the likes of Galileo and Kepler, the geocentric model slowly fell (14).
It did not stop some people from trying to come up with additional findings on the Copernican theory who were not qualified. Take Jean Bodin for example. In his Universe naturae theatrum (1595), he tried to fit the give perfect solids in between the Earth and the Sun. Using 576 as the Earth’s diameter, he noted that 576 = 242 and to add to its beauty is the sum of “orthogonals that are in the perfect solids.” The tetrahedron has 24, the cube also, the octahedron has 48, the dodecahedron has 360, and the icosahedron has 120. Of course, several problems plagued this work. No one had ever some up with that number for Earth’s diameter and Jean doesn’t even include the units of it. He just grasps for some relations he can find in a field he doesn’t even study. What was his specialty? “Political science, economics, and religious philosophy” (15).
Johannes Kepler, a student of Brahe, was not only more qualified (being an astronomer after all) but also a definite Copernican Theory man, but he wanted to know why where was only 6 planets and not more. So he turned to what he felt was the solution to unraveling the Universe, like many Greek astronomers before him: math. Throughout the summer of 1595 he explored several options in his hunt for clarity. He tried to see if a correlation between the planetary distance per period ration lined up with any arithmetic progression but none was to be found. His eureka moment would come on July 19 of that the same year when he looked at the conjunctions of Saturn and Jupiter. By plotting them on a circle he was able to see that they were separated by 111 degrees, which is close to 120 but not the same. But if Kepler drew 40 triangles that had a vertex of 9 degrees emanating from the center of the circle, then a planet would eventually hit the same spot again. The amount that this would fluctuate by caused a drift in the center of the circle, which therefore created an inner circle from the orbit. Kepler postulated that such circle would fit inside an equilateral triangle which itself would be inscribed in the orbit of the planet. But Kepler wondered if this would work for the other planets. He found that 2-D shapes didn’t work but if he went to the 5 perfect solids then they would fit inside the orbits of the 6 planets. What is amazing here is that he got the first combination he attempted to work. At 5 different shapes to nestle into each other, there are 5! = 120 different possibilities! (15-7).
So what was the layout of these shapes? Kepler had an octahedron between Mercury and Venus, an icosahedron between Venus and Earth, a dodecahedron between Earth and Mars, a tetrahedron between Mars and Jupiter, and a cube between Jupiter and Saturn. It was perfect to Kepler because it reflected upon a perfect God and His perfect creation. However, Kepler soon realized that the shapes would not perfectly fit but be a close fit. As he would later uncover, this was because of the elliptical shape of each planet’s orbit. Once known, the modern view of the solar system began to take hold, and we haven’t looked back since. But maybe we should… (17)
Fitzpatrick, Richard. Historical BackgroundFarside.ph.utexas.edu. University of Texas, Feb. 02, 2006. Web. 10 Oct. 2016.
Jaki, Stanley L. Planets and Planetarians: A History of Theories of the Origin of Planetary Systems. John Wiley & Sons Halsted Press, 1979: 5-17. Print.