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Opus in profectus

Heliocentrism

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early

Aristarchus of Samos (310–230 BCE) Greece

However, Aristarchus' only remaining work on the topic, On the Sizes and Distances of the Sun and Moon, is geocentric!

Pythagoras of Samos (582–496 BCE) Greece

Copernicus

Nicolaus Copernicus (1473–1543) Poland (latinized version of Mikołaj Kopernik). De Revolutionibus Orbium Cœlestium (On the Revolutions of Heavenly Spheres) 1543.

In medio uero omnium residet Sol.   In the center of all rests the Sun.

Quotes

Notes

De Revolutionibus Orbium Cœlestium

How heliocentrism deals with retrograde motion.

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Bruno

Giordano Bruno (1548–1600) Italy (Naples)

Galileo

Galileo Galilei (1564–1642) Italy. Three big (as in important) books.

  1. Siderius Nuncius (Starry Messenger). 1610
    telescopic evidence for the heliocentric model, the first printing sold out within days (March 12), four major observations
    1. mountains on the Moon — Moon was supposed to be perfect

      "From observations… repeated many times I have been led to the opinion and conviction that the surface of the Moon is not smooth, uniform, and precisely spherical as a great number of philosophers believe it (and other heavenly bodies) to be, but is uneven, rough, and full of cavities and prominence's, being not unlike the face of the Earth, relieved by chains of mountains and deep valleys."
    2. planets look like disks, stars still look like dots
    3. Milky Way made of stars — there are things invisible to the naked eye

      "I have observed the nature and the material of the Milky Way. With the aid of a telescope this has been scrutinized so directly and with such ocular certainty that all disputes which have vexed philosophers through so many ages have been resolved, and we are at last freed from worldly debates about it The galaxy is, in fact, nothing but a congress of innumerable stars grouped together in clusters. Upon whatever part of it the telescope is directed, a vast crowd of stars is immediately presented to view. Many of them are rather large and quite bright, while the number of smaller ones is quite beyond calculation."
    4. moons of Jupiter — was thought that the Moon could not keep up with moving Earth (first sighted January 7, realized they were moons on January 15), Jupiter shares something in common with the Earth, both are satellites of the Sun

      "On the seventh day of January in this present year 1610, at the first hour of night, when I was viewing the heavenly bodies with a telescope, Jupiter presented itself to me; and because I had prepared a very excellent instrument for myself, I perceived (as I had not before, on account of the weakness of my previous instrument) that beside the planet there were three starlets, small indeed, but very bright. Though I believed them to be among a host of fixed stars, they aroused my curiosity somewhat by appearing to lie in an exact straight line parallel to the ecliptic, and by their being more splendid than others of their size. Their arrangement with respect to Jupiter and each other was the following:" [Descriptive text removed between diagrams. Galileo uses a tipped-over zero or an "O" to represent Jupiter and asterisks to represent the "starlets".]

      "Such are the observations concerning the four Medicean planets recently first discovered by me…."

      Galileo then goes on to describe how these "starlets" wander around the bright dot that is Jupiter First appearing ahead then behind the planet, they follow Jupiter no matter which way it moves across the sky, be it in direct or retrograde motion. Like a miniature solar system (a concept that did not really exist at the time), each dot shifts from side to side within a restricted orbit, the closest one in having the shortest period and the farthest one out having the longest period. Galileo named them the "Medicean planets" after his benefactor Cosimo II de' Medici, the Grand Duke of Tuscany (1590–1621). He is using the word "planet" with its original meaning of "wandering star", which is what these objects look like when viewed from the Earth — bright flecks of light that move relative to the other "fixed stars". The meaning of the word has shifted, so that nowadays the word "planet" refers only to the eight or nine major bodies orbiting the Sun — a shift in meaning almost entirely due to the observations of Galileo. The "Medicean planets" are now called the "Galilean moons".

      Galileo discovered something new and hugely important — satellites of a satellite; bodies orbiting a body orbiting another, more significant body. Moons! The comparison is Earth-shaking. Jupiter is a planet (in current language, a major body orbiting the Sun). It has bodies that orbit it. The Earth has a body that orbits it. We call it the Moon. The Earth has one moon. Jupiter has many moons. Galileo saw four, but that was just the beginning. Jupiter is now known to have nearly sixty moons. This means that Jupiter and the Earth are similar and maybe even equal in stature. Jupiter is a planet and so is the Earth. (Gasp!)

      "Here we have a fine and elegant argument for quieting the doubts of those who, while accepting with tranquil mind the revolutions of the planets about the Sun in the Copernican system, are mightily disturbed to have the Moon alone revolve about the Earth and accompany it in an annual rotation about the Sun."

      Given what we now know about the cosmos, it gets even worse for the geocentrists. The Earth is certainly something, but now Jupiter is more than the Earth, and the Sun is even more than all of them combined. The Earth has one moon, one satellite, one thing that orbits it. Jupiter had four in Galileo's day and about sixty in our day. The Sun had six in Galileo's day — Mercury, Venus, Mars, Jupiter, Saturn, and now the Earth too. When you include all the objects known today — planets, asteroids, comets, and trans Neptunian objects — you up the number to about a thousand. The Earth goes from the center of all things to just one rock among many orbiting a bigger ball of fire.

      "[N]ow we have not just one planet rotating about another while both run through a great orbit around the Sun; our own eyes show us four stars which wander around Jupiter as does the Moon around the Earth, while all together trace out a grand revolution about the Sun…."
  2. Istoria e dimostrazioni intorno alle Macchie Solari e loro accidenti. (History and Demonstrations Concerning Sunspots and Their Phenomena.) 1613 — commonly called The Letters on Sunspots, further evidence for a heliocentric system
    1. sunspots — Sun is not perfect and it rotates
    2. phases of nevus — verifies heliocentric geometry
  3. Dialogo sopra i due massimi sistemi del mondo, Tolemaico, e Copernicano. (Dialogue Concerning the Two Chief World Systems, Ptolemaic and Copernican.) 1632.
    1. Salviati argues for the Copernican position and presents some of Galileo's views directly, calling him the "Academician" in honor of Galileo's membership in the Academia dei Lincei. He is named after Galileo's friend Filippo Salviati (1582–1614).
    2. Sagredo is an intelligent layman who is initially neutral. He is named after Galileo's friend Giovanni Francesco Sagredo (1571–1620).
    3. Simplicio is a dedicated follower of Ptolemy and Aristotle, who presents the traditional views and the arguments against the Copernican position. He is modeled after Ludovico delle Colombe (1565-1616) and Cesare Cremonini (1550–1631), both of whom were conservative philosophers. The character's name is not "Simpleton", but is taken from the sixth-century philosopher Simplicius, who wrote notable commentaries on Aristotle. [Maffeo Barberini - Pope Urban VII (1623-1644)?]
    • on the Index of Prohibited Books from 1616 to 1835 (with De Revolutionibus)
    • held under house for eight years arrest until his death
    • condemned in 1633, condemnation reversed gradually (last word in 1992)

Just Quotes

Tycho

Tycho Brahe (1546–1601) Denmark

Notes

Quotes

Kepler

Johannes Kepler (1571–1630) Holy Roman Empire (now Austria)

Kepler was a terrible high school teacher.

Kepler's first attempt fails

Mysterium Cosmographicum (Cosmic Mystery) 1596.

Videmus, Deum creasse corpora mundana ad cer tum numerum. Numerus autem est quantitatis accidens, numerus inquam inmundo. Nam ante mundum nullus erat numerus praeter trinitatem, quae est ipse Deus.   Before the universe was created, there were no numbers except the Trinity, which is God himself….
Quare si ad numerorum mensuram est conditus mundus, ergo ad quantitatum mensuram. At in linea nullus numerus nec in superficie, sed infinitas. In corporibus igitur. Removenda vero irregularia corpora, nempe in conditu ordinatissimae creaturae. Remanent igitur sex corpora: globus, sive potius sphaericum concavum et quinque rectilinea. Sphaericum ultimo coelo debetur. Nam duplex mundus, mobilis et quiescens. Hic est ad imaginem essentiae Divinae in se consideratae, ille ad imaginem Dei, quatenus creat: et propterea tanto minor (in margine: nam Deus non temere sumsit hunc numerum; nihil enim sine ratione optima facit. Quodsi dicas, potuisse numerum aliquem sumi ex spirituali mundo: tamen ad Deum recurret in illius ipsius creatione. Et absurdum erit, rem praestantissimam, sc. mundum creatum esse ad angelorum, non ad Dei imaginem. Ego angelos ipsos accenseo huic visibili mundo, perinde ut homines. In principio, ante angelos, creatum est Coelum et Terra). Curvum autem rectissime Deo, rectum creaturae comparatur. In globo igitur est trinitas, sphaericum, centrum, capacitas. Sic in mundo quieto, Fixae, Sol, aura sive aethra intermedia: et in Trinitate Filius, Pater, Spiritus. Jam mundus mobilis ex rectilineis censendus. Illorum autem quinque. Quare si illa pro terminis sive pro maceriebus habenda sunt (cujus etiam rationem bonam affero) non poterunt plures res distinguere, quam sex. Sex igitur mobilia Solem circumambeuntia. Habetur causa nnmeri planetarum. Sic igitur Sol in medio mobilium quietus ipse et tamen fons motns, gerit imaginem Dei patris creatoris. Nam quod est Deo creatio, hoc est Soli motus. Movet autem in fixis, ut pater in filio creat. Fixae enim nisi locum praebe rent sua quiete, nihil moveri posset. Quod axioma etiam dum Tubingae tenui. Dispertitur autem Sol virtutem motus per medium, in quo sunt mobilia: sicut pater per spiritum vel virtute spiritus sui creat. Atque jam ex necessitate praesuppositorum sequitur, motum cum distantiis in proportione esse. Sic igitur conclusi, ut, quae sententia eundem ordinem in motu et distantiis servaret, vera esset; quae non, falsa. Exinde probavi, corpora haec duorum esse ordinum, tria in uno, duo in reliquo ordine. Cubum esse primum omnium et sui ordinis etiam, post pyramida; ultimum primorum dodecaëdrum. Secundariorum primum esse octaëdron, ultimum icosaëdron: Hinc constitit ratio, quare res totius mundi praecipua, Terra nempe cum imagine Dei in homine distingueret inter ordines. Probavi igitur, quod primaria debeant extra terreni orbis complexum esse, secundaria intra: quod caput exterioris ordinis debeat ad fixas vergere, caput interioris ad Solem. Atque hic explicandae fuerunt omnes proprietates et cognationes horum corporum. His ita constitutis, accensui corporibus planetas, contentis a Terrae orbe, contentos a se; exclusis exclusos….    
    For, the line and the plane imply no numbers: here infinitude itself reigns. Let us consider, therefore, the solids. We must first eliminate the irregular solids, because we are only concerned with orderly creation. There remain six bodies, the sphere and the five regular polyhedra. To the sphere corresponds the outer heaven. For the universe is twofold: dynamic and static. The static is the image of God-Essence, while the dynamic is but the image of God-Creator, and is therefore of a lower order. In its very nature, the round corresponds to God and the flat to his creation. Indeed, the sphere is threefold: surface, center, volume; so is the static world: firmament, sun, ether; and so is God: Son, Father, Spirit. On the other hand, the dynamic world is represented by the flat-faced solids. Of these there are five: when viewed as boundaries, however, these five determine six distinct things: hence the six planets that revolve about the Sun. This is also the reason why there are but six planets. And because the Sun stands at the center of creation, and because it is at rest and yet the source of all motion, it is the true image of God, the Father, the Creator. For, what God is to creation, is motion to the Sun….
Nam si quis leviter geometriae peritus totidem verbis moneatur, illi statim in promtu sunt quinque regularia corpora cum proportione orbium circumscriptorum ad inscriptos: illi statim ob oculos versatur scholion illud Euclideum ad pro positionem 18. lib. 13. quo demonstratur impossibile esse, ut plura sint aut excogitentur regularia corpora quam quinque. Res admiratione digna, cum nondum constaret mihi de fingulorum corporum prærogatiuis in ordine, vsum me minimèarguta coniectura ex notis Planetarum distantijs deducta, adeò feliciter scopum tetigisse in ordine coporum, vt nihil in illis postea, cum exquisitis agerem rationibus, immutare potuerim. Ad reimemoriam ascribo tibi sententiam, ita vti incidit, & co momento verbis conceptam. Terraest Circulus mensor omnium; Illi circumscribe Dodecaedron: Circulus hoc comprehendens erit Mars. Marti circumscribe Tetraedron: Circulus hoc comprehendens erit Iupiter. Ioui circuscribe Cubum: Circulus hunc comprehendens erit Saturnus. Iam terra inscribe Icosaedron: Illi inscriptus Circulus erit Venus. Veneri inscribe octedron: Illi inscriptus Circulus erit Mercurius. Habes rationem numeri planetarum.    
    I have further shown that the regular solids fall into two groups: three in one, and two in the other. To the larger group belongs, first of all, the Cube, then the Pyramid, and finally the Dodecahedron. To the second group belongs, first, the Octahedron, and second, the Icosahedron. That is why the most important portion of the universe, the Earth — where God's image is reflected in man — separates the two groups. For, as I have proved next, the solids of the first group must lie beyond the Earth's orbit, and those of the second group within…
    Thus I was led to assign the Cube to Saturn, the Tetrahedron to Jupiter, the Dodecahedron to Mars, the Icosahedron to Venus, and the Octahedron to Mercury….
Johannes Kepler, 1596  
 

The Platonic solids

Kepler's failed model of the solar system

Kepler's Platonic solid model of the solar system
radius of sphere ratio R/r
platonic solid outer (R) inner (r) deviation
cubecube
√3
2
9.53876 au
Saturn
1
2
5.20283 au
Jupiter
1.732  
 
1.833  
−6%  
tetrahedrontetrahedron
√6
4
5.20283 au
Jupiter
√6
12
1.52369 au
Mars
3.000  
 
3.415  
−12%  
dodecahedrondodecahedron
√15 + √3
4
1.52369 au
Mars
√(250 + 110√5)
20
1 au
Earth
1.258  
 
1.524  
−17%  
icosahedronicosahedron
√(10 + 2√5)
4
1 au
Earth
3√3 + √15
12
0.72333 au
Venus
1.258  
 
1.383  
−9%  
octahedronoctahedron
1
√2
0.72333 au
Venus
1
√6
0.38710 au
Mercury
1.732  
 
1.869  
−9%  

Kepler decided the observations of the planets were wrong, not his model of nested platonic solids.

This model was rendered useless when Uranus (the seventh planet) was discovered in 1781, Neptune (the eighth planet) in 1846, Ceres (the first asteroid) in 1801, and Pluto (the first Kuiper belt object) in 1930. More than 10,000 objects orbiting the Sun have been identified.

The counter reformation steps in and Kepler is driven out of Graz. Philip III (1598-1621) Son of Philip II becomes leader of Spanish house of Hapsburg says to Pope: "I would rather lose a hundred lives, if I had them, than consent to rule over heretics." This rebellion would drag on until 1648, become part of the wider European struggle known as the Thirty Years War (1618-1648) 

Kepler's Good Stuff

Additional Quotes

Ubi materia, ibi geometria.   Where there is matter, there is geometry.
     
Geometria una et æterna est in mente Dei refulgens: cuius consortium hominibus tributum inter causas est, cur homo sit imago Dei.   Geometry is one and eternal shining in the mind of God: that share in it accorded to men is one of the reasons that Man is the image of God.
     
Mensus eram cœlos, nunc Terræ metior umbras. Mens cœlestis erat, corporis umbra jacet.   I used to measure the Heavens, now I measure the shadows of Earth. The mind belonged to Heaven, the body's shadow lies here.
     
    Geometry existed before the Creation. It is co-eternal with the mind of God. Geometry provided God with a model for the Creation. Geometry is God Himself.
     
    Geometry, which before the origin of things was coeternal with the divine mind and is God himself (for what could there be in God which would not be God himself?), supplied God with patterns for the creation of the world, and passed over to Man along with the image of God.
     
    My brain gets tired when I try to understand what I wrote, and I find it hard to rediscover the connexion between the figures and the text, that I established myself.

Kepler wrote the first work of science fiction — the Somnium (1634) — published by Kepler's son Ludwig, four years after his death.