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Westman in Gingerich, Nature of Scientific Discovery; Danielson, 191. p. 201 “Twice … drowning.” Danielson, 193. p. 201 “I excavated … wonderfully.” Danielson, 199. CHAPTER 10 p. 202 “I deem … contemplate it.” Caspar, 384. p. 202–3 “In truth … world.” Ferguson, 47. p. 207 “I consider … astronomy.” Astronomia Nova (Donahue, 43; Ferguson, 98–99). p. 207 “burning eagerness.” Ferguson, 155. p. 208 “Days and nights … wind.” Mysterium (Caspar, 63; Ferguson, 192). p. 209 “I build … world.” Epitome (Wallis, 10). p. 210 “I was … ridiculous me.” Astronomia nova (Gingerich and Ann Brinkley, quoted in Gingerich, Eye, 320). p. 210 “sacred frenzy.” Gingerich, Eye, 407. p. 210 “If you … much time.” Gingerich, Eye, 357. p. 210 “hesitating … machine.” Mysterium (Giora Han in Kremer and Wlodarczyk, 208). p. 211 “It is … Copernicus.”
No; rather, he wanted to warn people of their own mutability, while the Earth, home of the human race, remains always the same, the motion of the Sun perpetually returns to the same place, the wind blows in a circle and returns to its starting point, rivers flow from their sources into the sea, and from the sea return to the sources, and finally, as these people perish, others are born. Life’s tale is ever the same; there is nothing new under the Sun. You do not hear any physical dogma here. The message is a moral one, concerning something self-evident and seen by all eyes but seldom pondered. Solomon therefore urges us to ponder. —JOHANNES KEPLER, Astronomia nova, 1609 (TRANSLATED FROM THE LATIN BY WILLIAM H. DONAHUE) Chapter 7 The First Account It is also clearer than sunlight that the sphere which carries the Earth is rightly called the Great Sphere. If generals have received the surname “Great” on account of successful exploits in war or conquests of peoples, surely this circle deserved to have that august name applied to it. For almost alone it makes us share in the laws of the celestial state, corrects all the errors of the motions, and restores to its rank this most beautiful part of philosophy.
p. 211 “the unexpected … natural causes.” Rudolfine Tables (Ferguson, 346). p. 211 “Thee, O Lord … to that.” Harmonies of the World (Wallis, 240). CHAPTER 11 p. 214 “The constitution … the word.” Dedication in Galileo’s Dialogue (Drake, 3–4). p. 214 “Would it … effort.” Ferguson, 206. p. 217 “Summon men … at all.” Rosen, Scientific Revolution, 189. p. 217 “concerning … humanity” and “read the … class.” Astronomia nova (Donahue, 19, 21). Science historian William H. Donahue, who translated the New Astronomy from the Latin, says that Kepler’s arguments on the interpretation of Scripture became the most widely read of his writings, often reprinted in modern languages, and the only work by Kepler to appear in English before the 1870s. p. 218 “I believe … completely.” Galileo’s Letter to the Grand Duchess Cristina (Drake, Discoveries, 183–84).
To Explain the World: The Discovery of Modern Science by Steven Weinberg
Albert Einstein, Alfred Russel Wallace, Astronomia nova, Brownian motion, Commentariolus, cosmological constant, dark matter, Dava Sobel, double helix, Edmond Halley, Eratosthenes, Ernest Rutherford, fudge factor, invention of movable type, Isaac Newton, James Watt: steam engine, music of the spheres, On the Revolutions of the Heavenly Spheres, Pierre-Simon Laplace, probability theory / Blaise Pascal / Pierre de Fermat, retrograde motion, Thomas Kuhn: the structure of scientific revolutions
Kepler continued work on the motions of planets, trying and failing to reconcile Tycho’s precise data with Copernican theory by adding eccentrics, epicycles, and equants. Kepler had finished this work by 1605, but publication was held up by a squabble with the heirs of Tycho. Finally in 1609 Kepler published his results in Astronomia Nova (New Astronomy Founded on Causes, or Celestial Physics Expounded in a Commentary on the Movements of Mars). Part III of Astronomia Nova made a major improvement in the Copernican theory by introducing an equant and eccentric for the Earth, so that there is a point on the other side of the center of the Earth’s orbit from the Sun around which the line to the Earth rotates at a constant rate. This removed most of the discrepancies that had bedeviled planetary theories since the time of Ptolemy, but Tycho’s data were good enough so that Kepler could see that there were still some conflicts between theory and observation.
If by “soul” Kepler had meant anything like its usual meaning, then the transition from a “physics” based on souls to one based on forces was an essential step in ending the ancient mingling of religion with natural science. Astronomia Nova was not written with the aim of avoiding controversy. By using the word “physics” in the full title, Kepler was throwing out a challenge to the old idea, popular among followers of Aristotle, that astronomy should concern itself only with the mathematical description of appearances, while for true understanding one must turn to physics—that is, to the physics of Aristotle. Kepler was staking out a claim that it is astronomers like himself who do true physics. In fact, much of Kepler’s thinking was inspired by a mistaken physical idea, that the Sun drives the planets around their orbits, by a force similar to magnetism. Kepler also challenged all opponents of Copernicanism. The introduction to Astronomia Nova contains the paragraph: Advice for idiots.
This removed most of the discrepancies that had bedeviled planetary theories since the time of Ptolemy, but Tycho’s data were good enough so that Kepler could see that there were still some conflicts between theory and observation. At some point Kepler became convinced that the task was hopeless, and that he had to abandon the assumption, common to Plato, Aristotle, Ptolemy, Copernicus, and Tycho, that planets move on orbits composed of circles. Instead, he concluded that planetary orbits have an oval shape. Finally, in Chapter 58 (of 70 chapters) of Astronomia Nova, Kepler made this precise. In what later became known as Kepler’s first law, he concluded that planets (including the Earth) move on ellipses, with the Sun at a focus, not at the center. Just as a circle is completely described (apart from its location) by a single number, its radius, any ellipse can be completely described (aside from its location and orientation) by two numbers, which can be taken as the lengths of its longer and shorter axes, or equivalently as the length of the longer axis and a number known as the “eccentricity,” which tells us how different the major and minor axes are.
Big Bang by Simon Singh
Albert Einstein, Albert Michelson, All science is either physics or stamp collecting, Andrew Wiles, anthropic principle, Arthur Eddington, Astronomia nova, Brownian motion, carbon-based life, Cepheid variable, Chance favours the prepared mind, Commentariolus, Copley Medal, cosmic abundance, cosmic microwave background, cosmological constant, cosmological principle, dark matter, Dava Sobel, Defenestration of Prague, discovery of penicillin, Dmitri Mendeleev, Edmond Halley, Edward Charles Pickering, Eratosthenes, Ernest Rutherford, Erwin Freundlich, Fellow of the Royal Society, fudge factor, Hans Lippershey, Harlow Shapley and Heber Curtis, Harvard Computers: women astronomers, Henri Poincaré, horn antenna, if you see hoof prints, think horses—not zebras, Index librorum prohibitorum, invention of the telescope, Isaac Newton, John von Neumann, Karl Jansky, Louis Daguerre, Louis Pasteur, luminiferous ether, Magellanic Cloud, Murray Gell-Mann, music of the spheres, Olbers’ paradox, On the Revolutions of the Heavenly Spheres, Paul Erdős, retrograde motion, Richard Feynman, Richard Feynman, scientific mainstream, Simon Singh, Solar eclipse in 1919, Stephen Hawking, the scientific method, Thomas Kuhn: the structure of scientific revolutions, unbiased observer, V2 rocket, Wilhelm Olbers, William of Occam
When the planet is far from the Sun the radius vector is much longer, but it has a slower speed so it covers a smaller section of the circumference in the same time. Kepler’s ellipses provided a complete and accurate vision of our Solar System. His conclusions were a triumph for science and the scientific method, the result of combining observation, theory and mathematics. He first published his breakthrough in 1609 in a huge treatise entitled Astronomia nova, which detailed eight years of meticulous work, including numerous lines of investigation that led only to dead ends. He asked the reader to bear with him: ‘If thou art bored with this wearisome method of calculation, take pity on me who had to go through with at least seventy repetitions of it, at a very great loss of time.’ Kepler’s model of the Solar System was simple, elegant and undoubtedly accurate in terms of predicting the paths of the planets, yet almost nobody believed that it represented reality.
The Dutch clergyman and astronomer David Fabricius had this to say in a letter to Kepler: ‘With your ellipse you abolish the circularity and uniformity of the motions, which appears to me increasingly absurd the more profoundly I think about it… If you could only preserve the perfect circular orbit, and justify your elliptic orbit by another little epicycle, it would be much better.’ But an ellipse cannot be built from circles and epicycles, so a compromise was impossible. Disappointed by the poor reception given to Astronomia nova, Kepler moved on and began to apply his skills elsewhere. He was forever curious about the world around him, and justified his relentless scientific explorations when he wrote: ‘We do not ask for what useful purpose the birds do sing, for song is their pleasure since they were created for singing. Similarly, we ought not to ask why the human mind troubles to fathom the secrets of the heavens… The diversity of the phenomena of Nature is so great, and the treasures hidden in the heavens so rich, precisely in order that the human mind shall never be lacking in fresh nourishment.’
According to Kepler, the speed of each planet generated particular notes (e.g. doh, ray, me, fah, soh, lah and te). The Earth emitted the notes fah and me, which gave the Latin word fames, meaning ‘famine’, apparently indicating the true nature of our planet. A better use of his time was his authorship of Somnium, one of the precursors of the science fiction genre, recounting how a team of adventurers journey to the Moon. And a couple of years after Astronomia nova, Kepler wrote one of his most original research papers, ‘On the Six-Cornered Snowflake’, in which he pondered the symmetry of snowflakes and put forward an atomistic view of matter. ‘On the Six-Cornered Snowflake’ was dedicated to Kepler’s patron, Johannes Matthaeus Wackher von Wackenfels, who was also responsible for delivering to Kepler the most exciting news that he would ever receive: an account of a technological breakthrough that would transform astronomy in general and the status of the Sun-centred model in particular.
Isaac Newton by James Gleick
Albert Einstein, Astronomia nova, complexity theory, dark matter, Edmond Halley, Fellow of the Royal Society, fudge factor, Isaac Newton, On the Revolutions of the Heavenly Spheres, Richard Feynman, Richard Feynman, Thomas Kuhn: the structure of scientific revolutions
Meanwhile, Cohen and other scholars suggest that Newton’s reading, wide-sweeping though it became, may have never included Galileo’s Discorsi or anything of Kepler. Nor, at his death, did his considerable library contain any work by Ptolemy, Copernicus, or Tycho. Cf. Whiteside in Math, VI: 3 n. and 6 n. 5. Now we say these were the first two of Kepler’s three “laws.” We conventionally date these to 1609, when he published his great work, Astronomia Nova. He put forth a notion of gravity, too: “Gravity is the mutual tendency of cognate bodies to join each other (of which kind the magnetic force is).” Nevertheless, by the time of the Principia, at the far end of the century, few astronomers accepted Kepler’s ideas as firm truths; nor did Newton, in the Principia, see Kepler as a significant precursor. “It seems clear,” I. B. Cohen remarked, “that there was no Keplerian revolution in science before 1687.”
4th Rock From the Sun: The Story of Mars by Nicky Jenner
3D printing, Alfred Russel Wallace, Astronomia nova, cuban missile crisis, Elon Musk, game design, hive mind, invention of the telescope, Kickstarter, On the Revolutions of the Heavenly Spheres, placebo effect, Pluto: dwarf planet, retrograde motion, selection bias, silicon-based life, Skype, Stephen Hawking, technoutopianism
In a way, Brahe’s model was an intermediary between Ptolemy and Copernicus – it maintained the Earth’s importance, removed the solid planetary shells but kept circular orbits, scrapped the immutable stars and heavens, and kept the stars relatively close to the outermost planet (at the time, Saturn). In the late 1500s, Brahe met Johannes Kepler (1571–1630), who subsequently became his assistant. Brahe tasked Kepler with understanding Mars’s orbit, a task that was readily accepted. Sadly, Brahe died in 1601 before he could see his assistant’s conclusions, but Kepler continued his work in earnest and some eight years later published his Astronomia Nova (New Astronomy). Kepler’s big breakthrough was to picture planetary orbits as ellipses, not circles, with the Sun at one of the foci (essentially the ‘centres’ of the ellipse – a circle has just one focus, its centre, but ellipses have two due to their elongated shape along one axis). He also figured out that the planets didn’t move at constant speeds: they moved faster as they approached the Sun and slower when further away.