Johannes Kepler ( ) A Tale of Ravishing Delight by James D. Nickel Copyright

Two Good Resources Max Caspar, Kepler (New York: Dover Publications, [1959] 1993). James R. Voelke, Johannes Kepler and the New Astronomy (New York: Oxford University Press, 1999). Copyright

My Introduction to Kepler Great is our Lord and great His virtue and of His wisdom there is no number: praise Him, ye heavens, praise Him, ye sun, moon, and planets, use every sense for perceiving, every tongue for declaring your Creator. Copyright

My Introduction to Kepler Praise Him, ye celestial harmonies, praise Him, ye judges of the harmonies uncovered … and thou my soul, praise the Lord thy Creator, as long as I shall be: for out of Him and through Him and in Him are all things … [both the sensible and the intelligible]; Copyright

My Introduction to Kepler for both whose whereof we are utterly ignorant and those which we know are the least part of them; because there is still more beyond. To Him be praise, honor, and glory, world without end. Amen. Johannes Kepler, Epitome of Copernican Astronomy & Harmonies of the World, trans. Charles Glenn Wallis (Amherst: Prometheus Books, [ , 1939] 1995), p Copyright

Outline Scientific and mathematical heritage. Childhood and Education. First Cosmological Model. First and Second Planetary Laws: His war with Mars. Optics. Personal tragedy. Wine barrels and Calculus. Third Law of Planetary Motion: Harmony of the World. Last season of life. Epitaph. Copyright

Scientific and mathematical heritage Laws of Astronomy. Optics. Polyhedra. Packing problems. Logarithms. Volumes of solids and calculus. Astronomical Tables. Copyright

The World of Kepler

Vocation Calling … For a long time I was restless: But now see how God is, by my endeavors, also glorified in astronomy. As we astronomers are priests of the highest God in regard to the book of nature, we are bound to think of the praise of God and not the glory of our own capacities. Carola Baumgardt, Johannes Kepler: Life and Letters (New York: Philosophical Library, 1951), p. 31, 44. Copyright

Keplers First Cosmological Model

Copyright Keplers First Cosmological Model

Keplers Response The intense pleasure that I have received from this discovery can never be told in words. I regretted no more the time wasted; I tired of no labour; I shunned no toil of reckoning, days and nights spent in calculation, until I could see whether my hypothesis would agree with the orbits of Copernicus, or whether my joy was to vanish into air. Cited in Sir Oliver Lodge, Johann Kepler, in The Word of Mathematics, ed. James R. Newman (New York: Simon and Schuster, 1956), 1:223. Copyright

Keplers War with Mars Copyright minutes of an arc (8/60 1/8 ). Sir Oliver Lodge (1:227), I need not say that all these attempts and gropings... entailed enormous labour, and required not only great pertinacity, but a most singularly constituted mind, that could thus continue groping in the dark, without a possible ray of theory to illuminate its search. Grope he did, however, with unexampled diligence.

Copyright A line joining the planet to the Sun (called the radius vector) sweeps out equal areas in equal times as the planet describes its elliptical orbit. Keplers First and Second Laws of Planetary Motion

Optics Copyright For it was by all means the will of God the Creator that the human being, His image, should lift up his eyes from these earthly things to those heavenly ones, and should contemplate such great monuments of His wisdom. Hence the entire arrangement of the fabric of the world tends to bear witness to us of this will of the Creator, as if by a voice sent forth. Johannes Kepler, Optics: Paralipormean to Witela and Optical Part of Astronomy, trans. William H. Donahue (Santa Fe, NM: Green Lions Press, 2000), p. 323.

Tragedy Copyright

Wine barrels and Calculus Copyright

Thirteen Archimedean solids Truncated Tetrahedon Cuboctahedron Truncated Cube (truncated hexahedron) Truncated Octahedron Rhombicuboctahedron (small rhombicuboctahedron) Truncated Cuboctahedron (great rhombicuboctahedron) Copyright

Thirteen Archimedean solids Snub Cube (snub cuboctahedron) Icosidodecahedron Truncated Dodecahedron Truncated Icosahedron (soccer ball) Copyright

Thirteen Archimedean solids Rhombicosidodecahedron (small rhombicosidodecahedron). Truncated Icosidodecahedron (great rhombicosidodecahedron). Snub Dodecahedron (snub icosidodecahedron). Copyright

Keplers Third Law of Planetary Motion (Time and Distance) The ratio of the squares of the planetary periods (time) are the same as the ratio of the cubes of the mean radii of their orbits. The cubes of the distances of the planets from the Sun are proportional to the squares of the times taken by these planets to make a complete circuit. The square of the time of revolution of each planet is proportional to the cube of its mean distance from the Sun. Copyright

Keplers Third Law of Planetary Motion If D is the mean distance of a planet from the Sun, and T is the length of its year, then for all the planets T 2 /D 3 = c (a fixed number) or … T 2 = cD 3 where c is a fixed constant for all planets. In our Solar system, c = 1 … Amazing! Copyright

Planetary Data Copyright PlanetDistance, D, from Sun taking the Earths Distance as Unit Time, T, of a complete Circuit taking the Earths time (1 year) as Unit Square of Time divided by cube of Distance Pluto Neptune Uranus Saturn Jupiter Mars Earth1.00 Venus Mercury

Operations and Order of Algebra T 2 = cD 3 where c = 1 T 2 = D 3 Solve for T: T = D 3/2 or … y = f(x) = x 3/2 where x = mean distance y = time Copyright

Planetary Data Copyright Planetx = Dy = T Pluto Neptune Uranus Saturn Jupiter Mars Earth1.00 Venus Mercury y = f(x) = x 3/2

Copyright The uniform scale is awkward: cant fit all the data. Power Function y = f(x) = x 3/2

Take the log of the Power Function y = x 3/2 log y = log (x 3/2 ) log y = 3/2 log x Copyright

Take the log of the Power Function log y = 3/2 log x Let Y = log y Let X = log x By substitution, we get: Y = (3/2)X Copyright

The Log of the Data Copyright PlanetXlog XYlog Y Pluto Neptune Uranus Saturn Jupiter Mars Earth Venus Mercury

Copyright Y = (3/2)X log-log scale

Keplers Response What sixteen years ago, I urged as a thing to be sought... for which I have devoted the best part of my life... at length I have brought to light, and recognized its truth beyond my most sanguine expectations.... Copyright

Keplers Response Nothing holds me; I will indulge my sacred fury; I will triumph over mankind by the honest confession that I have stolen the golden vases of the Egyptians to build up a tabernacle for my God far away from the confines of Egypt. Copyright

Keplers Response If you forgive me, I rejoice; if you are angry, I can bear it; the die is cast, the book is written, to be read either now or by posterity, I care not which; it may well wait a century for a reader, as God has waited six thousand years for an observer. Cited in Lodge, 1:232. Copyright

Last season of life Biographer Max Caspar, They [the orbits of planets–JN] have the form of ellipses with the sun in one focus. But the eccentricities of these ellipses are no more arbitrary and without rule than any other measures. No, in this fine construction the highly artistic formative hand of the Creator is shown in a very special way. Copyright

Last season of life Since the eccentricities determine the rates of the planets at aphelion and perihelion, they have been so measured by the Creator that between them appear the harmonic proportions which are to be presented by geometry and which are the foundation of music. So a divine sound fills the whole world. Copyright

Last season of life To be sure, sensual hearing is unable to perceive the wonderful harmony. But the spiritual ear perceives it, just as it is also the spiritual eye with which we see the loveliness of the sizes. Max Caspar, Kepler (New York: Dover Publications, [1959] 1993), p Copyright

Last season of life I measured the skies, now the shadows I measure. Skybound was the mind. Earthbound the body rests. Copyright

Heaven weeps … Copyright

Keplers ethos Max Caspar, God is the beginning and end of scientific research and striving. Therein lies the keynote of Keplers thought, the basic motive of his purpose, the life giving soil of his feeling. His deep religiousness expresses itself not only in occasional bents and passions of a pious soul; it feeds not only on reminiscences from the time of his theological studies. Copyright

Keplers ethos It penetrates his entire creativity and spreads out over all the works he left behind. It is this feeling for religion which above all lends them the special warmth which we experience with such pleasure when reading them. Copyright

Keplers ethos All of its own accord at every opportunity the name of God crosses his lips; to Him he turns now with a request, now with praise and thanks; before Him he examines his deeds and omissions, his thoughts and words, to discover whether they can pass the test and are directed toward the proper goal. Caspar, p Copyright

Conclusion Keplers ethos (governing motivation of life): Soli deo gloria. Copyright