The History and Philosophy of Astronomy
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1 Astronomy 350L (Spring 2005) The History and Philosophy of Astronomy (Lecture 9: Kepler II) Instructor: Volker Bromm TA: Amanda Bauer The University of Texas at Austin
2 Tycho and Kepler meet in Prague ( ) Tycho needs Kepler: - difficult calculations to figure out orbit of Mars Kepler needs Tycho: - precision data to figure out true orbits of the planets Together embark on improved astron. tables (Tabulae Rudolphinae)
3 Johannes Kepler: The Great Theorist born into middle-class: - lifelong economic struggles completed Copernicus agenda The last mystic (last scientific astrologer)
4 Kepler: Geography of his Life
5 Europe: Deeply divided into multiple confessions
6 Kepler: Birth and Upbringing in Wuerttemberg Born 1571: Weil der Stadt (near Stuttgart) middle-class family father: a mercenary, mother: cantankerous
7 University Education at Tuebingen ( ) Leading Protestant University Undergrad (7 Liberal Arts) (Lutheran) Theology
8 University Education at Tuebingen ( ) Michael Maestlin, professor of mathematics and astronomy taught: Ptolemy and Copernicus lifelong friendship with Kepler
9 Neoplatonism: Search for hidden harmony God (William Blake, ) Realm of Ideas Realm of Experience Motion of planets
10 Neo-Pythagoreanism: A Universe governed by Numbers Divine Tetractys: = 10 - symbolizes the universe!
11 Kepler studies Theology and makes Enemies Last Supper Controversy : - Lutherans: Wine is Christ - Calvinists: Wine only symbolizes Christ Kepler, being a Lutheran, supports Calvinist view Source of great trouble, professionally and personally
12 Mathematician in Graz (Austria)
13 Mathematician in Graz Teacher at Protestant High School Styrian estate mathematician: horoscopes
14 Mysterium Cosmographicum Why are there exactly six planets? What determines their distances from the Sun? Cosmographic Mystery (1596)
15 Mysterium Cosmographicum: 5 Platonic Solids
16 Mysterium Cosmographicum planetary orbits nested between Platonic solids!
17 Kepler and Astrology One of his duties: Work out annual calendars, i.e., predict the events of the year ahead!
18 Kepler and Astrology (Kepler s nativity) Kepler: one of the last scientific astronomers! Henceforth, astronomy and astrology part company
19 Kepler: Fleeing the Counter Reformation in Graz
20 Kepler: Move to Imperial Prague Rudolph II - Emperor ( ) Great Patron of Arts and Sciences (Tycho, Kepler)
21 Tycho s Assistant in Imperial Prague Benatky Castle: Tycho s Final Domicile ( ) Tycho invites upstart young Johannes Kepler!
22 Kepler: The Inheritor of Tycho After Tycho s death (1601): Kepler moves quickly to get hold of Tycho s data Emperor Rudolph II appoints Kepler to become Imperial Mathematician Imperial order: Complete Rudolphine Tables Kepler s main agenda: Win the battle with Mars
23 Kepler s Warfare with Mars Tycho pointed out to Kepler that orbit of Mars is particularly difficult to understand! Orbit of Mars shows large deviation from circularity!
24 The New Astronomy: The Orbits of the Planets Astronomia Nova (New Astronomy, 1609) Kepler s 1 st and 2 nd Law: - planets move in elliptic orbits with Sun in one focus - law of areas Finally: A model that works! Introduce Celestial Physics
25 The New Astronomy: The Orbits of the Planets Problem: Observe (Mars-orbit) from moving platform (Earth)! But want to figure out orbit with respect to Sun! A convolved problem!
26 Long Process of Trial-and-Error Method: (1) Try given orbital geometry, and (2) compare with Tycho s data All combinations involving circles, can only give accuracy of ~ 8 arcmin But: Kepler knew that Tycho s data have accuracy of ~ 4 arcmin Thus: Reject circular orbits! Eventually: Try elliptic orbits with Sun in one focus!
27 Orbit of the Planets: Kepler s 1 st Law 1 st Law: Planets move in ellipses with the Sun in one focus!
28 Orbit of the Planets: Kepler s 1 st Law Ellipse is one of the three conic sections, and the circle is a special case! (Conic sections described by Apollonius of Perga in 200 BC)
29 Speed of the Planets: Kepler s 2 nd Law Sun Earth Start with Sun-centered version of Ptolemy s equant!
30 Speed of the Planets: Kepler s 2 nd Law Kepler realizes: Pseudo-equant is almost equivalent to equal area in equal times as seen from Sun!
31 Speed of the Planets: Kepler s 2 nd Law A=B=C 2 nd Law: A line drawn from the Sun to a planet sweeps out equal areas in equal times!
32 Finally solving the Problem of the Planets One unified framework valid for all planets! - No ad-hoc fixes allowed! For each planet, 2 free quantities (parameters) to choose: semi-major axis a, and eccentricity e It could not have been done without Tycho s data!
33 Coup-d Etat in Prague (1611) Emperor Rudolph deposed by his brother Rudolph II Kepler has to leave Prague Matthias
34 Move to Linz (Upper Austria)
35 Mathematician in Linz ( ) Teacher at Protestant High School Upper-Austrian estate mathematician: horoscopes
36 The Harmony of the Worlds Harmonice Mundi (Harmony of the Worlds, 1619) Kepler s 3 rd Law: - P 2 =a 3 full of mystical speculation
37 The Harmony of the Worlds Kepler s 3 rd - P 2 =a 3 Law:
38 The Harmony of the Worlds The Music of the Spheres recall: Pythagoras
39 Rudolphine Tables (Tabulae Rudolphinae) improve Reinhold s old (1551) Prutenic Tables based on Copernicus De Revolutionibus limited accuracy in light of Tycho s observations Kepler has promised Tycho on deathbed to complete this
40 Rudolphine Tables (Tabulae Rudolphinae) Tabulae Rudolphinae (1627) based on Kepler s new laws of planetary motion unprecedented accuracy (after all: Kepler s is the correct model) Astronomers adopt tables first, before the theoretical works
41 Rudolphine Tables Tables: non-glamorous, but very useful!
42 Rudolphine Tables: The Frontispiece Allegory of Astronomy
43 Witchcraft Trial of Kepler s Mother ( ) Water Trial Kepler (successfully) defended his old mother
44 Kepler: Pact with the Devil ( ) Entered the employ of generalissimo Wallenstein Wallenstein was firm believer in astrology Moved to Sagan Wallenstein, Supreme Commander of Imperial Troops In Thirty Years War
45 Journey s End: Death in Regensburg (1630)
46 Kepler s Epitaph: I measured the skies, now the shadows I measure. Skybound was the mind, eartbound the body rests
47 Kepler s role in the Scientific Revolution Newton ( ) - dynamics - law of gravity Standing on the shoulders of giants Kepler ( ) - celestial motion - 3 rd Law Galileo ( ) - laws of free-fall - principle of inertia
48 Kepler (part 2) Johannes Kepler: - finally solves the problem of the planets - break free from the old dogma of uniform circular motion - completes Copernican Revolution Kepler s Laws of Planetary Motion - 1 st Law: Planets move in ellipses with the Sun in one focus - 2 nd Law: A line from the Sun to a planet sweeps over equal areas in equal time ( Law of Areas ) - 3 rd Law: P 2 = a 3 Kepler calculates Rudolphine Tables - New standard of precision
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