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UT AST 350L - LECTURE NOTES

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The History and Philosophyof Astronomy (Lecture 9: Kepler II)Instructor: Volker BrommTA: Amanda BauerThe University of Texas at AustinAstronomy 350L (Spring 2005)Tycho and Kepler meet in Prague (1600-01)• Tycho needs Kepler:- difficult calculationsto figure out orbit of Mars• Kepler needs Tycho:- precision data to figure out true orbitsof the planets• Together embark onimproved astron. tables(Tabulae Rudolphinae)Johannes Kepler: The Great Theorist • 1571 – 1630• born into middle-class:- lifelong economic struggles• completed Copernicusagenda• The last mystic(last scientific astrologer)Kepler: Geography of his LifeEurope: Deeply divided into multiple confessionsKepler: Birth and Upbringing in Wuerttemberg• Born 1571: Weil der Stadt (near Stuttgart)• middle-class family • father: a mercenary, mother: cantankerousUniversity Education at Tuebingen (1589-94) • Leading ProtestantUniversity•Undergrad (7 Liberal Arts)• (Lutheran) TheologyUniversity Education at Tuebingen (1589-94) • Michael Maestlin, professorof mathematics and astronomy• taught: Ptolemy andCopernicus• lifelong friendship withKeplerNeoplatonism: Search for hidden harmonyGodRealm of IdeasRealm of Experience(William Blake, 1757-1827)Motion of planetsNeo-Pythagoreanism: A Universe governed by Numbers Divine Tetractys:1 + 2 + 3 + 4 = 10- symbolizes the universe!Keplerstudies 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 personallyMathematician in Graz (Austria)Mathematician in Graz • Teacher at Protestant High School• Styrian estate mathematician: horoscopesMysterium Cosmographicum• Why are there exactlysix planets?• What determines theirdistances from the Sun?• Cosmographic Mystery(1596)Mysterium Cosmographicum: 5 Platonic SolidsMysterium Cosmographicum• planetary orbits nested betweenPlatonic solids!Keplerand Astrology • One of his duties: Work out annual calendars, i.e.,predict the events of the year ahead!Keplerand Astrology • Kepler: one of the last scientific astronomers!• Henceforth, astronomy and astrology part company(Kepler’s nativity)Kepler: Fleeing the Counter Reformation in GrazKepler: Move to Imperial PragueRudolph II- Emperor (1576-1612)• Great Patron of Arts and Sciences (Tycho, Kepler)Tycho’s Assistant in Imperial PragueBenatky Castle: Tycho’s Final Domicile (1599 – 1601)• Tycho invites upstart young Johannes Kepler!Kepler: The Inheritor of Tycho• After Tycho’s death (1601): Kepler moves quicklyto get hold of Tycho’s data• Emperor Rudolph II appoints Kepler to becomeImperial Mathematician• Imperial order: Complete Rudolphine Tables• Kepler’s main agenda: Win the “battle with Mars”Kepler’s Warfare with Mars• Tycho pointed out to Kepler that orbit of Marsis particularly difficult to understand!• Orbit of Mars shows large deviation from circularity!The New Astronomy: The Orbits of the Planets • Astronomia Nova(New Astronomy, 1609)• Kepler’s 1stand 2ndLaw:- planets move in ellipticorbits with Sun in one focus- law of areas• Finally: A model that works!• Introduce Celestial PhysicsThe New Astronomy: The Orbits of the Planets • Problem: Observe(Mars-orbit) from movingplatform (Earth)!• But want to figure outorbit with respect to Sun!• A convolved problem!Long Process of Trial-and-Error• Method: (1) Try given orbital geometry, and(2) compare with Tycho’s data• All combinations involving circles, can onlygive accuracy of ~ 8 arcmin• But: Kepler knew that Tycho’s data have accuracyof ~ 4 arcmin• Thus: Reject circular orbits!• Eventually: Try elliptic orbits with Sun in one focus!Orbit of the Planets: Kepler’s 1stLaw• 1stLaw: Planets move in ellipses with the Sun inone focus!Orbit of the Planets: Kepler’s 1stLaw• 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)Speed of the Planets: Kepler’s 2ndLaw• Start with Sun-centered version of Ptolemy’s equant!EarthSunSpeed of the Planets: Kepler’s 2ndLaw• Kepler realizes: Pseudo-equant is almost equivalentto “equal area in equal times” as seen from Sun!Speed of the Planets: Kepler’s 2ndLaw• 2ndLaw: A line drawn from the Sun to a planet sweeps out equal areas in equal times!A=B=CFinally 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!Coup-d’Etat in Prague (1611)• Emperor Rudolph deposed by his brotherRudolph IIMatthias• Kepler has to leave PragueMove to Linz(Upper Austria)Mathematician in Linz (1612-28)• Teacher at Protestant High School• Upper-Austrian estate mathematician: horoscopesThe Harmony of the Worlds • Harmonice Mundi(Harmony of the Worlds, 1619)• Kepler’s 3rdLaw:-P2=a3• full of mystical speculationThe Harmony of the Worlds • Kepler’s 3rdLaw:-P2=a3The Harmony of the Worlds • The Music of the Spheres• recall: PythagorasRudolphine Tables (Tabulae Rudolphinae) • improve Reinhold’s old (1551)Prutenic Tables• based on Copernicus’De Revolutionibus• limited accuracy in light ofTycho’s observations• Kepler has promised Tychoon deathbed to complete thisRudolphine Tables (Tabulae Rudolphinae) • Tabulae Rudolphinae (1627)• based on Kepler’s newlaws of planetary motion• unprecedented accuracy(after all: Kepler’s is thecorrect model)• Astronomers adopt tables first,before the theoretical worksRudolphineTables • Tables: non-glamorous, but very useful!RudolphineTables: The Frontispiece • Allegory of AstronomyWitchcraft Trial of Kepler’s Mother (1620-21)“Water Trial”• Kepler (successfully) defended his old motherKepler: Pact with the Devil (1628-30)•


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