The History and Philosophy of Astronomy Lecture 10: Tycho. Kepler. Presentation

Astronomy 350L (Fall 2006)

The History and Philosophy of Astronomy (Lectu (Le cture re 10: Tycho Tycho/Ke /Keple plerr II)

Instructor: Volker Bromm TA: Jarrett Johnson The University of Texas at Austin

Tych Ty cho o an and d Kep Keple lerr me meet et in Pr Prag ague ue (16 (1600 00-01 -01)) • Tycho needs Kepler: - dif diffic ficult ult cal calcul culati ations ons to figure out orbit of Mars

• Kepler needs Tycho: - pr prec ecis isio ion n data data to figure out true orbits of the planets

• To Toge geth ther er em emba bark rk on improved astron. tables (Tabulae Rudolphinae )

Johannes Kepler: The Great Theorist

• 1571 – 163 0 • bo born rn int into o middl middle-c e-cla lass ss:: - lif lifelo elong ng econom economic ic strugg struggles les

• co comp mplet leted ed Cop Copern ernic icus us agenda • Th The e las lastt mys mysti tic c (last scientific astrologer)

Kepler: Geography of his Life

Europe: Deeply divided into multiple confessions

Kepler: Birth and Upbringing in Wuerttemberg

• Bo Born rn 15 1571 71:: We Weiil der der St Stad adtt (n (nea earr St Stut uttg tgar art) t) • mi midd ddlele-cl clas ass s fam familily y • fat father: her: a merce mercenary nary,, mother: mother: cantan cantankero kerous us

University Univ ersity Educa Education tion at Tuebin Tuebingen gen (1589-94) • Le Lead adin ing g Prot Protes esta tant nt University •Undergrad (7 Liberal Arts) • (L (Lut uthe hera ran) n) Theo Theolo logy gy

University Univ ersity Educa Education tion at Tuebin Tuebingen gen (1589-94) • Mi Mich chae aell Maes Maestl tlin in,, professor of mathematics and astronomy

• ta taug ught ht:: Pt Ptol olem emy y and  Copernicus • lilife felon long g frie friends ndshi hip p with with Kepler

Neoplatonism: Search for hidden harmony God

(William Blake, 1757-1827)

Realm of Ideas

Realm of Experience

Motion of planets

Neo-Pythagoreanism: Neo-Pytha goreanism: A Universe governed by Numbers

Divine Tetractys: 1 + 2 + 3 + 4 = 10 - sy symbo mboliz lizes es the the uni unive verse rse!!

Kepler Kepl er stud studies ies Theo Theology logy and makes Enemi Enemies es

• “L “Las astt Suppe Supperr Contro Controve versy rsy”: ”: is Christ - Lu Luth ther eran ans: s: Wi Wine ne is  Christ symbolizes Christ - Ca Calvi lvinis nists ts:: Wine Wine onl only y symbolizes  Christ

• Kepler, being a Lutheran, Lutheran, support supports s Calvinis Calvinistt view view • So Sour urce ce of of grea greatt trou troubl ble, e, professionally and personally

Mathematician in Graz (Austria)

Mathematician in Graz

• Tea Teache cherr at Pro Protes testan tantt High High Scho School ol • St Styr yria ian n es esta tate te mat mathe hemat matic icia ian: n: hor horos osco copes pes

Myster My sterium ium Co Cosmo smogra graph phicu icum m • Wh Why y are th ther ere e exac exactl tly y six planets? • Wh What at det deter ermi mines nes the their ir distances from the Sun? • Cosmographic Mystery  (1596)

Mysterium Mys terium Cosmo Cosmograph graphicum: icum: 5 Platon Platonic ic Solid Solids s

Myster My sterium ium Co Cosmo smogra graph phicu icum m

• pla planeta netary ry orbi orbits ts nest nested ed betw between een Platonic solids!

Kepl Ke pler er an and d As Astro trolo logy gy

• One of his his duties: duties: Work out annual annual calendars, calendars, i.e., predict the events of the year ahead!

Kepl Ke pler er an and d As Astro trolo logy gy (Kep (K eple ler’ r’s s na nati tivi vity ty))

• Kep Kepler: ler: one one of the last last scienti scientific fic astro astrologe logers! rs! • Hen Hencefo ceforth, rth, astro astronom nomy y and astrolog astrology y part company company

Kepler: Fleeing the Counter Reformation in Graz

Kepler: Move to Imperial Prague

Rudolph II - Em Empe pero rorr (1 (157 5766-16 1612 12))

• Great Patron of Arts Arts and and Sciences Sciences (Tycho (Tycho,, Kepler) Kepler)

Tycho Ty cho’s ’s Ass Assista istant nt in Impe Imperial rial Prag Prague ue

Bena Be natk tky y Ca Cast stle le:: Tyc Tycho ho’s ’s Fi Fina nall Dom Domic icilile e (15 (1599 99 – 16 1601 01))

• Ty Tych cho o inv invit ites es up upsta start rt yo young ung Jo Joha hanne nnes s Kepl Kepler! er!

Kepler: The Inheritor of Tycho • Af Afte terr Ty Tych cho’ o’s s de deat ath h (1 (160 601) 1):: Ke Kepl pler er mo move ves s qu quic ickl kly y to ge gett hol hold d of of Tyc Tycho’ ho’s s da data ta • Em Empe pero rorr Rud Rudolp olph h II II appo appoin ints ts Ke Kepl pler er to be becom come e Imperial Mathematician • Im Impe peri rial al ord order: er: Com Compl plet ete e Rudolphine Tables  • Ke Kepl pler’ er’s s ma main in age agenda nda:: Win Win th the e “batt “battle le wi with th Mar Mars” s”

Kep Ke ple ler’ r’s s `` ``W War arfa fare re’’ ’’ wit ith h Mars Mars

• Ty Tyc cho po poin inte ted d out out to Ke Kepl pler er th that at or orbi bitt of of Mar Mars s is particularly difficult to deviation understand! • Orbit of Mars Mars shows shows large large dev iation from from circul circularity! arity!

The New Astronomy: The Orbits of the Planets • Astronomia Nova (New Astronomy, 1609) • Kepler’s 1st and 2nd Law: - pl plan anets ets mo move ve in in elli ellipti ptic c orbits with Sun in one focus - law of areas • Fi Final nally ly:: A model model tha thatt works works!! • In Intr trod oduce uce Celes Celestia tiall Physi Physics cs

The New Astronomy: The Orbits of the Planets • Pr Prob oble lem: m: Ob Obse serv rve e (Mars-orbit) from moving platform (Earth)! • Bu Butt want want to fi figu gure re ou outt orbit with respect to Sun! • A co conv nvolv olved ed pro proble blem! m!

Long Process of Trial-and-Error • Met Method hod:: (1) Try Try given given orbital orbital geom geometry etry,, and (2)) comp (2 compare are wit with h Tych Tycho’s o’s da data ta • Al Alll combi combina natio tions ns invo involv lving ing circles , can only give accuracy of ~ 8 arcmin • Bu But: t: Ke Kepl pler er kn knew ew th that at Ty Tych cho’ o’s s da data ta ha have ve ac accu cura racy cy of ~ 4 arcmin • Thu Thus: s: Reje Reject ct cir circula cularr orbi orbits! ts! • Eventu Eventually: ally: Try ellipti elliptic c orbits orbits with with Sun in one one focus! focus!

Orbit Orb it of of the the Plan Planets: ets: Kep Kepler’ ler’s s 1st Law

• 1st Law: Planets move in ellipses with the Sun in one focus!

Orbit Orb it of of the the Plan Planets: ets: Kep Kepler’ ler’s s 1st Law

• Ell Ellipse ipse is is one of of the three three coni conic c section sections, s, and the circle is a special case! (Conic section sections s described described by Apollonius Apollonius of Perga in 200 BC) BC)

Speed Sp eed of the Pla Planet nets: s: Kepl Kepler’s er’s 2nd Law

Sun Earth

• Start with Sun-cen Sun-centered tered versi version on of Ptolem Ptolemy’s y’s equant! equant!

Speed Sp eed of the Pla Planet nets: s: Kepl Kepler’s er’s 2nd Law

• Ke Kepl pler er re real aliz izes es:: Pse Pseud udoo-eq equa uant nt is al almo most st eq equi uiva vale lent nt to “equal “equal area area in equal equal times times”” as seen seen from from Sun! Sun!

Speed Sp eed of the Pla Planet nets: s: Kepl Kepler’s er’s 2nd Law A=B=C

• 2nd Law: A line drawn from the Sun to a planet sweeps out equal areas in equal times!

Finally solving the Problem of the Planets all planets! • One uni unified fied fra framewo mework rk vali valid d for for all  planets! - No ad ad-ho -hoc c fixe fixes s all allowe owed! d! • For each each planet planet,, 2 free quanti quantities ties (par (paramet ameters ers)) to choose: semi-major axis a, and eccentricity e • It co coul uld d not not hav have e been been don done e with without out Ty Tycho cho’s ’s da data ta!!

Coup Co up-d’ -d’Etat Etat in Pra Pragu gue e (161 (1611) 1) • Emp Emperor eror Rud Rudolph olph depos deposed ed by his brot brother her

Rudolph II • Kepler ha has s to to le leav ave e Pra Pragu gue e

Matthias

Move Mo ve to Lin Linz z (Up (Upper per Aus Austria tria))

Mathematician in Linz (1612-28)

• Tea Teache cherr at Pro Protes testan tantt High High Scho School ol • Upp Upper-Au er-Austr strian ian estate estate mathemati mathematicia cian: n: horoscopes horoscopes

The Harmony of the Worlds • Harmonices Mundi  (Harmony of the Worlds, 1619) • Kepler’s 3rd Law: - P2=a3 • ful fulll of of myst mystica icall spec specula ulation tion

The Harmony of the Worlds

• Kepler’s 3rd Law: - P2=a3

The Harmony of the Worlds

• Th The e Musi Music c of of the the Sph Sphere eres s • re reca callll:: Pyth Pythag agor oras as

Rudo Ru dolp lphi hine ne Ta Tabl bles es (T (Tab abul ulae ae Ru Rudo dolp lphi hina nae) e) • im impro prove ve Rein Reinhol hold’s d’s old old (1551 (1551)) Prutenic Tables  • ba base sed d on Cop Coper erni nicu cus’ s’ De Revolutionibus  • lilimi mited ted acc accur urac acy y in lig light ht of of Tych Ty cho’s o’s ob obse serva rvati tion ons s • Kepler ha has s pro prom mis ise ed Ty Tycho on deathbed to complete this

Rudo Ru dolp lphi hine ne Ta Tabl bles es (T (Tab abul ulae ae Ru Rudo dolp lphi hina nae) e) Rudolphinae (1627) • Tabulae Rudolphinae (1627) • based on Kepler’s new laws of planetary motion • un unpre preced ceden ented ted ac accu cura racy cy (afte (af terr all: all: Kep Keple ler’s r’s is th the e correct model) • Ast Astrono ronomers mers adop adoptt tabl tables es firs first, t, before the theoretical works

Rud Ru dol olph phin ine e Ta Tab ble les s

• Tabl Tables: es: non-gl non-glamor amorous, ous, but but very very usefu useful! l!

Rudo Ru dolph lphine ine Tab Tables: les: The Fron Frontis tispiec piece e • Al Alle legor gory y of of Ast Astron ronom omy y

Witc Wi tchc hcraf raftt Tria Triall of of Kep Keple ler’ r’s s Mo Moth ther er (16 (1620 20-21 -21))

“Water Trial”

• Ke Kepl pler er (s (suc ucce cess ssful fully ly)) defen defende ded d his his ol old d mot mother her

Kepler: Kep ler: Pac Pactt with with the the Devil Devil (16 (1628-3 28-30) 0) • En Ente tere red d the the em empl ploy oy of generalissimo Wallenstein • Wallenstein was fi firm believer in astrology • Mo Mov ved to Sa Saga gan n

Wallenstein, Supreme Commander of Imperial Troops In Thirty Years War

Journey’s End: Death in Regensburg (1630)

Kep Ke ple ler’ r’s s Ep Epit itap aph: h:

“I measured the skies, now the shadows I measure. Skyb Sk ybo oun und d wa was s the the mi mind nd,, eart ea rtbo boun und d th the e bo body dy re rest sts” s”

Kepler’s Kepl er’s role in the Scien Scientific tific Revolu Revolution tion Newton (1642-1727) - dynamics - la law w of of gra grav vit ity y

Kepler (1571-1630) - ce cele lest stia iall mo moti tion on - 3rd Law

“Standing on the shoulders of giants”

Galileo (1564-1642) - la laws ws of fr free ee-f -fal alll - pr prin inci cipl ple e of ine inert rtia ia

Tycho/Kepler (part 2): Johannes Kepler • Jo Joha hann nnes es Ke Kepl pler er:: - final finally ly solves solves the the problem problem of the the planets planets - brea break k free from from the the old dogma dogma of uniform uniform circula circularr motion motion - com complete pletes s Copern Copernican ican Rev Revoluti olution on

• Ke Kepl pler er’s ’s La Laws ws of Pl Plan anet etar ary y Mo Moti tion on - 1st Law: Planets move in ellipses with the Sun in one focus - 2nd Law: A line from the Sun to a planet sweeps over equal areas in equal time (“Law of Areas”) - 3rd Law: P2 = a3

• Kepler calculates Rudolphine Tables  - New st stand andard ard of prec precisi ision on