Galileo’s Dilemma:Galileo’s Dilemma:Ptolemy, Copernicus, and the Ptolemy, Copernicus, and the

Transformation of the HeavensTransformation of the Heavens

Dr. Frank SummersDr. Frank SummersSpace Telescope Science InstituteSpace Telescope Science Institute

January 9, 2007January 9, 2007

Galileo Galileo –– Triumph and TrialsTriumph and Trials

15641564--16421642Wide range of Wide range of discoveries in physics discoveries in physics and astronomyand astronomyFirst telescopic First telescopic astronomerastronomerTrial by the InquisitionTrial by the Inquisition

1615 – Letter to the Grand Duchess Christina

“The bible was written to show us how to go to heaven, not how the heavens go.”

Cardinal Baronius (1598)

1632 – Dialogue Concerning the Two Chief World Systems

Galileo’s DilemmaGalileo’s Dilemma

1615 1615 –– Holy Office examines CopernicusHoly Office examines CopernicusCorrections: “theory” should be “hypothesis”Corrections: “theory” should be “hypothesis”Galileo ordered not to teach Galileo ordered not to teach heliocentrismheliocentrismIf irrefutable proof, matter could be reopenedIf irrefutable proof, matter could be reopened

Implied challengeImplied challengeGiven the science of the early 1600s, could Given the science of the early 1600s, could Galileo provide irrefutable proof of the Galileo provide irrefutable proof of the heliocentric hypothesis?heliocentric hypothesis?

Motions of the HeavensMotions of the Heavens

SunSunMoonMoonStarsStarsWanderersWanderers

Scientific HeritageScientific Heritage

Pythagoras (569Pythagoras (569--475 BC)475 BC)Plato (428Plato (428--348 BC)348 BC)TheaetusTheaetus of Athens (417of Athens (417--369 BC)369 BC)EudoxusEudoxus of of CnidusCnidus (400(400--347 BC)347 BC)Aristotle (384Aristotle (384--322 BC)322 BC)CallippusCallippus of of CyzicusCyzicus (370(370--300 BC)300 BC)Euclid (325Euclid (325--265 BC)265 BC)

Scientific HeritageScientific Heritage

AristarchusAristarchus of of SamosSamos (310(310--230 BC)230 BC)Archimedes (287Archimedes (287--212 BC)212 BC)ErasthonesErasthones of Alexandria (276of Alexandria (276--195 BC)195 BC)AppolloniusAppollonius of of PergePerge (240(240--190 BC)190 BC)HipparchusHipparchus of of NicaeaNicaea (190(190--120 BC)120 BC)

Claudius PtolemyClaudius Ptolemy

About 100About 100--175 AD175 ADAlexandria, EgyptAlexandria, EgyptMathematical Mathematical Systematic TreatiseSystematic Treatise, , circa 150circa 150Many other books on Many other books on Astronomy, PhysicsAstronomy, PhysicsNot an Egyptian kingNot an Egyptian king

Geocentric ModelGeocentric Model

Earth at center, Earth at center, stationarystationaryMoon, Mercury, Moon, Mercury, Venus, Sun, Mars, Venus, Sun, Mars, Jupiter, Saturn, starsJupiter, Saturn, starsPredict significant Predict significant eventsevents

Sun and SeasonsSun and Seasons

SpringSpring Vernal EquinoxVernal EquinoxMarch 21March 21

00:0700:07

SummerSummer Summer SolsticeSummer SolsticeJune 21June 2118:0618:06

FallFall Autumnal EquinoxAutumnal EquinoxSept 23Sept 2309:5109:51

WinterWinter Winter SolsticeWinter SolsticeDec 22Dec 2206:0806:08

Winter Solstice

Summer Solstice

Autumnal Equinox

Vernal Equinox

Winter Solstice

Summer Solstice

Autumnal Equinox

Vernal Equinox

Winter Solstice

Summer Solstice

Autumnal Equinox

Vernal Equinox

91.3 days

91.3 days91.3 days

91.3 days

Sun and SeasonsSun and Seasons

SpringSpring Vernal Vernal EquinoxEquinox

March 21March 2100:0700:07

92.8 days92.8 days

SummerSummer Summer Summer SolsticeSolstice

June 21June 2118:0618:06

93.7 days93.7 days

FallFall Autumnal Autumnal EquinoxEquinox

Sept 23Sept 2309:5109:51

89.8 days89.8 days

WinterWinter Winter Winter SolsticeSolstice

Dec 22Dec 2206:0806:08

89.0 days89.0 days

Winter Solstice

Summer Solstice

Autumnal Equinox

Vernal Equinox

90.1 days

94.5 days92.5 days

88.1 days

Winter Solstice

Summer Solstice

Autumnal Equinox

Vernal Equinox

90.1 days

94.5 days92.5 days

88.1 days

Geometric Orbit ModelsGeometric Orbit Models

Eccentric circleEccentric circleCircular motion observed from offCircular motion observed from off--centercenter

Deferent circle and epicycleDeferent circle and epicycleCircular motion about circular motionCircular motion about circular motion

EquantEquant motionmotionCircular motion Circular motion wrtwrt to offto off--center pointcenter point

Combinations of the aboveCombinations of the above

Circular Motion

t7

t1

t2

t3

t4

t5

t6

t8

Equant Motion

t7

t1

t2

t3

t4

t5

t6

t8

Complex and PowerfulComplex and Powerful

CompendiumCompendiumGathered and extended Greek knowledgeGathered and extended Greek knowledgeOrganized and justified with geometry and data (?)Organized and justified with geometry and data (?)Ptolemy’s Ptolemy’s AlmagestAlmagest vsvs Euclid’s Euclid’s ElementsElements

PredictionPredictionPositions on skyPositions on skyMathematical modelMathematical model

No distances in AlmagestNo distances in AlmagestNo accounting for change in sizeNo accounting for change in size

1500 years1500 years

Middle AgesMiddle Ages

99thth century Arabic translations of “alcentury Arabic translations of “al--mjstymjsty””Variations/extensions to Ptolemaic modelsVariations/extensions to Ptolemaic models1175 Latin translation of Arabic translation1175 Latin translation of Arabic translation1515 First printing of 1515 First printing of AlmagestAlmagest

Nicholas CopernicusNicholas Copernicus

14731473--15431543CracowCracow University, University, Bologna, Padua, Bologna, Padua, FerraraFerraraCanon of the Canon of the cathedral at cathedral at FrauenburgFrauenburg, Poland, Poland

1514 – Commentariolus (little commentary)

““little commentary on little commentary on hypotheses of hypotheses of motions of heavenly motions of heavenly spheres”spheres”Not published, Not published, selectively distributedselectively distributed

1543 – On the Revolutions of Heavenly Spheres

Myth #1Myth #1

Copernicus delayed publishing his work Copernicus delayed publishing his work for fear of reprisal from the churchfor fear of reprisal from the church

Myth #1Myth #1

Copernicus delayed publishing his work Copernicus delayed publishing his work for fear of reprisal from the churchfor fear of reprisal from the church

Reality checkReality checkCardinal Cardinal SchSchöönbergnberg and Bishop Giese urged and Bishop Giese urged Copernicus to publishCopernicus to publishBook was dedicated to Pope Paul IIIBook was dedicated to Pope Paul III

Myth #2Myth #2

Copernicus viewed his system as only a Copernicus viewed his system as only a mathematical device, not realitymathematical device, not reality

Myth #2Myth #2

Copernicus viewed his system as only a Copernicus viewed his system as only a mathematical device, not realitymathematical device, not reality

Reality checkReality checkAndreas Andreas OsianderOsiander inserted introductory letterinserted introductory letterBishop Giese attempted to get letter removedBishop Giese attempted to get letter removed

Myth #3Myth #3

Copernicus’ SunCopernicus’ Sun--centered model was centered model was much simpler than Ptolemy’s Earthmuch simpler than Ptolemy’s Earth--centered modelcentered model

Myth #3Myth #3

Copernicus’ SunCopernicus’ Sun--centered model was centered model was much simpler than Ptolemy’s Earthmuch simpler than Ptolemy’s Earth--centered modelcentered model

Reality checkReality checkSimplicity claim in Simplicity claim in CommentariolusCommentariolusCopernicus used eccentrics and epicyclesCopernicus used eccentrics and epicyclesNo new mathematical techniquesNo new mathematical techniques

Myth #4Myth #4

Copernicus’ SunCopernicus’ Sun--centered model was centered model was much more accurate than Ptolemy’s Earthmuch more accurate than Ptolemy’s Earth--centered modelcentered model

Myth #4Myth #4

Copernicus’ SunCopernicus’ Sun--centered model was centered model was much more accurate than Ptolemy’s Earthmuch more accurate than Ptolemy’s Earth--centered modelcentered model

Reality checkReality checkNo greater accuracy in predictionsNo greater accuracy in predictionsNo significant advances in observations usedNo significant advances in observations used

Myth #5Myth #5

Astronomers embraced Copernicus’ SunAstronomers embraced Copernicus’ Sun--centered modelcentered model

Myth #5Myth #5

Astronomers embraced Copernicus’ SunAstronomers embraced Copernicus’ Sun--centered modelcentered model

Reality checkReality check“Copernicans” were few, even a century later“Copernicans” were few, even a century laterGiordano Bruno burned at the stake in 1600Giordano Bruno burned at the stake in 1600

Ptolemy Ptolemy vsvs CopernicusCopernicus

Scientific basisScientific basisAlmagestAlmagest –– compendiumcompendiumRevolutionsRevolutions –– new ideasnew ideas

HeritageHeritageThousand years of refinement by manyThousand years of refinement by manyLone partLone part--time astronomertime astronomer

Common senseCommon senseAbsurdity of Earth motionAbsurdity of Earth motionAbsurdity of star motionAbsurdity of star motion

GalileoGalileo

15641564--16421642Professor of Math at Professor of Math at Pisa and PaduaPisa and PaduaMathematician and Mathematician and philosopher to Grand philosopher to Grand Duke at FlorenceDuke at Florence

1610 – Starry Messenger

Mountains on the MoonMountains on the MoonPhases of VenusPhases of Venus“Galilean” moons of “Galilean” moons of JupiterJupiterInnumerable stars in the Innumerable stars in the Milky WayMilky Way

RamificationsRamificationsAristotle wrongAristotle wrongPhilosophical support for Philosophical support for CopernicusCopernicus

TychonianTychonian ModelModel

Galileo’s ProofGalileo’s Proof

On the TidesOn the TidesManuscript written in 1616Manuscript written in 1616Final argument of the Final argument of the DialogueDialogueProposed title “On the flux and reflux of the tides”Proposed title “On the flux and reflux of the tides”

ArgumentArgumentEarth’s motion produces advance and recession of Earth’s motion produces advance and recession of the tidesthe tides‘the ocean, because of its fluid nature, is the only ‘the ocean, because of its fluid nature, is the only thing that can indicate motion of the Earth’thing that can indicate motion of the Earth’‘if Earth were stationary, the tides could not occur’‘if Earth were stationary, the tides could not occur’

Galileo’s ProofGalileo’s Proof

Argument (continued)Argument (continued)Small acceleration and retardation of Earth’s Small acceleration and retardation of Earth’s motion would create tides (sloshing)motion would create tides (sloshing)Daily and annual motion of Earth produce Daily and annual motion of Earth produce faster speed at faster speed at antisolarantisolar point and slower point and slower speed at speed at subsolarsubsolar pointpoint

Galilean TransformationGalilean Transformation

2 kph

Galilean TransformationGalilean Transformation

2 kph

30 kph

Total 32 kph

Orbital motion

Rotational motion

Subsolar point

Antisolar point

Slower motion

Faster motion

Galileo’s ProofGalileo’s Proof

Counter ArgumentCounter ArgumentFaster and slower motion is with respect to Faster and slower motion is with respect to the Sun, not Earththe Sun, not EarthHigh/low tides cycle in about 12 hoursHigh/low tides cycle in about 12 hoursTides occur relative to Tides occur relative to sublunarsublunar and and antilunarantilunarpointspoints

Galileo’s ProofGalileo’s Proof

Counter ArgumentCounter ArgumentSimplicioSimplicio –– “the moon, wandering through the “the moon, wandering through the sky, attracts and draws up toward itself a sky, attracts and draws up toward itself a heap of water which goes along following it, heap of water which goes along following it, so that the high sea is always in that part so that the high sea is always in that part which lies under the moon”which lies under the moon”SalviatiSalviati –– “the moon travels over the whole “the moon travels over the whole Mediterranean every day, but the waters are Mediterranean every day, but the waters are raised only at its eastern extremity and for us raised only at its eastern extremity and for us here at Venice”here at Venice”SagredoSagredo –– “those ridiculous older (opinions)"“those ridiculous older (opinions)"

Transformation of the HeavensTransformation of the Heavens

Galilean transformation Galilean transformation -- motion is relative motion is relative to frame of referenceto frame of referenceGeocentric Geocentric vsvs heliocentric is a change of heliocentric is a change of reference framesreference framesTychonianTychonian system is rotational system is rotational transformation of Copernican systemtransformation of Copernican system

“Take note, theologians, that in your desire to make matters of faith out of propositions relating to the fixity of sun and earth you run the risk of eventually having to condemn as heretics those who would declare the earth to stand still and the sun to change position – eventually, I say, at such a time as it might be physically or logically proved that the earth moves and the sun stands still.”

Note by Galileo in his own copy of Dialogue

New DataNew Data

TychoTycho BraheBrahe 15461546--16011601Astronomer to King Astronomer to King Frederick II of DenmarkFrederick II of DenmarkImperial Mathematician Imperial Mathematician to Emperor Rudolph II in to Emperor Rudolph II in Prague Prague Improvement in Improvement in astronomy relies on astronomy relies on accurate observationsaccurate observations

New IdeasNew Ideas

Johannes Johannes KeplerKepler 15711571--163016301600 Hired by 1600 Hired by BraheBrahe1601 Succeeded 1601 Succeeded BraheBrahe16091609 AstronomiaAstronomia NovaNova

Orbits as ellipsesOrbits as ellipsesEqual area in equal timeEqual area in equal time

1627 1627 RudolphineRudolphine tablestables

New MathematicsNew Mathematics

Isaac Newton 1643Isaac Newton 1643--17271727LucasianLucasian Professor of Professor of Mathematics, Trinity Mathematics, Trinity College, CambridgeCollege, Cambridge1687 1687 PrincipiaPrincipia

Mathematical theory of Mathematical theory of gravitygravityDerives Derives Kepler’sKepler’s lawslaws

ReconciliationReconciliation

1979 1979 –– Pope John Paul II creates Pope John Paul II creates commission to study Galileo’s casecommission to study Galileo’s case

Commission concludes that Galileo should Commission concludes that Galileo should not have been condemnednot have been condemned

1992 1992 –– Pope John Paul II publicly Pope John Paul II publicly endorsed the commission’s findingsendorsed the commission’s findings

The case had become “the symbol of the The case had become “the symbol of the church's supposed rejection of scientific church's supposed rejection of scientific progress, or of 'dogmatic' obscurantism progress, or of 'dogmatic' obscurantism opposed to the free search for truth."opposed to the free search for truth."

ReferencesReferences

Ptolemy’s AlmagestPtolemy’s Almagest, GJ , GJ ToomerToomer (trans)(trans)AlmagestAlmagest Flash animations:Flash animations:

http://www.csit.fsu.edu/~dduke/modelshttp://www.csit.fsu.edu/~dduke/modelsTheories of the World from Antiquity to the Theories of the World from Antiquity to the Copernican RevolutionCopernican Revolution, Michael J. Crowe, Michael J. CroweDialogue Concerning the Two Chief World Dialogue Concerning the Two Chief World SystemsSystems, , StillmanStillman Drake (trans)Drake (trans)