• WebegintodiscusstheconceptualrevolutionswroughtbyCopernicus,Kepler,Galileo,….– Readings: (readingassignmentslistedontheweb)

• Rohrlich,ch. 1-4• Sklar,pp.1-18• Cushingch. 4

• HomeworkforFridayJan.19:(homeworkassignmentsareontheweb)5pmonCOMPASS– DoestheEarthgoaroundtheSunordoestheSungoaroundtheEarth?

Howdoyouknow?Givesomeevidencetosupportyourargument.– Becausethisisthefirstassignment(andveryrushed!),youdonotneedtocite

readingmaterial.Ifyourememberanargumentbutcannotrecallwhereyousawit,useitanyway.Laterinthecourse,youwillbeexpectedtocitesourcesforinformation,andgivecreditforother’sarguments.

– Atmost750words.– Readthehomeworkguidelines,onthehomeworkpage.Theywillgiveyouan

ideahowtostructureyouressays.

Themesfortoday•WhydidtheEarth-centeredPtolemaicsystemlastsolong?

Whywasn’ttheheliocentrictheorypopularbefore1543?

•WhatproblemwasCopernicustryingtosolve?•Whatmakesa“good”theory?Whatcriteriaareusedtotestatheory?Let’strytoseeastronomyfromaviewpointof~1600A.D.Keepinmind:• Observationaldataavailablethen,including

• directastronomicalobservations• otherphysicalobservationsonhowthingsmove

• Thegeneralorganizationoftheworldview,includingmetaphysicalassumptions.

Aristotle:Dialectical:understandtheworldbythinkinghardandarguingopposingviewpointsNatural:generalizeexperienceoftheworld

DevelopmentofAstronomyEarlyexperimentconsistsofdirectobservationandmeasurementoflengthofshadows(thesunandmoon)andangles.Howdidtheymeasurethelengthoftheday?Whatwastheiroperationaldefinition?SolarMeasurements(i.e.sundialsorgnomen)1. Definenoonasthetimewhenthesun’sshadowistheshortest.Wecan

quantitativelymeasurethechangeofseasons.2. Definethesummerandwintersolsticesasthedaysonwhichtheminimumand

maximumshadowsoccur.3. Butmeasurementsdependonlocation

– North-southmovementschangelengths– East-westmovementschangetimes(whatdoesthatmean?howcouldtheyknow?)

Whydowethinktheearthisasphereandnotflat?• Shipsdisappearoverthehorizon• Theangleofthenorthstardependsonlatitude• Thetimeofaneclipsedependsonthelongitude• Theshadowoftheearthonthemooniscircular• Spheresaresimple(metaphysics)

Theastronomicaldata(remember,notelescopesuntilafter1600)

• Thepositionsofallcelestialobjects(dayornight)rotateaboutthenorthpoleapproximatelyonceperday.

• Thestarsmoveinlock-step(e.g.,constellationsdon’tchangeshape).• TheSunlosesonerotationperyearwithrespecttothe“fixed”stars.

– TheentirediskoftheSunislit.• TheMoonlosesonerotationpermonthw.r.t.thestars.

– OnlythatpartoftheMoonwhichfacestheSunislit.Duringasolareclipseitisbetweenthesunandtheearth.

• Themotionoftheplanetsiscomplicated(moreonthislater).• Acommentaboutthedata:

– ThedataavailableinthetimeofCopernicuswasmostlyoldandunreliable.SomehadclearlybeenfudgedtofitpredictionsofthePtolemaicmodel(seebelow).Eventhebestdatawasaccurateonlyto10minutesofarc(1/3thevisualsizeofthemoon):

2spheremodel

Theintuitivepicture(Aristotle)OnEarth

– TheEarthdoesn’tseemtobemoving.Itdoesn'tfeellikeyou'removing.– Objectsdon'tkeepmovingwithrespecttotheearth,butcometorestonthe

earth.• Matterresistsdisplacementandtriestoregainitsnaturalplace:

AIR>FIRE>WATER>EARTH• Explainsasphericalearth,withwaterandairincertainplaces.• Natureabhorsavacuum.HencethespacebetweenEarthandthestarsisfilledwith

aether.• Theonlymotionsthatarenaturalarelinearandcircular.

Inthesky(thankstoAristarchus,about250BC)viageometry,usinglunareclipsesandhalf-moons.• theMoonisabout1/3thediameteroftheEarth.• theSunismuchlargerthantheEarth.

Twospheremodel• Onesphere(theinnerone)is

theEarth,theother(theouterone)isthestars.TheEarthisstationary;thestarsrotateonceperday.ThepositionsoftheorbitsoftheSun,Moon,andplanetsareintermediate,sizedeterminedbyorbitalperiod.

• Thefigureisoversimplified.Thetheorymustexplainsomecomplications,startingwith:– Theseasons:

ThecircletheSunfollowsmovesnorthandsouth.(Themotionofitsspherew.r.t.theoutersphereisstillcircular,butwithanaxisatatiltcomparedtotheaxisofthestar-sphererotation.)

PeterApian's Cosmographia (Antwerp,1539)

Furthercomplications

• Theslightlynon-uniformmotionoftheSunandMoon.Theirspeedincreasesanddecreasesaroundthecircle.

• Thecomplicatedmotionoftheplanets.Sometimes,theymovebackwardswithrespecttothestars(i.e., westward,insteadofslippingslowlyeastward).

PlanetaryMotion• ThePtolemaicsolutionto

theplanetaryproblemmakestheactualtheoryquitecomplicated.Itusesepicycles,eccentrics,andequants.(seefigure)

• PtolemaicsystemwaslooselybasedonanEarth-centeredcosmology,buttheadhoc devicesviolatedthis.

Epicycles

Earth

What an earthbound astronomer seesin the sky. This is the motion withrespect to the fixed stars:

Retrograde motion

East West

Retrograde motion

Planet, Sun, or Moon

Only planets actually move backwards. Sun and Moon merely speed up andslow down.

Epicycle

Deferent

Eccentrics and Equants

Eccentric :

Center of uniform

circular motion is not

the Earth.

Equant :

Center is the Earth.

Angular motion is

uniform about another

center

Earth

Earth

Bothdevicescausetheapparentspeedofthemotionacrosstheskytovary.

OtherIssues• Althoughparticularversionsofthe

systemwerenotespeciallyaccurate,thatcouldalwaysbefixedbyaddingepicycles,etc.

• Thereweremorequalitativeproblems.– WhyareVenusandMercuryalwaysclosetotheSun?

– WhydoesretrogrademotionalwaysoccurwhenaplanetisinoppositiontotheSun?(oppositeinthesky)

– Howcanthemechanicalpictureof"crystalspheres"bereconciledwiththeepicycles,etc.?

Earth

West w ar d diur nal mot ion

2-sphere UniverseLooking Down a t the NorthPole

retrograde

MercuryVenus

Sellingpointsoftwo-spherepicture

• Conceptualeconomy.Ittiestogethermanyfactsinasimplegeometricalmodelstillusedtoday.

• It"preservesthephenomena",i.e.describesbasicastronomicalobservationsofdays,seasons,eclipses...

• Theuniverseisfinite.(infinityisadifficultconcept)• TheEarthstandsstill.• TheEarthisthecenterofeverything

– (intuitive,andinaccordwithmosttheologies).• MotionincreasesystematicallywithdistancefromtheEarth.• Heavy(“earthlike”)objectsareatthecenter.

“Firelike”objectsareattheoutside.– (heavyobjectsfallandfirerises...sothepatternconnectswith

terrestrialdynamics)

Philosophicalbackground• RenewedinterestinPlatonicandPythagoreanphilosophy(vs.

Aristotle’s)increasedvalueplacedonmathematicalsimplicity.Copernicusparticularlydislikedequants.

• So,therewasanimportantshiftintheanswerstotwoquestions:– Isitlegitimatetouseanypointofreferenceinastronomyotherthanthe

Earth?• TheAristotelian/Ptolemaicanswerwasno.ThePythagoreananswerwasyes.

• Infact,thefollowersofPythagoras,mostnotablyAristarchus,hadinventedheliocentriccosmologyinthefifthtothirdcenturiesBC.

– Istheuniverseasawhole,includingourEarth,fundamentallymathematicalinitsstructure?• Aristotleimplicitlyassumedyes,(hencetheperfectcircles),butdidn'tfollowuptheimplications.

• ThePythagoreansalsotendedtoassumeyes,butleftthequestionoftheparticularmathematicalformopen.

• Question:Whatjustificationistherefortheassumptionofmathematicalsimplicity?Occam’srazor?

Sun

Copernic us' universeLooking Down a t the North Pole

(not to sc a le)

Earth

Stars a re a t least 1000times as fa r from Sunas is the Earth

• MadetheEarth rotateonceevery23hours56minutes.

• MadetheSunstationary,atthecenter.

• Madethestellarspherestationary(andverylarge).

• PuttheEarthinacircularorbitaroundtheSun.

• PuttheplanetsincircularorbitsaroundtheSun.

• KepttheMooninacircularorbitaroundtheEarth.

• Whyhavemostobjects(includingtheEarth!)orbitthesun,buttohavetheMoonaloneorbittheEarth?

Copernicus(&Aristarchus)

ThomasDigges'1576Copernicanheliocentricmodelofthecelestialorbs

Copernicus’accomplishments• There'sapatterntowhichobjectmoves:

– Smallerobjectsalwaysorbitbiggerones.– Onemotion(Earth’srotation)explainsthemajormotionofall astronomical

objects(thediurnalmotion).• Retrogrademotion

– Eliminatesthemajorepicycles.– NaturallygivesREGULARITIESoftheretrogrademotionwithfewerarbitrary

parameters.Ithappenswhensuperiorplanets(fartheroutthanEarth)areoppositetotheSunandwheninferiorplanetsarebetweenEarthandSun.

• VenusandMercuryappearclosetotheSuninthesky,havesamenetmotionasSunontheaverage,becausetheyare closetoit.

• Fixesrelativesizesofplanetaryorbitswithoutrequiringanyadditionalassumptions(i.e.,noappealtootherprinciplessuchasnaturalmotion).

WhatCopernicusdidnotaccomplish:• Anysignificantimprovementinaccuracyofpredictions.• EliminationofmostPtolemaicdevices(minoreccentrics,etc.).Onlythebiggest

featureswerereplacedbytheEarth’smotion.

WhyarewecalledCopernicans,notAristarchans?Whatwasgoingonforthose1800years?

DrawbacksofCopernicus’theory• The“secondandthirdmotions”oftheEarth(seeKuhnp.165)

– TheearthissupposedtobecarriedaroundtheSunbyacrystalsphere.ThatwouldmaketheEarth'saxis(whichisn'tparalleltotherotationaxis)alsorotateyearly.ButtheapparentmotionsaredescribedbykeepingtheEarth'saxisfixed.SoCopernicusaddsanotherwobbletotheEarth,whichhastheoddeffectofjustcancelingtheeffectofthecrystalsphereontheEarth'saxis.

– Noticethatwe'veusedtwo hypotheses(crystalsphereandextrawobble)toexplainzero effects(Earth'saxisdoesn'twobble.)Itseemsthereshouldbeasimplerway.Butthenwewouldneedsomeotherway(notattachmenttoarigidsphere)toexplainwhytheEarthorbitstheSun.

– Asimplersolutionofthisproblemrequiresanewdynamics.• TheEarthmoves!

– Doesn'tfitwithAristotelianphysics,whichisstronglybasedonintuition.– Throwarockup!Afallingbodywouldbeleftbehind– Theatmospherewouldbeleftbehind—ahugewind(Aristotle)– Theearthitselfwouldflyapartowingtoforceofrotation.– Copernicusdoesnotdispute—hishypothesisissimplytomakepredictions.

• Onesystematicpattern- therelationbetweentheapparenttype ofobjectanditscosmicplace- islost.Theearthisjustoneofseveralplanets—itisnotunique.

• Starsarefarawaybecauseparallaxisnotobserved.Whydidthecreatorwasteallthatspace?• Copernicusexplicitlyusedthesamecriteriaforevaluatingascientificexplanationthatwetypicallyuse

today:“Wefindtheninthisarrangementanadmirableharmonyoftheworld,andadependable,harmoniousinterconnectionofthemotionandthesizeofthepaths,suchascannototherwisebediscovered...Andallthisresultsfromthesamecause,namelythemotionoftheEarth.“

ScorecardCopernicus Ptolemy

Approximate mathematicalsimplicity

Agreeswithordinaryphysicalintuition

Ptolemaiccosmologyheldonforabout60yearsafter1543.

• Istheresomecrucialobservationtosettlewho'srightorwrong?

• Ifwecaneliminateoneofthesetheories,willwethenknowwhethertheearthgoesaroundthesun?

Thetwocosmologiesmadedifferentpredictions,buttheywere~unobservableuntiltheinventionofthetelescope.In1609,Galileolookedattheheavenswithatelescopeandobservedforhimselfnew“facts”supportingCopernicus. (seeKuhn,pp.219-225)

ThephasesofVenus

ProvesthatVenusorbitstheSun,andshowsthatVenusisspherical

SUN

SUN

EARTH

APPEARANCEFrom Earth

Copernicus Ptolemy

SUN

EARTH

APPEARANCEFrom Earth

Copernicus Ptolemy

SUN

Ptolemic modeliscompletelyruledout

Othertelescopicevidence:– ThemoonsofJupiter• Showsanothercenteroforbitalmotion.SowhyshouldtheEarthbethecenteroftheuniverse?

– Thestarshavesmallerangularsizethanwasthought.• Weakensoneargumentagainsttheirgreatdistance- theymightnothavetobemuchlargerthantheotherknownsourceoflight,theSun

Firsthomeworkisduetomorrowat5pm(FridayJan22rd)onCompass.