Download Lecture 3 - Concord University

PHYS420:Astrophysics
&Cosmology
Dr RichardH.Cyburt
AssistantProfessorofPhysics
Myoffice:402cintheScienceBuilding
Myphone:(304)384-6006
Myemail:[email protected]
Mywebpage:www.concord.edu/rcyburt
Inpersonoremailisthebestwaytogetaholdofme.
MyOfficeHours
TR5:30-17:00am
W5:00-5:00pm
Meetingsmayalsobearrangedatothertimes,byappointment
DouglasAdams
Hitchhiker’sGuidetotheGalaxy
ExploringYourCosmicContext
YourCosmicContext
• BigBangTheory
• EvolutionofUniverse
• Structureformation
• EmergenceofLife
Observations
• Stars,galaxies&otherobjects
• Scale&OrganizationofUniverse
• DarkMatter
• DatafromtheUniverse
You
ToolsforUnderstandingObservations
• ScientificMethod
• InformationfromLight
• Gravity
• UnderstandingSpace&Time
• InteractionofLightw/Matter
• Nuclear&ParticlePhysics
• Questions
• Experience/beliefsabouttheworld
• Yourpersonalcosmology
Whatareyour
thoughts?
BuildingaScientificModel
ScientificModelsmust:
oexplainobservations
opredictfutureobservations
Theprincipleofscience,thedefinition,almost,isthefollowing:Thetest
ofallknowledgeisobservation.Experimentisthesolejudgeofscientific
“truth.”Thefirstprincipleisthatyoumustnotfoolyourself–andyouare
theeasiestpersontofool.
—RichardFeynman
CosmologicalModels:Naked-EyeSky
Anyviablemodelmustexplainallobservationsincludingretrogrademotionof
planetsRetrogradeMotion
modelschange:
owhenpredictionsfail
owhennewobservationsrequirenewexplanations
modelrefined→theory
theoryisendproduct
notmerespeculationoroffhand/wackyidea
GreekCosmology
Pythagoreansoutlook:geometryiseverything,perfected
inspheres
oEarth:sphericalshapeobservationsofEratosthenes
(276-195BC)altitudeofnoondaySunatsolstice:
odirectlyoverheadatSyene,Egyptθ =7◦ fromverticalat
Alexandria
Q:whatdowelearnfromthesimplefactthattheangles
differ?
opaceoffdistances∼ 800kmgeometry:
s/R=θ radians=2π(7◦/360◦)⇒ R∼ 6700km:close!
oMoon,Sun,planets,starsfixedonsphereswhichmove
inuniformcircularmotion
Geocentrism
AncientGreeks:Earthiscenterofuniverse(“geocentric”)
orise&setofsun/moon/planetscanbeexplainedQ:how?
owedon’tfeelEarthisspinningwouldmeanwemoveat900mphw.r.t.Earth
center
→whyaren’tweflungoff?
oapparentlackofstellarparallax
Proofbycontradiction:whatifearthorbitssun?
linesofsightforegroundstarshouldappearstoshiftw.r.t.backgroundstars
⇒ butparallaxeffectnotobserved!Why?
Geocentrism
Nakedeyecannotresolveangles<1’=1arcmin=60arcsec
Thetypicalshiftonthesky~1”=1arcsec…..Verysmalleffect
Parallaxnotdetecteduntil~1830
Aristotleexplaineddataavailableatthetimeandgavestrongevidenceagainst
Sun-centeredpicture!!
GeocentricGrunge
MustexplainRetrogrademotioncannotdothiswithcircularorbits(having
constantangularvelocity)
solutionmustcomplicatetheorbit:adddifferentandepicycle
Epicycles
ClaudiusPtolemy~125AD
Constructedcompletegeocentricmodeleveryplanethadepicycles—infact,epicycles
ontopofepicyclescomplicated/elaboratemodel,butalsosophisticated
Ptolemyaccountedfor
onon-uniformangularspeed
oretrogrademotion
obecauseMercuryandVenusneverseeninoppositioncenteroftheirepicyclesplaced
onlineconnectingearthandsun
howgood:observationsdecide!
oErrorsgenerally<5deg:notbadbutobservable!remainedinusefor∼1400years!!
Voteyourconscience!
IsPtolemy’ssystemascientificmodelforthenaked-eyesky?
◦ Yes
◦ No
ACosmologicalRevolution
wefastforward1.5millenia
→RenaissanceEurope,theageofdaVinci,Michelangelo,ElisabethI,Shakespeare...and:
NicolausCopernicus1473–1543Polish:offendedbyPtolemy’ssystem(onestheticgrounds:
“ugly”)adoptedheliocentric (Sun-centered)cosmologicalmodel
CopernicanModel
oEarthspins⇒ dailymotionofcelestialobjects
oEarthorbitsSun⇒ apparentSunmotioninzodiac
oMercury&VenusorbitsinsideEarth’s⇒ alwaysseennearSun
oretrogrademotion:naturallycausedbyEarth–planetpassing
o simplyexplainsretrogradecorrelationsw/planetlocationRetrogradeMotion
olackofstellarparallax⇒ mustassumelargedistancetostars
CopernicusandDistances
Copernicusmodelalsoallowedhimtocalculaterelative
distancesofplanets
Venus:maxium angle(max“elongation”)fromSunobserved
asαmax =sin46◦
Q:maxelongationgeometryinheliocentricmodel?
fromdiagram:sinαmax =sin46◦ =RV/RE ⇒ RV =0.72RE
Newunit:“astronomicalunit”=averageEarth-Sundistance
1AU≡RE =1.50× 108 km
oEarth(average)orbitradius:1AU
oVenusorbit:0.72AU
Copernicus:What’sNewandWhat’sNot
oplanetsstillonspheres
oCopernicusstillusedepicycles!
opredictionsnotbetterthaninPtolemy’smodel→geometricallyequivalent
oCopernicus’modelnotgenerallyacceptedandPtolemaic–Copernican
o disagreementthoughttobemetaphysical,unanswerablequestion
oQ:sohowdowedecidewhichisright?
Tycho Brahe1546-1601:Danish
AstronomyExtraordinaire
inyouth:observed“novastella”(supernova)
→heavenscorruptible!
observedSun,Moon,planetsfor20years:
careful,accuratedata
butnotagoodnumbercruncher
→likeanygoodprofessor:
madegradstudentdothework!
JohannesKepler1571–1630:Harmonyof
theWorlds
AnalyzedTycho’s datafor20years(!),especiallyMarsmotions
usedheliocentricmodelwithcircles
butobservationsdidn’tquiteagreeasmallerror(fewarcmin!)remained
...tookseriously→afteryearsoftrial&error:
completely&accuratelydescribedplanetorbits
KeplerILaw:LawofEllipses
Eachplanet’sorbitisanellipsewithSunatonefocus
Note:KeplerILawonlygivesorbitshape
saysnothingabouthoworbitevolvesintime
→needmoreinfotofullydescribeorbit,hence...
Kepler’sIILaw:LawofEqualAreas
astraightlinefromtheplanettothesunsweepsoutequalareasinequaltimes
Note:thatthisamountstotellingaboutspeedofplanet
Q:wherefastest?slowest?Answer
Q:Thisstilldoesn’tfullycharacterizeanorbits–whynot?
Kepler’sLaws
KeplerIgivesorbitshapeinspace
KeplerIIgivesorbitevolutionovertime
buthaven’tyetconnectedthetwo:
howdoesspatialcharacter(e.g.,semimajor axisa)relatetotimecharacter(e.g.,
periodP)?
Needonelastlaw...
Kepler’sIIILaw:TheMightyEquaiotion
periodPandsemi-majoraxisaarerelated:P2 ∝ a3
⇒ P2/a3 =const,holdsforallplanets,withsame
constantandsincemustholdforEarth:
P2yrs =a3AU
KudostoKepler
Severalpointsworthnoting...
oAnamazingdiscovery–mathematicsunderliestheworkingsofthecosmos!
oOrbitshaveasimplegeometry...butnotsimplest:ellipsenotcircle
oKepler’slawsremain(almost)perfectlyaccuratetothisday– indeed,inslightly
generalizedformwillshowupinmany(most!)situationswheremotionsare
controlledbygravity
oYetnotewhatwestilldon’thave:anunderstandingofwhy Kepler’slawshold
→thatis,whatisthemechanism thatmakesplanetsmovethisway...forthat,
needtowaitforKepler’ssuccessors...
GalileoGalilei:Astronomer
FirsttousetelescopeinAstronomy
Contributions
omountainsonthemoon
omoonsofJupiter
oSunspots
ThesearebadforPtolemy(butmaybe
notdeadly)Q:how?
Galileoreportingtothefundingagency
GalileoGalilei:Astronomer
Crucial,decisiveexperiment:PhasesofVenus
PtolemaicPredictions
ObservedPhases
CapernicanPredictions
observationscontradictedAristotle,supportedCopernicus
“paradigmshift”(Kuhn)
radicalchangeinoutlook/conceptualframework
GalileoGalilei:Astronomer
Note:Galileoputontrial,forcedtorecantheliocentrism
ohiswork,Copernicus,Keplerbanneduntil1832
oofficialsemi-apology(“mistakesweremade”)1992
complex:crackdownasmuchpoliticalastheologicalshowsviewoftheworld
peoplehad
1. reallynotatallobviousthatsunatcenter
2. theparadigmshiftdifficult,challengedoutlook