The Revolution of the Moons of Jupiter.docx

The Revolution of the Moons of Jupiter.docx

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TheRevolutionoftheMoonsofJupiter

TheRevolutionoftheMoonsofJupiter

StudentManual

AManualtoAccompanySoftwarefortheIntroductoryAstronomyLabExerciseDocumentSM1:

Circ.Version1.1.1

DepartmentofPhysics

GettysburgCollege

Gettysburg,PA17325

Telephone:

（717）337-6028

email:

clea@gettysburg.edu

ContemporaryLaboratoryExperiencesinAstronomy

Contents

Goals3

Equipment4

HistoricalBackground4

Introduction4

OverallStrategy6

BeforeYouStart6

Procedure7

CalculatingJupiter’sMass9

QuestionsandDiscussion12

ExtraCredit13

DataSheets14

Equipment

ThisexperimentusesaWindowscomputer,theCLEAprogramTheRevolutionoftheMoonsofJupiter,andascientificcalculator.（Notethatthecomputermentionedabovemayprovidesuchacalculator.）

HistoricalBackground

Astronomerscannotdirectlymeasuremanyofthethingstheystudy,suchasthemassesanddistancesoftheplanetsandtheirmoons.Nevertheless,wecandeducesomepropertiesofcelestialbodiesfromtheirmotionsdespitethefactthatwecannotdirectlymeasurethem.In1543NicolausCopernicushypothesizedthattheplanetsrevolveincircularorbitsaroundthesun.TychoBrahe（1546-1601）carefullyobservedthelocationsoftheplanetsand777starsoveraperiodof20yearsusingasextantandcompass.TheseobservationswereusedbyJohannesKepler,astudentofBrahe’s,todeducethreeempiricalmathematicallawsgoverningtheorbitofoneobjectaroundanother.Kepler’sThirdLawistheonethatappliestothislab.Foramoonorbitingamuchmoremassiveparentbody,itstatesthefollowing:

where

Misthemassoftheparentbodyinunitsofthemassofthesun

aisthelengthofthesemi-majoraxisinunitsofthemeanEarth-Sundistance,1A.U.（astronomicalunit）.Iftheorbitiscircular（asweassumeinthislab）,thesemi-majoraxisisequaltotheradiusoftheorbit.

pistheperiodoftheorbitinEarthyears.Theperiodistheamountoftimerequiredforthemoontoorbittheparentbodyonce.

In1609,thetelescopewasinvented,allowingtheobservationofobjectsnotvisibletothenakedeye.GalileousedatelescopetodiscoverthatJupiterhadfourmoonsorbitingitandmadeexhaustivestudiesofthissystem,whichwasespeciallyremarkablebecausetheJupitersystemisaminiatureversionofthesolarsystem.Studyingsuchasystemcouldopenawaytounderstandthemotionsofthesolarsystemasawhole.Indeed,theJupitersystemprovidedclearevidencethatCopernicus’heliocentricmodelofthesolarsystemwasphysicallypossible.UnfortunatelyforGalileo,theinquisitiontookissuewithhisfindings;hewastriedandforcedtorecant.

Introduction

WewillobservethefourmoonsofJupiterthatGalileosawthroughhistelescope,knowntodayastheGallileanmoons.TheyarenamedIo,Europa,GanymedeandCallisto,inorderofdistancefromJupiter.Youcanremembertheorderbythemnemonic“IEatGreenCarrots.”

IfyoulookedatJupiterthroughasmalltelescope,youmightseethefollowing:

Figure1

JupiterandMoonsThroughaSmallTelescope

Themoonsappeartobelinedupbecausewearelookingedge-onattheorbitalplaneofthemoonsofJupiter.Ifwewatched,asGalileodid,overasuccessionofclearnights,wewouldseethemoonsshuttlebackandforth,moreorlessinaline.Whilethemoonsactuallymoveinroughlycircularorbits,youcanonlyseetheperpendiculardistanceofthemoontothelineofsightbetweenJupiterandEarth.IfyoucouldviewJupiterfrom“above”（seeFigure2）,youwouldseethemoonstravelinginapparentcircles.

Figure2

ViewfromabovethePlaneofOrbit

RapparentshowstheapparentdistancebetweenthemoonandJupiterthatwouldbeseenfromearth.

AsyoucanseefromFigure3onthenextpage,theperpendiculardistanceofthemoonshouldbeasinusoidalcurveifyouplotitversustime.Bytakingenoughmeasurementsofthepositionofamoon,youcanfitasinecurvetothedataanddeterminetheradiusoftheorbit（theamplitudeofthesinecurve）andtheperiodoftheorbit（theperiodofthesinecurve）.Onceyouknowtheradiusandperiodoftheorbitofthatmoonandconvertthemintoappropriateunits,youcandeterminethemassofJupiterbyusingKepler’sThirdLaw.YouwilldetermineJupiter’smassusingmeasurementsofeachofthefourmoons;therewillbeerrorsofmeasurementassociatedwitheachmoon,andthereforeyourJupitermassesmaynotbeexactlythesame.

Figure3

GraphofApparentPositionofaMoon

Theapparentpositionofamoonvariessinusoidallywiththechanginganglefromthelineofsight,θ,asitorbitsJupiter.Heretheapparentpositionismeasuredinunitsoftheradiusofthemoon’sorbit,R,andtheanglemeasuredindegrees.

Thisprogramsimulatestheoperationofanautomaticallycontrolledtelescopewithacharge-coupleddevice（CCD）camerathatprovidesavideoimagetoacomputerscreen.Italsoallowsconvenientmeasurementstobemadeatacomputerconsole,aswellasadjustmentofthetelescope’smagnification.Thecomputersimulationisrealisticinallimportantways,andusingitwillgiveyouagoodunderstandingofhowastronomerscollectdataandcontroltheirtelescopes.Insteadofusingatelescopeandactuallyobservingthemoonsformanydays,thecomputersimulationshowsthemoonstoyouastheywouldappearifyouweretolookthroughatelescopeatthespecifiedtime.

OverallStrategy

Thisistheoverallplanofactionforthislaboratoryexercise.

•StartuptheprogramanduseittofamiliarizeyourselfwiththeJupitersystem.

•Setupobservingsessions.

•MeasurepositionsofJupiter’smoonsoversuccessiveclearnights.

•Plotagraphofyourobservationsforeachmoon,usingtheRevolutionofJupiter’sMoonsprogram.

•Usingthisprogramtohelpyou,fitasinecurvetoeachgraph.

•Determinetheperiodandsemi-majoraxisfortheorbitofeachmoonfromitsgraph,thenconvertthevaluestoyearsandAU,respectively.

•CalculatethemassofJupiterfromyourobservationsofeachmoon,thendeterminetheaveragevalueforJupiter’smassfromyourindividualvalues.

BeforeYouStart

Nowisanidealtimetohavealittlefunwiththeprogramandintheprocessvisualizewhatyouwillbedoingandwhy.StartuptheJupiter’sMoonslab;thenselectLogin...fromtheFilemenu.Enteryourname（s）andtablenumberinthedialogueboxthatappearsandselectOK.NowselectFile...>Run...;whenthenextwindowpopsup,simplyselectOKtoacceptthedefaultsfortheStartDate&Time;youwillbegoingbacktochangetheseafteryou’vefamiliarizedyourselfwiththeprogramandthemotionsoftheJupitersystem.Nowthewindowpicturedbelowappears,showingJupitermuchasitwouldappearinatelescope.Jupiterappearsinthecenterofthescreen,whilethesmall,point-likemoonsareoneitherside.SometimesamoonishiddenbehindJupiterandsometimesitappearsinfrontoftheplanetandisdifficulttosee.Youcandisplaythescreenatfourlevelsofmagnificationbyclickingonthe100X,200X,300X,and400Xbuttons.Thescreenalsodisplaysthedate,UniversalTime（thetimeatGreenwich,England）,theJulianDate（arunningcountofdaysusedbyastronomers;thedecimalisanexpressionofthetime）,andtheintervalbetweenobservations（oranimationstepintervalifAnimationisselected）.

Figure4

ObservationScreen

Todosomethingyoucan’tdowiththerealsky,selectFile>Preferences>Animation,thenclickontheCont.（Continuous）buttononthemainscreen.Watchthemoonszipbackandforthasthetimeanddatescrollby.Withthisanimation,it’sfairlyeasytoseethatwhatthemoonsarereallydoingiscirclingtheplanetwhileyouviewtheirorbitsedge-on.Toreinforcethis,stopthemotionbyselectingCont.again,selectFile>Preferences>TopView,andstartthemotionagain（Cont.）.NotethatunderthePreferencesmenuyoucanalsochooseIDColorandavoidconfusingthefourmoons.

WhenyouaresatisfiedthatyouunderstandthemotionsofJupiter’smoonsandwhytheyappearthewaytheydo,youarereadytostartthelab.AtanytimeyoumayselectHelpintheupperrightcornerofthemainscreentoviewhelpscreensonawidevarietyoftopics.

TurnofftheAnimationfeaturebeforegoingontothenextsection.

Procedure

DataCollection

Ifyouhavealreadyloggedinasdescribedabove,stopthemotionofthemoons（ifyouhavenotalready）andselectRun...again.TheStartDate&Timewindowwillappear,andnowyouwillchangethedefaults.Eachtablewillperformadifferentsetofobservingsessions.Thestartingdatesofobservationsforeachtable,aswellastheintervalbetweenobservations,willgiventoyoubyyourinstructor.（Atypicalapproachistoobserveattwelve-hourintervalsuntilyouhavesuccessfullyobserved18times.）Fillinthetablebelowfirst;thenentertheinformationintotheprogram.Itisgoodscientificpracticetokeepbothpaperandcomputerrecordswhenpossible.（Notethatthistimeyouwillbereplacingthedefaults,whichareforthecurrentdateandtime.）

TableNumber__________________

Year__________________

Month__________________

Day__________________

TimeZone__________________

NumberofObservations__________________

IntervalBetweenObs.__________________

Inordertomeasurethepositionofamoon,movethepointertothemoonandleft-clickthemouse.Thelowerright-handcornerofthescreenwilldisplaythenameofthemoon（forexample,II.Europa）,theXandYcoordinatesofitspositioninpixelsonyourscreen,anditsXcoordinateexpressedindiametersofJupiter（Jup.Diam.）totheeastorwestoftheplanet’scenter.Thisisthecrucialf