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