Mastering Astronomy-Assignment 6-Solutions PDF

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11/2/2018

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Assignment6

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Assignment6 Due:11:59pmonSunday,November4,2018 Tounderstandhowpointsareawarded,readtheGradingPolicyforthisassignment.

PrelectureOverview:JovianPlanetSystems Description:Thisassessmentisdesignedasaquickcheckofwhetherastudenthasactuallywatchedtheprelecturevideoforthischapter.Itshouldbeeasyiftheyhave.Keepin mindthatthesevideosofferonlyabriefintroductiontoselectedtopicsfromthechapter,intendedtospurinterestthatwillleadtomoreindepthstudy. First,launchthevideobelow.Then,closethevideowindowandanswerthequestionsatright.Youcanwatchthevideoagainatanypoint.

PartA Thetwojovianplanetsthatcontainthehighestproportionsofhydrogencompoundsare___________.  Hint1.Whatconditionsarenecessaryforfusion? Fusionrequiresbringingtwopositivelychargednucleisoclosetogetherthatthestrongnuclearforcecanholdthemagainsttheelectromagneticrepulsionoftheirpositive charges.Whatconditionsmakefusionpossible? ANSWER: xtremelyhightemperatureandhighdensity xtremelyhightemperaturebutlowdensity owtemperatureanddensity

Ittakeshightemperaturefornucleitogetintocloseenoughcontactforfusion,andhighdensityforthistohappenwithenoughlikelihoodthatfusionwillcontinue.An increaseineitherthetemperatureordensitywillincreasethefusionrate.Whenyouthinkaboutthisfact,youshouldbeabletocompletePartA.

Hint2.Howdoesthecoretemperaturedependonthecoreradius? WhentheSun’scorecontracts,thecoretemperature__________. ANSWER:

ncreases ecreases taysthesame

Justaswhenyoucompressairinabicycletirepump,compressingtheSun’scoreincreasesitstemperature.Now,rememberthatthefusionrateisverysensitiveto temperature(openthefirsthinttolearnwhy),andyoushouldbeabletocompletePartA.

ANSWER:

upiterandNeptune  upiterandUranus  ranusandNeptune  aturnandNeptune upiterandSaturn  aturnandUranus

PartB Matchthewordsatthelefttothecorrectblanksinthesentencesatright. Useeachchoiceonlyonce.

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ANSWER:

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Scientistshavedetectedlakesofliquidmethaneandethaneonthesurfaceof Titan . 

 ThetwomoonsthatarelargerthantheplanetMercuryareTitanand Ganymede ,whichisalsothe 

largestofJupiter'smoons(andlargestmooninthesolarsystem).

 Jupiterhasthreemoonsforwhichthereisevidenceofaglobal,subsurfaceoceanofliquidwater,with 

thestrongestevidencefavoringanoceanon Europa .  Io isthemostvolcanicallyactiveworldinthesolarsystem.

SpacecraftimagesshowfountainsoficesprayingintospacefromSaturn'smoon Enceladus .

PartC Whichofthefollowingbestdescribesthenatureofplanetaryrings?  ANSWER: heyarecomposedofreflectivemoleculesofgas.  hearesolid,concentricringsaroundaplanet.  heyareasolidsheetofmaterialaroundaplanet,lookingmuchlikeaDVDorbluraydisk.  heyarecomposedofcountlessindividualparticles. 

Theparticlesrangeinsizefromdustgrainstolargeboulders,andeachparticleorbitsitsplanetindependentlyinaccordwithKepler'slaws.

PrelectureVideo:TidalHeating Description:Supportedbyaprelecturevideo.Studentsansweraseriesofquestionsthathelpsthemunderstandhowourtheoryoftidalheatingexplainstheobservablephenomena oftheGalileanmoons. LearningGoal: TounderstandhowweusethetheoryofgravityandtidalheatingtoexplainobservablecharacteristicsoftheGalileanmoonsofJupiter. Launchthevideobelow,thenanswerthefollowingquestions.Youmaywatchthevideoagainatanypoint.

PartA Ioexperiencestidalheatingprimarilybecause__________.

Hint1.WhatisthestrengthofthetidalforceactingonIo? WatchtheportionofthevideothatshowsthegravitationalforceonthenearandfarsidesofIoasitorbitsJupiter.WhatcanyouconcludeaboutthetidalforceactingonIo? ANSWER:

hetidalforceistheconstantthroughoutIo'sorbit. hetidalforcevaries.ItisstrongestwhenIoisclosesttoJupiterandweakestwhenIoisfarthestfromJupiter. hetidalforcevaries.ItisstrongestwhenIoisfarthestfromJupiterandweakestwhenIoisclosesttoJupiter.

ThisvaryingtidalforceessentiallystretchesandcompressesIo'sinteriorasitorbitsJupiter,generatingfrictionandheat.

Hint2.Definitionoftidalheating Tidalheatingisasourceofinternalheatcreatedbytidalfriction.Thisfrictionisgeneratedasaresultofavaryingtidalforce.

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Hint3.Definitionoftidalforce Atidalforcearisesfromadifferenceinthestrengthofagravitationalattractionacrossanobject,causingtheobjecttostretch.Forexample,theMoonexertsagravitational attractiononEarth,butthisattractionisstrongeronthesideofEarththatisfacingtheMoonthanonEarth’soppositeside.Notethatinthevideo,thetidalforceisrepresented bythedifferenceinthelengthsofthetwoarrows(whichrepresentthegravitationalforcebetweenJupiterandthetwosidesofIo).

ANSWER: islocatedveryclosetoJupiter. ismadeofrelativelysoftmaterialsthatdeformquiteeasily. sellipticalorbitcausesthetidalforcetovaryasIoorbitsJupiter. hasanelongatedshapethatmakesitlookmorelikeaneggthanasphere.

ThestrengthofthetidalforcedependsonIo'sdistancefromJupiter,sothetidalforcevariesasIomovesarounditsellipticalorbit.Thetidalbulgeevenchangesdirectionslightly becausetheorbitalspeedvaries.ThesetidaleffectsessentiallystretchandcompressIo'sinterior,andthistidalfrictioncausesthetidalheating.

PartB AsyousawinPartA,Io'sellipticalorbitisnecessarytoitstidalheating.Thisellipticalorbit,inturn,isaresultoftheorbitalresonanceamongIo,Europa,andGanymede.Thisorbital resonancecausesIotohaveamoreellipticalorbitthanitwouldotherwise,because__________.

Hint1.WhatistheorbitalresonanceamongIo,Europa,andGanymede? WhatistheorbitalresonanceamongIo,Europa,andGanymede? ANSWER:

ocompletesexactly4orbitsforevery2orbitsofEuropaandevery1orbitofGanymede. o,Europa,andGanymedeallorbitJupiterinthesamedirectionandinnearlythesameplane. Ganymede'sorbitisexactlytwiceasfarfromJupiterasEuropa,andexactlyfourtimesasfarfromJupiterasIo.

Asshowninthevideo,thismeansthatthesemoonsperiodicallylineupinwaysthatcontributethesamegravitationaltugsastheymoveintheirorbits.

Hint2.Definitionoforbitalresonance Anorbitalresonancemeansthatoneobject'sorbitalperiodisasimplefractionofanother's,suchas1/2or1/3or1/4.Insuchcases,theobjectsperiodicallylineupinawaythat allowstheirmutualgravitytoaffecttheirorbits.

ANSWER:

llthreemoonsorbitwiththesameperiod,stayingalignedatalltimes uropaandGanymedeareunusuallylargemoons uropaandGanymedealwayspullonIofromthesamedirectionasJupiterpullsonIo o,EuropaandGanymedeperiodicallyreturntothesameorbitalpositions,creatingthesamegravitationaltugs

TherepeatedpassesatthesameorbitalpositionmeanthatIoexperiencesrepeatedgravitationaltugsatthesameplaceineachorbit,andthesetugsmakeitsorbitmoreelliptical thanitwouldbeotherwise.

PartC Wecannotseetidalforcesortidalheating;rather,wepredictthattheymustoccurbasedontheorbitalcharacteristicsofthemoons.Whatobservationalevidenceconfirmsthattidal heatingisimportantonIo?

Hint1.Whatdoestidalheatingdo? Ifaworldissubjecttotidalheating,we'dexpectittohavea__________. ANSWER:

hapethatisnonspherical ighinternaltemperature ighsurfacetemperature

Tidalheatingaffectstheinteriorofaworld,makingtheinteriormuchhotterthanitwouldbeotherwise.

Hint2.Definitionoftidalheating Tidalheatingisasourceofinternalheatcreatedbytidalfriction,whichisfrictiongeneratedasaresultofavaryingtidalforce.

ANSWER:

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ANSWER:

o'sunusual,egglikeshape ctivevolcanoesonIo o'ssurprisinglyellipticalorbit heorbitalresonancebetweenIo,Europa,andGanymede

IoisbarelylargerthanourMoon,andtheMoonlongagocooledenoughsothatitnolongerhasvolcanicactivity.Withoutsomeongoingsourceofinternalheating,Iowouldbe similarlyinactive.Therefore,thefactthatIoisthemostvolcanicallyactiveworldinthesolarsystemindicatesthatitmusthaveanongoinginternalheatsource,whichweidentify astidalheating.

PartD OrbitalresonancealsogivesEuropaanellipticalorbit,soitexperiencestidalheating,too.However,EuropaexperienceslesstidalheatingthanIo,becauseEuropa__________than Io.

Hint1.WhatisthesourceofthetidalforceactingonIo? ThetidalforcethatactsonIoisdueprimarilytothegravityof__________. ANSWER: othEuropaandGanymede upiter uropa

Asindicatedbytheforcearrowsinthevideo,thetidalforceonIoiscausedbythegravityofJupiter.Keepinmindthat,becausegravityweakenswithdistance,tidalforces mustalsoweakenwithdistance.Infact,thetidalforceweakensmorerapidlywithdistancethanthegravitationalforce.

Hint2.Definitionoftidalheating Tidalheatingisasourceofinternalheatcreatedbytidalfriction,whichisfrictiongeneratedasaresultofavaryingtidalforce. Hint3.Definitionoftidalforce Atidalforceisaforcearisingfromadifferenceinthestrengthofagravitationalattractionacrossanobject,causingtheobjecttostretch.Forexample,theMoonexertsa gravitationalattractiononEarth,butthisattractionisstrongeronthesideofEarththatisfacingtheMoonthanonEarth’soppositeside.Notethatinthevideo,thetidalforceis representedbythedifferenceinthelengthsofthetwoarrows(whichrepresentthegravitationalforcebetweenJupiterandthetwosidesofIo).

ANSWER:

ontainsmuchmoreice moreperfectlysphericalinshape muchsmaller fartherfromJupiter

ItisJupiter'sgravitythatexertstheprimarytidalforceontheGalileanmoons,andboththisforceandthedifferenceinthisforceacrossamoon(thesourceoftidalheating) weakenwithdistancefromJupiter.IoisclosesttoJupiterandthereforeexperiencesthemosttidalheating;Europaexperienceslesstidalheating,andGanymedeexperiencesthe leasttidalheating.(Callistoisnotexpectedtohaveanytidalheatingsinceitdoesnotparticipateintheorbitalresonancethatmakestheothermoons’orbitsmoreelliptical.)

PartE WenowknowofmanyJupitersizeplanetsaroundotherstars.Supposethatfutureobservationsshowthatoneoftheseplanetshastwoorbitingmoons.Whatadditionalinformation,if any,wouldweneedtodecidewhetherthesemoonsexperiencetidalheating?

Hint1.Howmanyorbitingobjectsarerequiredforanorbitalresonance? Whatistheminimumnumberofmoonsthatmustbeorbitingaplanetforthemoonstohaveanorbitalresonance? ANSWER:

Anorbitalresonanceoccurswhenonemoon'sorbitalperiodisasimplefractionoftheother's,suchas1/2or1/3or1/4.Thismeansthatatleasttwomoonsarerequired.

ANSWER:

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Weneedtoknowwhethereithermoonisvolcanicallyactive. Weneedtoknowtheirorbitalperiods. Weneedtoknowwhethertheplanetalsohasathirdmoon. ootherinformationisneeded:Withtwomoons,thereissuretobetidalheating. ootherinformationisneeded:Withtwomoons,thereisnochanceofanytidalheating.

Weexpecttidalheatingtobepossibleonlyifthereisanorbitalresonancethathelpsmaintainanellipticalorbit.Anorbitalresonanceoccurswhenonemoon'sorbitalperiodisa simplefractionoftheother's,suchas1/2or1/3or1/4.Therefore,bymeasuringtheirorbitalperiods,wecandetermineifthereisaresonance.Havinganorbitalresonance doesn'tautomaticallymeanthatthereistidalheating,butitmakesitagoodpossibility.

RankingTask:JovianPlanetSize,Mass,Distance Description:Asetofthreerankingtasksinwhichstudentsrankthefourjovianplanets,andEarth,accordingtodistancefromtheSun,radius,andmass.

PartA ThefollowingimagesshowEarthandthefourjovianplanetsofoursolarsystem.RanktheseplanetsfromlefttorightbasedontheirdistancefromtheSun,fromclosesttofarthest. (Nottoscale.)

Hint1.HowdothedistancesfromtheSuntothejovianplanetscomparetothedistancesfromtheSuntotheterrestrialplanets? TrueorFalse?Inoursolarsystem,thejovianplanetsareallfartherfromtheSunthanaretheterrestrialplanets. ANSWER:

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Asyourresponseindicates,alloftheterrestrialplanetsareclosertotheSunthanarethejovianplanets.Considerhowthatwillaffectyourranking.

ANSWER:

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PartB ThefollowingimagesshowEarthandthefourjovianplanetsofoursolarsystem.Ranktheseplanetsfromlefttorightbasedontheirsize(averageequatorialradius),fromsmallestto largest.(Nottoscale.) ANSWER:

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PartC ThefollowingimagesshowEarthandthefourjovianplanetsofoursolarsystem.Ranktheseplanetsfromlefttorightbasedontheirmass,fromlowesttohighest.(Nottoscale.) ANSWER:

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Problem11.51 Description:Saturn’smoonsPrometheusandPandoraorbitat139350and141700kilometers,respectively.(a)UsingNewton'sversionofKepler'sthirdlaw,findorbitalperiodof Prometheus.(b)UsingNewton'sversionofKepler'sthirdlaw,findorbitalperiodof... Saturn’smoonsPrometheusandPandoraorbitat139350and141700kilometers,respectively.

PartA UsingNewton'sversionofKepler'sthirdlaw,findorbitalperiodofPrometheus. ANSWER: = 14.7 

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PartB UsingNewton'sversionofKepler'sthirdlaw,findorbitalperiodofPandora. ANSWER: = 15.1 

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Part C

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PartC Findthepercentdifferenceintheirdistances. ANSWER:

= 1.66  

PartD Findthepercentdifferenceintheirorbitalperiods. Expressyouranswerusingtwosignificantfigures. ANSWER: = 2.6  

PartE ConsiderthetwoinaracearoundSaturn:InonePrometheusorbit,howfarbehindisPandora(inunitsoftime)? Expressyouranswerusingonesignificantfigure. ANSWER: 0.4 

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PartF InhowmanyPrometheusorbitswillPandorahavefallenbehindbyoneofitsownorbitalperiods?Convertthisnumberofperiodsbackintounitsoftime.Thisishowoftenthesatellites passbyeachother. ANSWER: 23.1 

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JovianPlanetCompositionsandDensities Description:Thistutorialusesaseriesofmultiplechoicequestionstobuildstudentunderstandingofhowandwhythejovianplanetsdifferincompositionanddensity. LearningGoal: Tounderstandhowandwhythejovianplanetsdifferincompositionanddensity.

Introduction.Thejovianplanetssharemanyimportantcharacteristics,buttheyalsohavesomeimportantdifferences.Beforeyoubegin,studyFigure1,whichshowsthejovianplanetsto scaleandprovidessomebasicdataaboutthem.(Earthisshownforscalecomparison.)

PartA Whichofthefollowingstatementsbestdescribesthegeneralpatternofcompositionamongthefourjovianplanets?

Hint1.Majorcategoriesofingredientsinplanetarycomposition Thefollowingtableshowsthefourmajorcategoriesofingredientthatwerepresentinthesolarnebulaandfromwhichplanetsaremade.Notethatthesecategoriesare abbreviatedinFigure1as“H,He”forhydrogenandheliumgas,and“Hcompounds”forhydrogencompounds.  Typical Condensation Relative Abundance

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HydrogenandHeliumGas HydrogenCompounds

Temperature

hydrogen,helium water(

),methane( ammonia( )

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(bymass)

donotcondenceinnebula ), 

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98%...