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Chapter 2 Gravity in the Solar System（第1页）

Chapter2GravityintheSolarSystem

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TheSolarSystem，ingtheEarth，isourmostimmediatelaboratoryfthecesofgravity.ThegravitatioheSolarSystemisdomiheSun，whichisfarmoremassivethanas.

InorbitsthatarerelativelyclosetotheSuhefoursmallestplas:Merus，Earth，andMars.Furtherout，therearefourmuchlargerplaer，Saturn，Uranus，aheSolarSystemsaherobjects，suets，asteroids，moons，andman-madespacecraft.Bythemotios，andinsomecasesbyiingwiththem，weagreatdealaboutthebehaviravity.

&udyofexperimentalaionalgravityintheSolarSystemtookofidurierhalfofthe20thtury.Whileastronomershadbeentragthemotiosforturies，thedevelopmeeologiesahodsihturyallowedobservatiostobecarriedoutinwaysthathadneverpreviouslybeenpossible.Iryaheresultsofthisworkinsomekindofsensibleorder，Iwillclassifythemihatprobethefoundationalassumptionsofgravitytheories;experimentsthatprobeon’slaerimentsthatprobethesubtleefectsthatresultfromEiheory.

&ingfoundationalassumptions

Thereareanumberoffoundationalassumptionsthatgoiheravity.Theseihattherestmassofashouldbeisposition，aofitsmotioootherbodies.Otherassumptiohatthespeedoflightshouldbethesameiion，andthatallobjectsshouldfallatthesamerate（intheabsen-gravitationalforces）.Overthecourseofthepastturyalltheseideashavebeeremelyhighaccuracy.I’lloutlihebestofthesetestshere，beforewemoveontothinkisthattesttheparticularsofoein’stheravity.

&ofbythinkingaboutmass.Recallthatmassisthequantitythattellsushowmuchforeedtoapplytoaiomakeitacceleratebyafixedamount.It’sthoughttobeapropertyoftheobjectitself.Thisisdifere，whichisthehedownwardsforobjectexertsonyourhandwhenyouholdit，andwhichwouldbediferentifyouheldthesameobjectwhilestandingo.Itismassthatappearsion’slawofgravity，anditismassthatwasshowtyiein’sfamousformula（E=mc2）.Becausethesetwoequatioraltogravity，weohavesomeideaofwhetherornotthemassofareallyisispositionandmotioninagravitatiohislybedoally.

Oddlyeestofendsonpositionistolookathowlightgescolourasittravelsthroughagravitatiohebasicideabehihatphotons（particlesoflight）shouldlyastheyesthegravitationalfieldsofmassiveobjectssuchasstarsorplahisisbecauseittakeseopullsomethingupwardsthroughagravitationalfield.So，justasyouwouldhavetytorunupaflightofstairs，ittakesaphotoytotravelupwardsfromthesurfaceoftheEarth，orawayfromthesurfaceoftheSun.Aenergyofaphotosiscolour（itswavelength），andsoabeamoflighttravellingthroughagravitationalfieldshouldbeexpectedtohaveadiferentcolourdependingonhowfaritisabovethesourceofthatfield.Thisisthereasonwhylightdetectedfarfromthesurfaceofastarisfoulyredder，erihanitasemitted.Theefeowioingoflight.

So，howthegravitatioingoflightbeexpectedtotellusanythingaboutwhetherthemassofadependsonitspositioninagravitatiooahis，let’ssiderthemostdireeasuringthemassofainagravitatioingitupiheamouooktodoso.Thisenergyshouldbedirectlyrelatedtothemassoftheobject，stheeolifttheobjetwhtsshouldtellussomethiaboutitsmassat，ahosetwopositions.U’sdiculttoaccuratelymeasuretheamountyusedbyawinch，astheyteeiheygiveyi，aheropeandtheirowhisiswherethegravitatioingoflightesin.Thefrequencyoflightbemeasuredthpredtheeonslosebygoutofthegravitationalfieldisexpectedtobeexactlythesameasthatwhichwouldbeusedtoliftahamassthatdstothesameenergy（ascalculatedusingE=mc2）.Ifwemeasuretheredshiftingoflight，wethereforehaveahighlyaccurateproxyexperiment，whichisexpectedtoveyexactlythesameinformationasthewi.

&desighegravitatioingoflighterformedforthefirsttimebythestistsRobertPoundaheearly1960s.TheyusedatowerattheJefersonPhysicalLaboratoryatHarvardUy，aheredshiftingofphotoravelledupitsheight.Theyfoundthatthelightdidindeedgecolourasittravelledupwards，andbyanamountthatwasentirelytwithmassbeiofposition.Theoionspossiblewouldhavetobesmallerthantheaccuracyoftheexperimentitself，whichwasatthelevelofabout1pert.AsimilarexperimenthassincarriedoutusiemittedfromtheSun，whichalsohadresultsthatweretwithmassbeiofposition，againatanaccuracyofabout1pert.

&ly，atomicclockshavebeeoprobethesameefect.Theideabehisisthatbeamsoflightarethemselves，insomesense，likeclocks.Thechtisdetermihewavelengthofthephotonsthatmakeupthelight，whichisitselfrelatedtothefrequencyatwhichtheyoscillate.Ifweweretotaketheseosstobethebasisofaclock，bysayingthateachosisooftime，thenweseethattheredshiftingoflightisequivalenttotheappearanceofclocksatdiferentpatdiferentrates.Ieveomeasurethefrequencyoflighttoperformthisexperiment，becauseifaclockbasedoionsofaphotoorunslow，thensomusteveryotherclock.Allwehavetodoisputtwoclocksattwhtsahemtotraheydisplayviaradiosignals.Thediferewhichtheyappeartotick，agtnalsthatareobserved，istheirelyequivalewhichalightsighemshouldberedshifted.

&hereforetaketwohighlyacicdputoneowhileleaviourfeet.Ifthetherosmitsitstimeviaradiosignals，thenarethissigimedisplayedbytheclockwekeptbesideus.Theyshould，inge:aknownasgravitatioiowascarriedoutforthefirsttimebyRobertVessotandMartinLevinein1976.Theyobservedthetimedilatioly，andfoundittobetwithmassbeiofpositiontoanaccuracyofabout1partin10，000（aboutahuimesmoreaccuratethantheHarvardexperiment）.Thisexperimentthereforeprevidemassisiofpositioninagravitatiohaccuracy.

Movingonfrompositioispossibletostructexperimentsthattestwhetherthespeedoflight，orthemassofa，aredepeoheseexperimeoricallyveryimportant，becausebeforeEinsteiheravityitwaswidelybelievedthattherewasasubstaherthatpermeatedthewholeofspace.Theetherwasihemediumthroughwhichwavesoflighttravelled，andhysitilaslateasthe20thtury.Iftheetherexisted，thenthespeedoflightthatanobservermeasuredshoulddepeioravelledthroughit.Eiheoryisinpatiblewiththeexisteher，ashehadstructeditsothatallobserversmeasurethesamespeedoflight，iheirstateofmtestsfortheexisteherwasthereforeanimportantparthistheory.ThemostfamousofthesetestswastheMiorleyexperimein1887.Itisatesttoseeifthespeedoflightdependsoiation.

TheMiorleyexperimentusedadeviasaer，goftwoarms，builtatright-aher.Thisisillustratedifromalaserisshohearms，aedbaitselfbymirrorspositioheirehereflectedlightreachedtheiiowoarmsitwasallowedtoi.Aslightisknoropertiesofawave，itwouldbepossibletoletthetwobeamsoflightioformapattersofwavesiingonthesurfaceofapond）.Theformofthepatternthatisprodutheierdepehofeas，atakesthelaserlighttotravelalohespeedoflightwasdiferedires，thenMiorleyshouldhaveseenthecesofthisbyusingtheirapparatus.

6.Aschematicdiagramofaer.Thebeamsplitterseparatesthelaserlightintotwobeams，eachofwhichisre’eirrhttheh，as，befdiretothedetector.

Miorley’sexperimenthada.Nodiferencewasobservedinthespeedoflight，asittravellediwodiferehisectedbymathetime，astheEarthosedtobeinmotiootheether.Iflightwasawaveihespeedoflightshouldhavebeeioonlyinalaboratorythatwasstationarywithrespecttotheether.Thiswasn’tthoughttobethecasefortheEarth，whichorbitstheSunataround30，000metrespersed.TheexperimentperformedbyMiorleyisthereforetakerongevidetheexisteher，andinfavourofaspeedoflightthatistrulythesameiion.Thiswasveryimportaein’stheory.

&hediredependenasswasgivesthatwereilyperformedbyVernonHughesandRoheearly1960s.Theseiorssideredtheelesthatexistwithinlithiumatoms，andthatorbitthevelocitiesofaroundamillioresperseow，thegravitatioioheseeledaheirimmediatee，isextremelysmall.Thisisbecauseeleshavesuymasses.isstillpossiblethtboundsonanypossiblediredepeheirmass.Thisisbecauseelesgiveoutphotoheyergylevelswithinatoms，ahesephotonshaveaveryspecificsetoffrequenastransitiohemassoftheelesdepeheirdireotiohisrecisepositioioresultedfromenergylevels.Carefulstudies，bybothHughesandDrever，foundhediredepehemassoftheeleelyhighaccuracy.

&’sheideaoftheUyofFreeFall.Rememberthatthisistheheideathatallobjectsfallatthesamerate，asdemalileo.ButGalileo’sexperiment，whilegr，robablynotveryaccurate（bymodernstandards）.So，giventheenheUyofFreeFallforbothoeiherehassubsequeofeforttoverifyittothehighestpossiblelevelofaccuracy.Thishasnowbeendoneinanumberofdiferentes，inumerouslaboratoryexperimentsasace-basedobservations.

So，tosummarize，theresgoodevidenavarietyofdiferes，thatthemassofaisihitspositioionofitsmotion.Thereisalsevidehespeedoflightisthesameiion，andthatallobjectsfalluyatthesamerate.Thesearethefoundationalassumptionsunderwhi’saheorieswerestructed.Let’soexperimentsthataimtoiheoriesthemselves.

&hatprobeon’slaw

&hischapterwewillsiderthepredisofEiheory，whiotedtosupplantthatofon.Hothaton’sinversesquarelawofgravityisagoodenoughapproximatioeiodescribeawidevarietyofbothterrestrialandastronomiena.It’sthereforeverymuchworthwhiletestion’slawtoseeexactlyhowwellitdescribesgravity.Herewewillsidersomeofthemostimportahavebeenperformedsofar.

&laboratorytestoftheinversesquarelaerformedbyHetheehtury.dish’sexperimentmadeuseofatorsioheov’s（illustratedinFigure7）.Uv’s，hoositioramassesiomakethetorsioe.Heputthesemassesclosetotheowereattachedtothetravitatioweeshangingfromthetorsioheextramassesthatdishintroduced，beiherateofrotatious.Theneulledatthemassesattachedtotheththegravitatioweenthem，ahebartorotate.Theresultsofdish’sexperimentthusallravitatioobeprobedoveradistances.Hefoundthatgravityoperatedonthesesawaythatwasentirelytwithon’sinversesquarelaerimehesesameideasonmuchsmallerdistancescales.

Thegesiion’slawofgravityioryariseprincipallyduetotheweakhegravitationalforparedtotheotherforature.Thisweakeveresidualelectricapieetotallyoverwhelmthegravitationalforgitimpossibletomeasure.Allexperimethereforeobepreparedwiththegreatestofdtheiricchargesthatshroughhavetobesedbyintrodugmetalshieldsthatreducetheirihismakesthestruoflaboratoryexperimeyextremelydidexplainswhywehavesofarravitydowlebelow1mm（thisparedtoaroundabillionthofabillionthofamillimetrefortheelectricforce）.