千米小说网

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

Chapter2GravityintheSolarSystem

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）。

&hreegroupsofexperimehaveledthewayinlaboratorytestsofgravityiimes:oheUyofWashingtoheUyofColorado，andathirdatStanfordUheWashingtongrouptookapendulumwithteoitaoveradiskthatedaofholes。Thependulumwasfoundtotwistduetothemissinggravitatiohemissingmassihisallowedgravitytobemeasureddowntoscalesassmallasatwehofamillimetre。ThegroupsatColoradoandStanford，oherhahegravitationalfieldmass，ahisinformatiravityallthewaydownto140ofamillimetre。Theresultsoftheselaboratoryexperimentshavesofarallbeeirelytwithon’sinversesquarelawofgravity，evenontheverysmallestofscales。