Theleapsecond:itshistoryandpossiblefutureR.A.Nelson,D.D.McCarthy,S.Mal - PDF document

metrologia Theleapsecond:itshistoryandpossiblefutureR.A.Nelson,D.D.McCarthy,S.Malys,J.Levine,B.Guinot,H.F.Fliegel,R.L.BeardandT.R.BartholomewAbstract.Thispaperreviewsthetheoreticalmotivationfortheleapsecondinthecontextofthehistoricalevolutionoftimemeasurement.TheperiodicinsertionofaleapsecondstepintothescaleofCoordinatedUniversalTime(UTC)necessitatesfrequentchangesincomplextimekeepingsystemsandiscurrentlythesubjectofdiscussioninworkinggroupsofvariousinternationalscientiŽcorganizations.UTCisanatomictimescalethatagreesinratewithInternationalAtomicTime(TAI),butdiffersbyanintegralnumberofseconds,andisthebasisofciviltime.Incontrast,UniversalTime(UT1)isanastronomicaltimescaledeŽnedbytheEarth’srotationandisusedincelestialnavigation.UTCispresentlymaintainedtowithin0.9sofUT1.AstheneedsofcelestialnavigationthatdependonUT1cannowbemetbysatellitesystems,suchastheGlobalPositioningSystem(GPS),optionsforrevisingthedeŽnitionofUTCandthepossibleroleofleapsecondsinthefutureareconsidered.1.Introduction:whywehaveleapsecondsApproximatelyonceayear,aleapsecondisintroducedintoUTC,theworld’satomictimescaleforciviltime,inordertokeepitinphasewiththerotationoftheEarth.Leapsecondsensurethat,onaverage,theSuncontinuestobeoverheadontheGreenwichmeridianatnoontowithinabout1s.WhentheatomicdeŽnitionoftheInternationalSystemofUnits(SI)secondwasintroducedin1967,itwaseffectivelymadeequivalenttoanastronomicalsecondbasedonameansolardayof86400sinabout1820.However,overapproximatelythepast1000years,theEarth’srotationhasbeenslowingatanaveragerateof1.4mspercentury,sothatthedayisnowabout2.5mslongerthanitwasin1820.Adifferenceof2.5msperdayamountstoabout1sper R.A.Nelson:SatelliteEngineeringResearchCorporation,7701WoodmontAvenue,Suite208,Bethesda,MD20814,USA.D.D.McCarthy:USNavalObservatory,3450MassachusettsAvenue,NW,Washington,D.C.,20392,USA.S.Malys:NationalImageryandMappingAgency,ResearchandTechnologyOfŽceATTR(MSD-82),4600SangamoreRoad,Bethesda,MD20816,USA.J.Levine:NationalInstituteofStandardsandTechnology,DepartmentofCommerceMS847,325Broadway,Boulder,CO80303,USA.B.Guinot:ObservatoiredeParis,DÂepartementd’AstronomieFondamentale,61avenuedel’Observatoire,F-75014Paris,France.H.F.Fliegel:TheAerospaceCorporation,2350E.ElSegundoBlvd.,ElSegundo,CA90245,USA.R.L.Beard:NavalResearchLaboratory,4555OverlookAvenue,SW,Code8150,Washington,D.C.,20375,USA.T.R.Bartholomew:LittonTASC,Inc.,131NationalBusinessParkway,AnnapolisJunction,MD20701,USA.yearandthisisthereasonforthemoreorlessregularinsertionofleapseconds.Superimposedonthisveryslowlyincreasingdifferenceareshorter-termvariationsinthelengthoftheday.Periodsbetweenleapsecondsarenot,therefore,constantand,infact,overthepastthirtyyearstherehavebeenseveralyearsinwhichleapsecondshavebeenomitted.Theprimaryreasonforintroducingtheconceptoftheleapsecondwastomeettherequirementofcelestialnavigationtokeepthedifferencebetweensolartimeandatomictimesmall.However,themotivationfortheleapsecondhasdiminishedbecauseofthewideavailabilityofsatellitenavigationsystems,suchasGPS,whiletheoperationalcomplexitiesofmaintainingprecisetimekeepingsystemshavemadetheinsertionofleapsecondadjustmentsincreasinglydifŽcultandcostly.ThequestioncurrentlybeingdebatedinrecentlycreatedworkinggroupsofvariousinternationalscientiŽcorganizationsiswhethertherecontinuestobeaneedfortheleapsecond,withitsmanytechnicalinconveniences,orwhetheritwouldbebettersimplytoletatomictimerunfreelyandacceptthattheworld’sciviltimescalewillslowlydivergefromtherotationoftheEarth?Thisarticlegivesthehistoryanddetailedtechnicalbackgroundtothecurrentpracticeandoutlinesvarioussolutions.2.Measurementoftime2.1ClocksTwoelementsareneededtomeasurethepassageoftime:(a)atime“reckoner”,whichisarepeatableMetrologia,2001,38,509-529509 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phenomenonwhosemotionorchangeofstateisobservableandobeysadeŽnitelaw,and(b)atimereference,withrespecttowhichthepositionorstateofthetimereckonercanbedetermined.Theseelementscorrespondtothetwopropertiesoftimemeasurement:intervalandepoch.Together,thetimereckonerandthetimereferenceconstituteaclock.Fromremoteantiquity,thecelestialbodies–theSun,Moonandstars–havebeenthefundamentalreckonersoftime.TherisingandsettingoftheSunandthestarsdeterminethedayandnight;thephasesoftheMoondeterminethemonth;andthepositionsoftheSunandstarsalongthehorizondeterminetheseasons.SundialswereamongtheŽrstinstrumentsusedtomeasurethetimeofday.TheEgyptiansdividedthedayandnightinto12heach,whichvariedwiththeseasons.Whilethenotionof24equalhourswasappliedintheoreticalworksofHellenisticastronomy,theunequal“seasonalhour”wasusedbythegeneralpublic[1].WhentheŽrstreliablewaterclockswereconstructed,greatcarewastakentoreectthebehaviourofasundialinsteadoftheapparentmotionoftheheavens[2].Itwasnotuntilthefourteenthcenturythatanhourofuniformlengthbecamecustomaryduetotheinventionofmechanicalclocks.TheseclocksweresigniŽcant,notonlybecausetheyweremasterpiecesofmechanicalingenuity,butalsobecausetheyalteredthepublic’sperceptionoftime[3,4].Intheeraoftelescopicobservations,pendulumclocksservedasthestandardmeansofkeepingtimeuntiltheintroductionofmodernelectronics.Quartz-crystalclocksweredevelopedasanoutgrowthofradiotechnologyinthe1920sand1930s[5].HaroldLyons[6]attheNationalBureauofStandardsinWashington,D.C.(nowtheNationalInstituteofStandardsandTechnology,Gaithersburg,Md.)constructedtheŽrstatomicclockin1948usingthemicrowaveabsorptionlineofammoniatostabilizeaquartzoscillator.LouisEssenandJ.V.L.Parry[7]attheNationalPhysicalLaboratoryinTeddington,UK,constructedapracticalcaesiumbeamatomicclockin1955.Commercialcaesiumfrequencystandardsappearedayearlater.NormanRamseydevelopedthehydrogenmaseratHarvardUniversityin1960[8].Oncepracticalatomicclocksbecameoperational,theBureauInternationaldel’Heure(BIH)andseveralnationallaboratoriesbegantoestablishatomictimescales[9].TheresponsibilityforthemaintenanceoftheinternationalstandardisnowgiventotheBureauInternationaldesPoidsetMesures(BIPM).Someformofatomictimehasbeenmaintainedcontinuouslysince1955[10].2.2TimescalesThreeprimarymethodsofmeasuringtimehavebeenincommonuseformodernapplicationsinastronomy,physicsandengineering.Thesemethodshaveevolvedasthedesignandconstructionofclockshaveadvancedinprecisionandsophistication.TheŽrstisUniversalTime(UT),thetimescalebasedontherotationoftheEarthonitsaxis.ThesecondisEphemerisTime(ET),thetimescalebasedontherevolutionoftheEarthinitsorbitaroundtheSun.ThethirdisAtomicTime(AT),thetimescalebasedonthequantummechanicsoftheatom.EachofthesemeasuresoftimehashadavarietyofreŽnementsandmodiŽcationsforparticularThetruemeasureoftheEarth’srotationisUT1,whichistheformofUniversalTimecorrectedforpolarmotionandusedincelestialnavigation.However,owingtoirregularitiesintheEarth’srotation,UT1isnotuniform.UT2isUT1correctedfortheseasonalvariation.EphemerisTime(ET)isatheoreticallyuniformtimescaledeŽnedbytheNewtoniandynamicallawsofmotionoftheEarth,Moon,andplanets.Thismeasureoftimehasbeensucceededbyseveralnewtimescalesthatareconsistentwiththegeneraltheoryofrelativity.ThescaleofInternationalAtomicTime(TAI)ismaintainedbytheBIPMwithcontributionsfromnationaltimekeepinginstitutions.TAIisapracticalrealizationofauniformtimescale.ThebasisofciviltimeisCoordinatedUniversalTime(UTC),anatomictimescalethatcorrespondsexactlyinratewithTAIbutiskeptwithin0.9sofUT1bytheoccasionalinsertionordeletionofa1sstep.ThedecisiontoinsertthisleapsecondismadebytheInternationalEarthRotationService(IERS).Since1972,whenUTCwasintroduced,therehavebeentwenty-twoleapseconds,allofwhichhavebeenpositive.3.TimemeasuredbytherotationoftheEarth3.1UniversalTimeUniversalTime(UT1)isthemeasureofastronomicaltimedeŽnedbytherotationoftheEarthonitsaxiswithrespecttotheSun.ItisnominallyequivalenttomeansolartimereferredtothemeridianofGreenwichandreckonedfrommidnight.ThemeansolardayistraditionallydescribedasthetimeintervalbetweensuccessivetransitsoftheŽctitiousmeanSunoveragivenmeridian.Historically,theunitoftime,themeansolarsecond,wasdeŽnedas1/86400ofameansolarday[11,12].TheeclipticistheapparentannualpathoftheSunagainstthebackgroundofstars.Theintersectionoftheeclipticwiththecelestialequatorprovidesafundamentalreferencepointcalledthevernalequinox.Inpractice,UniversalTimeisdetermined,notbythemeridiantransitofthemeanSun,butbythediurnalmotionofthevernalequinoxinaccordancewithaconventionalformulaspecifyingUT1intermsofGreenwichMeanSiderealTime(GMST).The510Metrologia,2001,38,509-529 Theleapsecond:itshistoryandpossiblefuture currentdeŽningrelationforUT1withrespecttotheastronomicalreferencesystemoftheFifthFundamentalKatalog(FK5)[13]isgivenin[14].UT0,adesignationnolongerincommonuse,isUT1corruptedbythetorque-freeprecessionalmotionoftheEarth’saxisofrotationwithrespecttotheEarth’ssurface[15].Thiseffect,calledvariationoflatitude,waspredictedbyLeonhardEuler[16]in1765asapropertyofrigidbodymotionandwasidentiŽedobservationallybySethChandler[17]in1891.Thedifference[UT0–UT1]hasamaximumvalueofabout20msatmeanlatitude[18].Apparentsolartime,asreaddirectlybyasundialormorepreciselydeterminedbythealtitudeoftheSun,isthelocaltimedeŽnedbytheactualdiurnalmotionoftheSun.However,becauseofthetiltoftheEarth’saxisandtheellipticalshapeoftheEarth’sorbit,thetimeintervalbetweensuccessivepassagesoftheSunoveragivenmeridianisnotconstant.Thedifferencebetweenmeanandapparentsolartimeiscalledtheequationoftime.Themaximumamountbywhichapparentnoonprecedesmeannoonisabout16.5minaround3November,whilethemaximumamountbywhichmeannoonprecedesapparentnoonisabout14.5minaround12February.Untiltheearlynineteenthcentury,apparentsolartimewasusedastheargumentforastronomicalephemerides.However,asclocksimprovedandtheirusebyshipsatseaandbyrailroadsgrew,apparentsolartimewasgraduallyreplacedbymeansolartime.3.2SiderealTimeLocalSiderealTime(LST)isthemeasureofastronomicaltimedeŽnedbytherotationoftheEarthwithrespecttothestars.LSTmaybedeŽnedastherightascensionofthelocalmeridian,whichistheanglebetweenthevernalequinoxandthelocalmeridianmeasuredalongthecelestialequator.Inparticular,GreenwichsiderealtimeistherightascensionoftheGreenwichmeridian.Thesiderealdayisthetimeintervalbetweensuccessivetransitsofthevernalequinox.ItrepresentstheEarth’speriodofrotationrelativetothestarsandisapproximately86164.0905meansolarseconds.OwingtoprecessionoftheEarth’saxiswithrespecttothecelestialreferencesystem,thesiderealdayisabout0.0084sshorterthantheactualperiodofrotationininertialspace.ThusthetruerotationalperiodoftheEarthisapproximately86164.0989meansolarseconds.However,themeansolardaypresentlyexceedsadayofexactly8400SIsecondsbyabout2.5ms.Therefore,theEarth’speriodofrotationiscurrentlyabout86164.1014SIseconds.EvenLSTisnotauniformmeasureofastronomicaltime.Intheearlytwentiethcentury,theinherentaccuracyoftheShorttfree-pendulumclocksŽrstrevealedtheperiodiceffectsofnutation.Theprincipaltermconsistsofaneighteen-yearoscillationwithanamplitudeofabout1s.Theseeffectscannotbeneglectedanditbecamenecessarytointroducetheconceptofmeansiderealtime,whichisaffectedonlybyprecession.GreenwichMeanSiderealTime(GMST)ismeansiderealtimewithrespecttotheGreenwichmeridian,fromwhichUniversalTime(UT1)isderived.Inthepast,UT1wasdeterminedusingaworldwidenetworkofvisualtransittelescopes,photographiczenithtubesandimpersonal(prismatic)astrolabes.ThreebasictechniquesarenowusedtoestimateUT1:(a)VeryLongBaselineInterferometry(VLBI)measurementsofselectedradiopointsources,mostlyquasars;(b)satellitelaserranging;and(c)trackingofGPSsatellites.Strictlyspeaking,becauseofthemotionofsatelliteorbitalnodesinspace,VLBIprovidestheonlyrigorousdeterminationofUT1.ArevisedconventionalcelestialreferenceframebasedontheobservedpositionsofextragalacticobjectsisbeingdevelopedthatchangesthebasisforUT1,removestheneedfortheequinox,andchangestheuseofprecessionandnutation.3.3VariationsintheEarth’srotationThreetypesofvariationintheEarth’srotationhavebeenidentiŽed:asteadydeceleration,randomuctuations,andperiodicchanges[19].Asearlyas1695,SirEdmondHalley[20]wasledtosuspectanaccelerationinthemeanmotionoftheMoonfromastudyofancienteclipsesoftheSunrecordedbyClaudiusPtolemyandthemedievalArabianastronomer,Muhammedal-BattÅanÅõ.Bythemid-eighteenthcentury,thelunaraccelerationwasfullyestablished.In1754,ImmanuelKant[21]suggestedthatthisaccelerationmightbeanapparentphenomenoncausedbyasteadydecelerationintheEarth’srotationduetotidalfriction.PartoftheeffectwaslaterattributedtothevariationinthesolarperturbationontheMoon’sorbit.AsshownbyPierre-SimonLaplaceandJohnCouchAdams,theplanetaryperturbationscausetheEarth’sorbitaleccentricitytodiminishand,asaconsequence,theSun’smeanactionontheMoonalsodiminishes.Inaddition,theobservedlunaraccelerationisaffectedbytherecessionoftheMoonfromtheEarthinordertocompensatethedecreaseintheEarth’srateofspinbyconservationofangularmomentum.ItwasnotuntilthetwentiethcenturythatanapparentaccelerationoftheSunwasalsoidentiŽed[22-24].RecentstudiesofeclipsesbyF.R.StephensonandL.V.Morrison[25,26]suggestthatthelong-termaveragerateofincreaseinthelengthofthedayisabout1.7mspercentury(–4.5 10–22rad/s2).Althoughtheincreaseinthelengthofdayseemsminiscule,ithasacumulativeeffectonatimescalebasedontheEarth’sMetrologia,2001,38,509-529511 R.A.Nelsonetal. rotation.Inthepast2000yearstheEarthactingasaclockhaslostover3h.Forexample,thecalculatedpathofthetotaleclipseoftheSunwitnessedinBabylonin136B.C.wouldbeinerrorby48.8 ,correspondingtoatimedifferenceof11700s,assumingauniformrateofrotation[27].SirHaroldJeffreysmadetheŽrstquantitativeestimateofglobaltidalfrictionin1920[28,29].Hefoundthattheenergydissipationintheshallowseasappearedtobeofthecorrectorderofmagnitudetoaccountfortheapparentlunarandsolaraccelerations.Therateofenergydissipationbytidalfrictionisnowconsideredtocorrespondtoarateofincreaseinthelengthofdayof2.3mspercentury(–6.1 10–22rad/s2).Toaccountfortheobserveddeceleration,theremustalsobeacomponentintheoppositedirectionofabout0.6mspercentury(+1.6 10–22rad/s2),whichispossiblyassociatedwithchangesintheEarthoblatenessparameter causedbypost-glacialrebound[30]orwithdeepoceandissipation[31].Evidenceforalong-termdecelerationintheEarth’srotation,extendingovermillionsofyears,alsoexistsincoralfossilsthatexhibitbothdailyandannualgrowthrings[32].Forexample,severalcoralsdatingfromthemiddleoftheDevonianPeriod,some370millionyearsago,indicatethatthenumberofdaysintheyearwasbetween385and410.Theevidencesuggeststhattherateofdecelerationwassubstantiallythesamethenasitisnow[33].Besidesasteadydecrease,theEarth’srotationissubjecttofrequentsmallchangesthatarerandomandcumulative[34,35].ThisvariationwasinferredfromstudiesofstatisticalirregularitiesinthedisplacementsoftheMoon,Sun,MercuryandVenusinproportiontotheirmeanmotions.RandomuctuationswereŽrstobserveddirectlybyatomicclocksinthemid-1950s[36].Thereisalsoaperiodicseasonalvariationcausedprincipallybymeteorologicaleffects.TheseasonalvariationwasŽrstreportedin1936byA.ScheibeandU.Adelsberger[37],whoperformedmeasurementsoftheEarth’srotationwithexcellentquartz-crystalclocksatthePhysikalische-TechnischeBundesanstalt(Germany).N.Stoyko[38]attheBIHin1937foundthatthelengthofthedayinJanuaryexceededthatinJulyby2ms,basedontheperformanceofShorttpendulumclocksandbycomparisonoftheratesofquartz-crystalclocksatthenationaltimeservices.Theseasonalvariationinthelengthofthedayisnowknowntobeoftheorderof0.5msaboutthemean[39].TherotationoftheEarthrunsslowbyabout30msinMayandrunsfastbyasimilaramountinNovember.Byinternationalagreement,anempiricalcorrectionfortheseasonalvariationhasbeenappliedsince1January1956,resultinginthetimescaleUT2.ThedifferencebetweenUT2andUT1,ascurrentlyapplied,isgivenin[40].UT2hasapeak-to-peakamplitudeofabout60ms.4.TimemeasuredbytheorbitalmotionsofthecelestialbodiesTheneedformoreuniformmeasuresofastronomicaltimeresultedinthedeŽnitionoftimescalesdeterminedfromthemotionsofthecelestialbodiesinthesolarsystem.OriginallybasedonNewtonianmechanics,theyhavebeenreŽnedtotakeintoaccounttheeffectsofgeneralrelativity.Inaddition,theunitoftime,previouslywithintheexclusivedomainofastronomy,wasincorporatedintothecreationoftheSI.In1948,attherequestoftheInternationalUnionofPureandAppliedPhysics(IUPAP),the9thGeneralConferenceonWeightsandMeasures(CGPM)resolvedtoadoptforinternationaluseapracticalsystemofunitscoveringallbranchesofmetrology.Alimitedsetofbaseunits,includingthesecond,wasselectedbythe10thCGPMin1954andarepresentativelistofderivedunitswascompiledbytheInternationalCommitteeforWeightsandMeasures(CIPM)in1956.TheSIwasofŽciallyestablishedbythe11thCGPMin1960[41].4.1EphemerisTimeBecausethevariationsintheEarth’srotationarecomplex,theCIPMreferredthestudyofanewdeŽnitionofthesecondtotheInternationalAstronomicalUnion(IAU)in1948.AtthesuggestionofG.M.Clemence[42],theConferenceontheFundamentalConstantsofAstronomyheldinParisin1950recommendedtotheIAUthat,insteadoftheperiodofrotationoftheEarthonitsaxis,thenewstandardoftimeoughttobebasedontheperiodofrevolutionoftheEartharoundtheSun,asrepresentedbyNewcomb’sTablesoftheSunpublishedin1895.ThemeasureofastronomicaltimedeŽnedinthiswaywasgiventhenameEphemerisTime(ET).TheworkingdeŽnitionofEphemerisTimewasthroughNewcomb’sformulaforthegeometricmeanlongitudeoftheSunforanepochofJanuary0,1900,12hUT[43],L=279 41 48 .04+129602768 .13T+1 .089T2,where isthetimereckonedinJuliancenturiesof36525days.ThelinearcoefŽcientdeterminestheunitoftime,whiletheconstantdeterminestheepoch.TheIAUadoptedthisproposalin1952atits8thGeneralAssemblyinRome[44].Initially,theperiodofrevolutionoftheEarthwasunderstoodtobethesiderealyear.However,itwassubsequentlypointedoutbyAndrÂeDanjonthatthetropicalyearismorefundamentalthanthesiderealyear,asthelengthofthetropicalyear(equinoxtoequinox)isderiveddirectlyfromNewcomb’sformula,whereasthelengthofthesiderealyear(ŽxedstartoŽxedstar)dependsontheadoptedvalueoftheprecession[45].FromthevalueofthelinearcoefŽcientinNewcomb’sformula,thetropicalyearof1900contains512Metrologia,2001,38,509-529 Theleapsecond:itshistoryandpossiblefuture [(360 60 60)/129602768.13] 36525 86400=31556925.9747s.Therefore,attherecommendationoftheCIPM,the10thCGPMin1954proposedthefollowingdeŽnitionofthesecond:“Thesecondisthefraction1/31556925.975ofthelengthofthetropicalyearfor1900.0.”ButalthoughtheIAUapprovedthisdeŽnitionatitsGeneralAssemblyin1955,DanjoncommentedthatthefractionoughttohaveaslightlymoreprecisevaluetobringaboutexactnumericalagreementwithNewcomb’sformula[46].Consequently,theCIPMin1956,undertheauthoritygivenbythe10thCGPMin1954,deŽnedthesecondofephemeristimetobe“thefraction1/31556925.9747ofthetropicalyearfor1900January0at12hoursephemeristime”.ThisdeŽnitionwasratiŽedbythe11thCGPMin1960[47].Referencetotheyear1900doesnotimplythatthisistheepochofameansolardayof86400s.Rather,itistheepochofthetropicalyearof31556925.9747s.AlthoughETwasdeŽnedintermsofthelongitudeoftheSun,inpracticeitwasrealizedindirectlybycomparisonofobservationsoflunarpositionswithlunarephemerides.Thus,asetofsecondarytimescales(denotedbyET0,ET1andET2)weredeŽnedthatdifferedbecauseofsubsequentimprovementstotheconventionalephemerides[48].In1958,theIAUGeneralAssemblyadoptedaresolutionthatdeŽnedtheepochofEphemerisTimetocoincidewithNewcomb’sformulaasfollows[49]:“EphemerisTime(ET),orTempsdesEphÂemÂerides(TE),isreckonedfromtheinstant,nearthebeginningofthecalendaryearA.D.1900,whenthegeometricmeanlongitudeoftheSunwas279 41 48 .04,atwhichinstantthemeasureofEphemerisTimewas1900January0d12hTheresolutionalsoincludedthedeŽnitionofthesecondgivenbytheCIPMin1956.Inaseparateresolution,theepochforUniversalTimewaschosenas1900January0d12hUTbasedontheFourthFundamentalKatalog(FK4)[50].However,theequinoxofNewcomb’sSun,thelunartheory,andtheFK4didnotagreepreciselyandtheyweremovingwithrespecttooneanother.ThustheactualinstantintimecorrespondingtotheepochofETwasapproximately4slaterthantheepochofUT[51].EphemerisTime(ET)isadynamicaltimedeterminedbythetheoryofcelestialmechanicsandistheoreticallyuniform[52].ETmaybecharacterizedastheindependentvariablethatbringstheobservedpositionsofthecelestialbodiesintoaccordwiththeircalculatedpositionsconstructedfromtheNewtonianlawsofmotion.Therefore,ineffect,itisdeŽnedbytheselaws[53].4.2RelativistictimescalesIn1960,ETreplacedUT1astheindependentvariableofastronomicalephemerides.However,ETdidnotincluderelativisticeffectsanddidnotdistinguishbetweenpropertimeandcoordinatetime.Accordingly,atthe16thGeneralAssemblyinGrenoblein1976,theIAUdeŽnedtime-likeargumentsthatdistinguishcoordinatesystemswithoriginsatthecentreoftheEarthandthecentreofthesolarsystem,respectively,andareconsistentwiththegeneraltheoryofrelativity[54].In1979,thesetimescalesreceivedthenamesTerrestrialDynamicalTime(TDT)andBarycentricDynamicalTime(TDB)[55].TDTreplacedETin1984asthetabularargumentofthefundamentalgeocentricephemerides.TDThasanoriginof1January19770hTAI,withaunitintervalequaltotheSIsecond,andmaintainscontinuitywithET.Atthisepoch,aratecorrectionof–10 10–13wasappliedtoTAItobringtheunitofTAImorecloselyintoaccordwiththeSIsecond[56].In1991theIAUrenamedTDTsimplyTerrestrialTime(TT).ApracticalrealizationofTTis[57][TT]=[TAI]+32.184s.TheconstantoffsetrepresentsthedifferencebetweenETandUT1atthedeŽningepochofTAIon1January1958.TherelationshipbetweenTTandTAIisnotstrictlyrigorousfortwofundamentalreasons[58].First,TAIisastatisticallyformedtimescalebasedoncontributionsfromthemajortimingcentres,whereasTTistheoreticallyuniform.Second,ascaleoftimebasedonthelawsofgravitationmaynotbephilosophicallyequivalenttoonebasedonthequantummechanicsoftheatom.Forephemeridesreferredtothebarycentreofthesolarsystem,theargumentisTDB.Throughanappropriatelychosenscalingfactor,TDBvariesfromTTorTDTbyonlyperiodicvariations,withamplitudeslessthan0.002s.FromthedeliberationsoftheIAUWorkingGrouponReferenceSystemsformedin1988,therearoseninerecommendationsthatwerecontainedinResolutionA4adoptedbythe21stIAUGeneralAssemblyin1991[59].Thegeneraltheoryofrelativitywasexplicitlyintroducedasthetheoreticalbasisforthecelestialreferenceframeandtheformofthespace-timemetrictopost-NewtonianorderwasspeciŽed.TheIAUalsoclariŽedthedeŽnitionofTerrestrialTime(TT)andadoptedtwoadditionaltimescales,GeocentricCoordinateTime(TCG)andBarycentricCoordinateTime(TCB)[60].The“coordinate”timescalesTCGandTCBarecomplementarytothe“dynamical”timescalesTT(orTDT)andTDB.TheydifferinratefromTTandarerelatedbyfour-dimensionalspace-timecoordinatetransformations[61].ThesedeŽnitionswereMetrologia,2001,38,509-529513 R.A.Nelsonetal. furtherclariŽedbyresolutionsadoptedatthe24thIAUGeneralAssemblyheldinManchesterin2000[62].5.InternationalAtomicTimeAlthoughETwasauniformtimescale,itwasnoteasilyrealizedordisseminated.TherapiddevelopmentofatomicclockspermittedyetanotherdeŽnitionoftime[63].5.1ExperimentalatomictimescalesTheŽrstoperationalcaesiumbeamfrequencystandardappearedin1955attheNationalPhysicalLaboratory(NPL,UK)[64].TheRoyalGreenwichObservatory(RGO)establishedatimescale,knownasGreenwichAtomic(GA),usingfree-runningquartz-crystalclocksperiodicallycalibratedintermsofthisstandard.Acommercialcaesiumfrequencystandard,the“Atomichron”,wasdevelopedin1956[65].TheUSNavalObservatory(USNO)inaugurateditsA.1atomictimescaleon13September1956,initiallybasedonacaesiumclockattheNavalResearchLaboratory(NRL)consistingofanAtomichroncaesiumstandardandaquartz-crystalclock.Thefrequencyofthecrystalwasmatcheddailytothecaesiumstandard,whichwasnotoperatedcontinuously[66].TheNationalBureauofStandards(NBS)inBoulder,Colo.,alsomaintainedanatomictimescale,NBS-A,starting9October1957.TheepochsofA.1andNBS-AweremadecoincidentandsetequaltoUT2on1January1958[67].TheA.1timescalewasintroducedforworlduseon1January1959.By1961,A.1wasbasedonatomicos-cillatorsattheUSNO,NRL,NBS,USNOTimeServiceSub-Station(Richmond,Florida),HarvardUniversity,NationalResearchCouncil(Ottawa),NPL,CentreNationald’ÂEtudesdesTÂelÂecommunications(Bagneux),andObservatoiredeNeuchÃatel(Switzerland)[68,69].Oncecontinuousatomictimebecameestablishedatvariouslaboratories,theBIHbeganameanatomictimescalebasedonfrequencycomparisonsbymeansofVLFcarriersat3kHzto30kHzusedforlong-distancecommunicationsandradionavigation[70].InitiallyitwasdesignatedAM,andthenA3,representinganaverageofthethreebestscales.In1960,theBIHbeganpublicationofthedifferencesbetweenUT2andvariousindividualatomictimesobtainedbyintegrationofaccuratefrequencycomparisons.By1969theBIHhadredeŽnedA3tobeanaveragedatomictimescale(TA)basedonseveralprimarylaboratorystandards.In1971,thisscalebecamethescaleofInternationalAtomicTime(TAI)[71].5.2AtomicdeŽnitionofthesecondInJune1955,LouisEssenandJ.V.L.ParryoftheNPLmeasuredtheoperationalresonancefrequencyofthelaboratory’scaesiumstandardwithrespecttothesecondofUT2as(9192631830±10)Hzbycomparisonwiththeadoptedfrequencyofaquartzstandard,whichwascalibratedfromastronomicalmeasurementsperformedattheRGO[72].Overthefollowingthreeyears,incooperationwithWilliamMarkowitzandR.G.HallattheUSNO,theydetermineditsvalueintermsofthesecondofEphemerisTime.PhotographsoftheMoonandsurroundingstarsweretakenbytheUSNOdual-rateMooncameraovertheperiod1955.50to1958.25todeterminetheEphemerisTimefromthepositionoftheMoonataknownUT2.TheUT2scale,basedonobservationsmadewithphotographiczenithtubes(PZTs)attheUSNO,wascalibratedwiththecaesium-beamatomicclockinTeddingtonviasimultaneousobservationsoftheintervalsbetweentimepulsesbroadcastbyradiostationsWWV(theninGreenbelt,Md.)andGBR(Rugby,UK).Themeasuredcaesiumfrequencywas9192631770Hzwithaprobableerrorof±20Hz[73].Theprincipaluncertaintyarosefromtheastronomicalmeasurementsthemselves.OnlysevenyearsafterthedeŽnitionoftheephemerissecondasanSIunitin1960,the13thCGPMinOctober1967adoptedtheatomicsecondasthefundamentalunitoftimeintheInternationalSystemofUnits.ThesecondwasdeŽnedas[74]“thedurationof9192631770periodsoftheradiationcorrespondingtothetransitionbetweenthetwohyperŽnelevelsofthegroundstateofthecaesium133atom”.ThesecondofatomictimeisinprincipleequivalenttothesecondofEphemerisTime.However,thisdecisiondidnotconsiderarecommendationofCommissions4(Ephemerides)and31(Time)oftheIAUin1967inPrague,whichrequestedtheCGPMtorecognizetheephemerissecondasapartoftheIAUsystemofastronomicalconstants,thuscausingobjectionsfromsomeastronomers[75].5.3EstablishmentofTAIAprevalentopinionamongastronomersinthemid-1960shadbeenthattheatomicstandardscouldprovidetheunitoftime,butnotthecontinuousscaleoftimethattheyneeded[76].But,onthecontrary,theBIHwasconvincedthatanatomicstandardwasthebestreferencefortimeanddevoteditsresourcestotheestablishmentofapracticalinternationalscaleofatomictime[77].In1967,IAUCommissions4and31[78]recommendedthattheBIHcomputeaninternationalscaleofatomictime,comprisingindependenttimescalesofthemajornationaltimeservicesbasedonexperiencegainedfromtheexperimentalscaleA3.Italsosuggestedthatthisscalebepublishedintheformofcorrectionstothecontributingtimescaleswithrespecttotheinternationalscale.SimilarrecommendationsfollowedfromtheInternationalUnionofRadioScience514Metrologia,2001,38,509-529 Theleapsecond:itshistoryandpossiblefuture (URSI)in1969andtheInternationalRadioConsultativeCommittee(CCIR)in1970.TheComitÂeConsultatifpourlaDÂeŽnitiondelaSeconde(CCDS)oftheCIPMrecommendedguidelinesfortheestablishmentofInternationalAtomicTime(TAI)in1970.TheCCDSstated[79]:“InternationalAtomicTime(TAI)isthetimereferencecoordinateestablishedbytheBureauInternationaldel’HeureonthebasisofreadingsofatomicclocksoperatinginvariousestablishmentsinaccordancewiththedeŽnitionofthesecond,theunitoftimeoftheInternationalSystemofUnits.”InconformitywiththerecommendationsofIAUCommissions4and31in1967,theCCDS[80]deŽnedtheoriginsothatTAIwouldbeinapproximateagreementwithUT2on1January1958,0hUT2.The14thCGPMapprovedtheestablishmentofTAIin1971.Yetanimportanttaskremained.TodeŽnethescaleofatomictimecompletely,onemustdeŽnewhereintheuniversetheSIsecondistoberealized.Inrecognitionoftheframeworkofgeneralrelativity,thedeŽnitionwascompletedin1980bythestatement[81]:“TAIisacoordinatetimescaledeŽnedinageocentricreferenceframewiththeSIsecondasrealizedontherotatinggeoidasthescaleunit.”ThusrelativisticcorrectionsarerequiredfortheprimarylaboratoryrealizationsoftheSIsecondusedinthecalibrationofTAItocompensatethefrequencyshiftsbetweentheirindividuallocationsandapointŽxedonthesurfaceoftherotatinggeoid.TAI,whenformallyadoptedin1971,wasanextensionoftheBIHatomictimescalethathadbeencontinuousbackto1955.In1988,responsibilityformaintainingTAIwastransferredfromtheBIHtotheBIPM.AdistributionofapproximatelytwohundredclocksmaintainedinŽftylaboratoriescontributetoTAIusinganoptimizedweightingalgorithm.6.CoordinatedUniversalTimeThereweretwocommunitiesofusers.Some,suchasastronomers,geodesistsandnavigators,wantedabroadcasttimeconnectedwiththeangleoftheEarth’srotationinspace.Others,suchasphysicistsandengineersattimeandfrequencylaboratories,wantedittobeperfectlyuniformtoagreewiththebestclocks.AttemptstomeettheneedsofbothcommunitiesledtothecreationofCoordinatedUniversalTime(UTC).6.1OriginalUTCsystemOriginally,radiotimesignalscontrolledfromtheRoyalGreenwichObservatorywerekeptcloselyinphasewiththeEarth’srotationusingdirectastronomicalobservations,resultinginanominaltimeintervalofasecondthatcouldvaryslightlyfromdaytoday.Beginningin1944,thetimesignalsweregeneratedbyquartz-crystalclocksatauniformrate,withstepcorrectionsintroducedwhennecessarytomaintainagreementwithastronomicaltime.WhenanatomicstandardbecameavailableattheNPLin1955,theMSFtimeandfrequencybroadcastserviceoftheUKbaseditssignalontheprovisionalfrequencyof9192631830Hzforcaesium.In1958,theNPLadoptedthefrequency9192631770Hz,butannouncedthattheMSFservicewouldhaveanannualrateoffsetofastatedamount,inadditiontostepcorrections,tokeepthedisseminatedtimesignalsclosetothescaleofUT2[82].Followingthecreationoftheiratomictimescalesintheperiod1956-57,theUSNOandtheNBSeachmaintainedtwosystemsofatomicclocktime.TheUSNOsystemofuniformtime,A.1,wasrelatedtoEphemerisTime,whiletheUSNOMasterClockwasadjusteddailytoUT2fromPZTobservations.Similarly,theNBStimescaleNBS-AhadauniformratesynchronizedwithA.1,whileNBS-UAwasderivedbyapplyingrateoffsetsandsmallstepstofollowUT2andwasdisseminatedbyradiostationWWV.AsummaryofthecorrectionsutilizedbyWWVisgivenin[83].AtŽrst,timesignalsbroadcastfromvariouscountriesweresolooselycontrolledthatalistenermonitoringseveralstationscouldhearthepulsesarrivingatdifferenttimes.Toreducethedisparities,theWorldAdministrativeRadioConference(Geneva)in1959requestedtheCCIRtostudythequestionofestablishingandoperatingaworldwidestandardfrequencyandtimesignalservice.ThenauticalalmanacsoftheUKandtheUSAwerecombinedin1957,beginningwiththeeditionsfor1960.InAugust1959itwasalsoagreedtocoordinatetheirtimeandfrequencytransmissions.Coordinationbegan1January1960.TheparticipatingobservatoriesandlaboratoriesweretheUSNO,RGO,NBS,NRLandNPL.Graduallyothercountriesjoinedthesystem,whichwasentrustedtotheBIHin1961.InJanuary1965,theBIHdecidedtoattachUTCtoitsatomictimeA3(whichbecameTAI)byamathematicalrelationship[84].ThiswastheoriginofthelinkbetweenTAIandUTC.Thename“CoordinatedUniversalTime(UTC)”wasapprovedbyaresolutionofIAUCommissions4and31atthe13thGeneralAssemblyin1967[85].6.2RevisedUTCsystemDetailsoftheUTCsystemwereformalizedbyCCIRStudyGroup7inGenevain1962andwereadoptedbytheCCIRinitsRecommendation374[86]of1963.ThefrequencyoffsetwasannouncedbytheBIH,afterconsultationwiththeobservatoriesconcerned,tomatchasnearlyaspracticaltherotationalspeedoftheEarthandremainedconstantforeachyear,whilestepsof100mswereinsertedperiodicallyatthebeginningofMetrologia,2001,38,509-529515 R.A.Nelsonetal. themonth,ondatesdeterminedbytheBIH,tomaintainthetimesignalstowithinabout0.1sofUT2.AsUTCincludedrateoffsetstoreducetheneedforstepadjustments,thebroadcasttimesignalsindicatedneithertheSIsecondnorthemeansolarsecond,butrathervariableintervalstostayinstepwithUT2,fromwhichtheSIsecondcouldbeobtainedbyapplyingaknowncorrection.Attemptstofollowtheseuctuationsnecessitatedrevisionsincomplexequipmentonafrequentbasisandriskedtemporaryinterruptionsofservice.AtaninterimsessioninMonteCarloduringMarch1965,StudyGroup7suggestedthatexperimentalbroadcastsandstudiesshouldbemadetoinvestigatehowtoprovideboththeepochofUniversalTimeandtheinternationalunitoftimeintervalinthesameemission[87].TherevisedCCIRRecommendation374-1[88]of1966allowedforthelimitedandprovisionaluseofanexperimental“SteppedAtomicTime(SAT)”,inwhichthebroadcasttimeratewastheatomictimerate,withnocarrierdeviation,butinwhichfrequentstepadjustmentsof200mswereappliedtomatchUT2towithin0.1s.Theexistenceoftwoparallelsystems,UTCandSAT,wasregardedasaphaseintheevolutionandadoptionofasingle,practicalandinternationallyacceptablesystem[89].6.3PresentUTCsystemAtthe15thGeneralAssemblyoftheURSIinMunichin1966,Commission1expressedtheopinionthatallproposedmethodsofoperatingstandardtimeandfrequencyservicescontaineddefectsandthattheseservicesmustinevitablydeveloptowardsasystemofuniformatomictimeandconstantfrequency.Forthoserequiringastronomicaltime,someformofcorrectionwouldbenecessary[90,91].In1967,atameetingheldinBrusselsundertheauspicesoftheURSItoconsiderfrequencycoordinationinEurope,itwasunanimouslyagreedthatbothrateoffsetsandstepadjustmentsshouldbediscontinued.ItwassuggestedthatthedeviationsofUTCfromUT2wouldhavenosigniŽcanceforcivilpurposes,butcouldbedisseminatedtonavigatorsintablesorinthetransmissionsthemselves[92].DissatisfactionwiththeexistingformofUTCandtheneedtostudytheimplicationsofthenewdeŽnitionofthesecondadoptedin1967prompteddiscussionsbytheCIPMandtheCCIR.FollowingarecommendationoftheCCDS,theCIPMformedapreparatorycommissionfortheinternationalcoordinationoftimescales.Theconceptoftheleapsecond,analogoustotheleapdayinthecalendar,wasproposedindependentlybyG.M.R.Winkler[93]andLouisEssen[94]atameetingofthecommissionheldattheBIPMinMay1968[95,96].Itwasproposedthatintegerstepsofsecondsreplacethestepsof100msor200msthenbeingusedbecausetheyweretoofrequentandtoosmall.ConsiderationofpossiblemodiŽcationstoUTCwasalsogivenbyCCIRStudyGroup7inBoulderinAugust1968[97].Theviewwasexpressedthatthebestsystemwouldbeonewith1sstepswithoutrateoffsets,sothatequipmentgeneratingapulsetrainwouldnotrequireachangeinfrequency.Tomeettheneedsofnavigators,itwassuggestedthatcodedinformationmightbeincorporatedintheemissiontoindicatethedifferencebetweenUTCandUT2tohigherresolution.AnInterimWorkingParty,IWP7/1,wasformedtoinvestigaterequirements,submitproposals,andŽxadatefortheintroductionofthenewsystem.Theoptionsunderconsiderationatthistimeweresummarizedasfollows[98]:“Discardingthesuggestion(forpracticalreasonsandtoavoidconfusions)oftwotimescales,oneapproachingUT(thepresentUTC)andtheotherwithoutoffsetsandadjustments,onlythreealternativesremain:(a)stepadjustmentof0.1sor0.2stomaintaintheUTCsufŽcientlyneartoUT2topermittoignorethedifferenceinmostoftheapplications;(b)completedisuseofUTCsystem,replacingitwithacoordinateduniformtimescalewithoutoffsetsandstepsandthereforenotapproachingUT;(c)stepadjustmentof1sexactly.”SpeciŽcproposalsweremadebyStudyGroup7inGenevainOctober1969,whichwereapprovedbytheCCIRXIIthPlenaryAssemblyinNewDelhiinJanuary1970.InitsRecommendation460[99],theCCIRstatedthat(a)carrierfrequenciesandtimeintervalsshouldbemaintainedconstantandshouldcorrespondtothedeŽnitionoftheSIsecond;(b)stepadjustments,whennecessary,shouldbeexactly1stomaintainapproximateagreementwithUniversalTime(UT);and(c)standardsignalsshouldcontaininformationonthedifferencebetweenUTCandUT.TheCCIRalsodecidedtobeginthenewUTCsystemon1January1972.AttheIAU’s14thGeneralAssemblyinBrighton,UK,inAugust1970,thechairmanofCCIRIWP7/1,H.M.Smith,soughttheviewsofCommissions4(Ephemerides)and31(Time).TheappropriatemethodofprovidingbothpreciseEarthorientationtonavigatorsanduniformtimetotimeandfrequencylaboratorieswasdiscussed.AsthenavigatorrequiresknowledgeofUT1ratherthanUT2,itwasrecommendedthatradiotimesignalsshoulddisseminatedifferencesintheformof[UT1–UTC].SeveralastronomersemphasizedthatvisualobserversinastronomicalandrelatedŽeldsrequireUT1toaprecisionof0.1s,asthisisaboutthelimitofhumantimediscrimination.Inaddition,thealmanacsweredesignedtopermitadeterminationofpositionto0.1minuteofarc,andforthisacomparableprecisionintimeof0.25swasrequired.AtBrighton,Commission31adoptedrecommendationssimilartothoseoftheCCIR.Also,theIAUGeneralAssemblyresolvedthatadequatemeansshouldbeprovidedtoensurethatthedifference[UT1–UTC]wouldbe516Metrologia,2001,38,509-529 Theleapsecond:itshistoryandpossiblefuture availablebeforepermittingUTCtodepartfromUT1bymorethanabout0.1s[100].DetailedinstructionsfortheimplementationofCCIRRecommendation460weredraftedatafurthermeetingofStudyGroup7thatwasheldinFebruary1971[101].ThedeŽningepochof1January1972,0h0m0sUTCwasset10sbehindTAI,whichwastheapproximateaccumulateddifferencebetweenTAIandUT1sincetheinceptionofTAIin1958,andauniquefractionofasecondadjustmentwasappliedsothatUTCwoulddifferfromTAIbyanintegralnumberofseconds.TherecommendedmaximumdepartureofUTCfromUT1was0.7s.Theterm“leapsecond”wasintroducedforthesteppedsecond.AnadditionalcorrectionDUT1wasintroduced,havingintegralmultiplesof0.1s,tobeembodiedinthetimesignalssuchthat,whenaddedtoUTC,theywouldyieldabetterapproximationtoUT1.Forexample,thissecondlevelofcorrectionwasachievedbyNBSradiostationsWWVandWWVHbyusingdoubleticksorpulsesafterthestartofeachminuteinitsUTCbroadcasts[102].TherecommendationsoftheIAUwereformalizedbyresolutionsofCommissions4and31atthe15thGeneralAssemblyinSydneyin1973and,afterfurtherdiscussion,thenameUTCwasretained[103].UTCwasrecommendedasthebasisofstandardtimeinallcountries,thetimeincommon(civil)useasdisseminatedbyradiosignals.Thelimitof[UT1–UTC]wassetat±0.950s,asthisisthemaximumdifferencethatcanbeaccommodatedbythecodeformat.ThemaximumdeviationofUT1from[UTC+DUT1]wassetat±0.100s.In1974,theCCIRincreasedthetolerancefor[UT1–UTC]from0.7sto0.9s.ThepresentUTCsystemisdeŽnedbyITU-R(formerlyCCIR)RecommendationITU-RTF.460-5[104]:“UTCisthetimescalemaintainedbytheBIPM,withassistancefromtheIERS,whichformsthebasisofacoordinateddisseminationofstandardfrequenciesandtimesignals.ItcorrespondsexactlyinratewithTAIbutdiffersfromitbyanintegralnumberofseconds.TheUTCscaleisadjustedbytheinsertionordeletionofseconds(positiveornegativeleapseconds)toensureapproximateagreementwithUT1.”TheintervalbetweentimesignalsofUTCisthusexactlyequaltotheSIsecond.AhistoryofrateoffsetsandstepadjustmentsinUTCisgivenin[105].7.Theleapsecond7.1RateofincreaseinlengthofdayBecausetheEarth’srotationisgraduallyslowingdown,andinadditionhasbothrandomandperiodicuctuations,itisnotauniformmeasureoftime.Thetimedifference T [ET–UT1] [TT–UT1]representsthedifferencebetweentheuniformscaleofEphemerisTimeorTerrestrialTimeandthevariablescaleofUniversalTime.Valuesof Taresummarizedin[106].Before1955,thevaluesaregivenby T [ET–UT1]basedonobservationsoftheMoon.After1955,valuesaregivenby T [TT–UT1] [TAI+32.184s–UT1]frommeasurementsbyatomicclocksaspublishedbytheBIHandtheBIPM.AccordingtoStephensonandMorrison[107],overthepast2700years canberepresentedbyaparabolaofapproximatelytheform T=(31s/cy2)(T–1820)2/(100)2–20s,where TisexpressedinsecondsandTistheyear.Figure1plotsthisequationtogetherwithobservationssince1620.Thecurvehasaminimumattheyear1820andpassesthrough0attheyear1900.Actualvaluesof TbasedonastronomicaldatamaydiffersomewhatfromthissmoothedŽt.Forexample,thevalueof Tis32.184sat1958.0,theoriginofTAI.However,nosingleparabolacansatisfactorilyrepresentallmodernandhistoricaldata.Thederivativeof Tis Lday (0.0017s/d/cy)(T–1820)/100,Figure1.ObservationsandparabolicŽtof Tversustimesince1620(afterStephensonandMorrison[26]).Figure2.Changeinthelengthofdaywithrespecttoareferencedayof86400sversustime(afterStephensonandMorrison[26]).Metrologia,2001,38,509-529517 R.A.Nelsonetal. Figure3.Changeinthelengthofdaysince1620(afterStephensonandMorrison[25]).whichrepresentsthechangeinthelengthofday(LOD)inSIsecondsrelativetothestandardreferencedayofexactly86400SIseconds.ThisequationisplottedinFigure2.Accordingtothislong-termtrend,therateofincreaseinthelengthofthedayisabout1.7mspercentury.Figure3illustratesobservationsofchangesinthelengthofdayduringtheeraoftelescopicobservations,from1620onwards.Overthismodernperiod,theLODhasbeenincreasingatabout1.4mspercentury[108].Thatis,todayisapproximately1.4mslongerthanadayacenturyago.Otherstudiesimplyslightlydifferentvalues[109,110].TheactualvalueoftheLODwilldepartfromanylong-termtrendduetoshort-termuctuationsofbetween–3msand+4msonatimescaleofdecades.Theepochatwhichthemeansolardaywasexactly86400SIsecondswasapproximately1820.ThisisalsotheapproximatemeanepochoftheobservationsanalysedbyNewcomb,rangingindatefrom1750to1892,thatresultedinthedeŽnitionofthesecondofEphemerisTimefromwhichtheSIsecondwasderived[111].7.2MotivationfortheleapsecondUTCiskeptwithin0.9sofUT1bytheoccasionalinsertionofaleapsecondadjustment.WhenthepresentUTCsystemwasestablishedin1972,thetimedifference T [TT–UT1]=[TAI+32.184s–UT1]wasequalto42.23s.ThusthedifferencebetweenTAIandUT1in1972wasapproximately10s.TomaintaincontinuitywithUT1,UTCwasinitiallysetbehindTAIbythisamount.Asof1January2001,22positiveleapsecondshavebeenadded.ThusUTCispresentlybehindTAIby32s.Figure4illustratestherelationshipsbetweenTAI,UTCandUT1.The1sincrementsareindicationsoftheaccumulateddifferenceintimebetweenauniformtimeandatimemeasuredbytheEarth’srotation.Byanalogy,ifawatchthatloses2sperdayweresynchronizedwithaperfectclockatthebeginningofacertainday,thenafteronedaythewatchwouldbeinerrorby2s.Attheendofamonth,thewatchwouldbeinerrorbyroughly1min.Itwouldthenbeconvenienttoresetthewatchbyinserting1minoftime.Figure4.DifferencebetweenTAIandUT1since1955(fromQuinn[70]).Figure5.DifferencebetweenTAIandUTCduetoleapsecondssince1972.Similarly,theinsertionofleapsecondsisduetothefactthatthepresentlengthofthemeansolardayisabout2.5mslongerthanadayofprecisely86400SIseconds,asaconsequenceofthelong-termtrend,sothattheEarth’srotationrunsslowwithrespecttoatomictime.TheSIsecondisequivalenttothesecondofEphemerisTime,whichinturnisequaltothemeansolarsecondoftheearlynineteenthcentury.Thelengthofthedaywasexactly86400SIsecondsinabout1820.Beforethen,themeansolardaywaslessthan86400sandsincethenithasbeengreaterthan86400s.Attherateofabout1.4mspercenturyoverthepast180years,thelengthofthedayhasincreasedbyroughly2.5ms,sothattodaythelengthofthedayisabout86400.0025SIseconds.Thedifferenceof2.5msperdayaccumulatestonearly1soveranentireyear.Itisthisaccumulateddifferencethatiscompensatedbytheoccasionalinsertionofaleapsecondtomakethelengthoftheyear1slonger.AchangeinthefrequencyofoccurrenceofleapsecondsisanindicationoftheslowingdownoraccelerationoftheEarth’srotation.Aleast-squaresŽtofthedifference[TAI–UTC]since1972,showninFigure5,impliesanearlylinear518Metrologia,2001,38,509-529 Theleapsecond:itshistoryandpossiblefuture increasewithaslopeof(2.10±0.05)msperday.Thisvaluerepresentstheaverageexcessinthelengthofdayduringthepastthreedecadesandisinapproximateagreementwiththevaluecomputedonthebasisofthelong-termtrend.Recentglobalweatherconditionshavecontributedtoashort-termchangeinthelengthofday.DecadeuctuationsduetotheinteractionbetweentheEarth’scoreandmantleandglobaloceancirculationmayalsocontribute.Thusatpresent,thedayisactuallycloserto86400SIsecondsandleapsecondshavenotbeenrequired.However,thisconditioncannotpersistandthelong-termtrendwillbeeventuallyrestored.Themotivationfortheleapsecond,therefore,isduetothefactthatthesecondaspresentlydeŽnedis“tooshort”tokeepinstepwiththeEarth.However,hadthesecondbeendeŽnedtobeexactlyequaltoameansolarsecondattheoriginofTAIin1958,thediscrepancywouldnothavebeenremoved;theagreementbetweentheSIsecondandthemeansolarsecondwouldhaveonlybeentemporaryandtheirdifferencewouldsimplyhavebecomegraduallymoreapparentoverthenextcentury.7.3OperationaldifŽcultiesofpreservingtheleapsecondModerncommercialtransportsystemsdependalmostentirelyonsatellitenavigationsystems.Futuresystemsarelikelytorelyonthesesystemsandtheiraugmentationsystemstoimprovenavigationaccuracy,reliability,integrityandavailabilitybeyondcurrentcapabilities.Increasingworldwiderelianceonsatellitenavigationforairtransportislikelytodemandsystemsfreeofanyunpredictablechangesinepoch.Manytelecommunicationssystemsrelyonprecisetimesynchronization.Forexample,spread-spectrumcommunicationsarenotpossiblewithoutacoherenttimereference.Thus,duringtheintroductionofaleapsecond,communicationscanbelostuntilsynchronizationisre-established.However,onlysystemsthatdependspeciŽcallyontimeareaffectedbytheintroductionofleapseconds;systemsdependingonfrequencyhavelittleornosensitivitytoepoch.Anotherimportantconsiderationisthegrowinguseofcomputers.Intoday’sworldofhigh-speedintercomputercommunicationsthattimestampmessagesatthesub-secondlevel,1scanbeasigniŽcantlengthoftime.Inaddition,clocksnormallycountfrom59sto0softhenextminute.Leapsecondsrequireacountsequenceof59s,60s,andthen0softhenextminute.Manycomputersystemshaveaproblemintroducingthesecondlabelled“60”.AsimilarconcernisthatwhendatingeventsusingtheJulianDay(JD)orModiŽedJulianDay(MJD)includingfractionsofaday,apositiveleapsecondwouldcreateasituationwheretwoevents1sapartcanreceiveidenticaldateswhenthosedatesareexpressedwithanumericalprecisionequivalentto1s.Inglobalsynchronizationoperationsinvolvingmultiplelocations,onefrequentlydealswithdifferinghardwareandsoftwaresystemsbasedondifferentstandardsandoperatingpractices.Thepossibleintroductionofoneortwo61sminutesperyearintocontinuoussiteprocesseswoulddirectlyaffectsynchronizationiftheleapsecondswerenottreatedidenticallyatthesameinstantatallcooperatingsites.Thereal-worldoperationoftimingsystemsisconfrontedbyequipmentupgradesandpersonnelchanges.Thepossibleeffectsofmaintenanceproce-duresandhumanfactorsinaccommodatingleapsecondstepsshouldbegivenconsiderationinassessingthereliabilityofsuchsystems.Stand-alonedata-gatheringsystems,isolatedbyspeciŽcspecializedtechnicalapplications,arenowextremelyrare.Moderndatasystemsrelyoncontinu-ous,highlyaccuratetime.Thepossibilityofdisruptionstocontinuousservicewouldhaveamajorimpactontheirinteractiveoperation.Insomecases,theneedtoavoiddisruptionshasledtoconsiderationsofusingnon-traditionaltimekeepingsystems,suchasGPSTimeoratimescalemaintainedbyanindividualgovernmentcontractor,asameansofservingthispurpose.Continuinguseofanon-uniformtimescalein-cludingleapsecondsinthefaceoftheseconsiderationscouldleadtotheproliferationofindependentuniformtimesadoptedtobeconvenientforparticularobjectives.Ifthathappens,UTCwouldreceivelessacceptanceasaninternationalstandard.7.4OperationaldifŽcultiesofeliminatingtheleapsecondManyastronomersandsatelliteground-stationoperatorswouldpreferthatleapsecondsshouldnotbeeliminated.ThereisasigniŽcantamountofoperationalsoftwareatastronomicalobservatoriesandsatellitegroundstationsthatassumesimplicitlythatDUT1willalwaysbeasmallnumberlessthan1s.Thisassumptionwouldnolongerbetrueifleapsecondswereeliminated.Fixing,testinganddocumentingallthecomputercodescouldbeanenormoustask.ThecurrenttransmissionformatsforradioandtelephonebroadcastsoftimesignalsdependonthefactthatDUT1islessthan1s.ItmaybedifŽculttochangetheseformatsduetotheprevalenceoflegacyhardware.Incommercialindustry,therearecertainclocksthatreceiveradiobroadcasttimesignalstoautomaticallydisplayaccuratetime.Theseandsimilardevicesmightbeaffectedadverselybyachangeinthebroadcastformat.8.SatellitenavigationsystemsHistorically,therationalebehindthedeŽnitionofUTCwasforitsapplicationtocelestialnavigationwhileprovidingaprecisestandardfortimeandfrequency.Metrologia,2001,38,509-529519 R.A.Nelsonetal. CelestialnavigationusingstellarobservationsrequiresknowledgeofUT1atthetimeoftheobservations.Whenitwasintroduced,UTCwasstillthemostreadilyavailableworldwidesystemforindependentdeterminationofposition.ButastheformationofUTCprogressed,theabilitytotracksatellitesonaworldwidebasisandthegrowingglobalcommunicationandpositioningcapabilitiestheycouldprovidebecamemajorconsiderations.Today,withGPS[112]andGLONASS[113],complementedbyLORANandotherradionavigationsystems,celestialpositiondeterminationisnotascommon.Thesesystemsandtheaugmentationsystemstheyhavefosteredhavebeenincorporatedintovirtuallyeveryfacetofinternational,telecommunication,militaryandcommercialtechnology.Withextremelyhighaccuracyandglobalcoverage,satellitenavigationsystemshavecollectivelybecomeanewpublicutilityknownbythegeneraldesignationofGlobalNavigationSatelliteSystem(GNSS).8.1GPSTheGlobalPositioningSystem(GPS)isasatellitenavigationsystemdevelopedbytheUSDepartmentofDefense.Theprogrammeevolvedfromearliersystemsandwasformallycharteredin1973[114].TheGPScomprisesanominalconstellationoftwenty-foursatelliteswithanorbitalradiusof26560km,correspondingtoaperiodofrevolutionof12siderealhours(11h58min).Therearesixorbitalplanesinclinedat55 withfoursatellitesperplane.TheconstellationgeometryensuresthatbetweenfourandelevensatellitesaresimultaneouslyvisibleatalltimesfromanypointontheEarth.BlockIdevelopmentalprototypesatelliteswerelaunchedbetween1978and1985,whileBlockIIproductionsatelliteswerelaunchedbeginningin1989.Thesystemwasdeclaredfullyoperationalin1995.ThecurrentGPSconstellationconsistsoftwenty-eightBlockII/IIA/IIRsatellites.Eachsatellitecarriesmultiplecaesiumandrubidiumatomicclocks.Thefundamentalclockfrequencyis10.23MHz.ThesatelliteandglobaltrackingnetworkatomicclocksareusedtogeneratethecontinuoussystemtimeknownasGPSTime,whichisspeciŽedtobewithin1msofUTCasmaintainedbyUSNO,exceptleapsecondsarenotinserted.ThealgorithmdeŽningtherelationshipbetweenGPSTimeandUTCthusincludesacorrectionforleapseconds.TheoriginofGPSTimeismidnightof5/6January1980,withtheconsequencethatTAIisaheadofGPSTimeby19s,aconstantvalue.Asof1January2001,GPSTimeisaheadofUTCby13s.Withappropriatecorrectionsforsignalpropagation,relativity,andothereffects,GPSprovidesareferencefortimewithaprecisionof10nsorbetter.TheGPSsatellitestransmitsignalsattwocarrierfrequenciesinL-band:theL1componentwithacentrefrequencyof1575.42MHzandtheL2componentwithacentrefrequencyof1227.60MHz.TheprecisionPcode(ortheencryptedYcodeusedinplaceofthePcode)isaspread-spectrum,pseudo-randomnoise(PRN)codewithabitrate(“chiprate”)of10.23MHz.TheP(Y)codehasaperiodof38.058weeks,butitistruncatedintoone-weeksegmentstodistinguishindividualsatellites.Thecoarse/acquisitionC/AcodeisaPRNcodewithabitrateof1.023MHzthatrepeatsitselfevery1ms[115,116].GPSprovidestwolevelsofservice.ThePrecisePositioningService,intendedforauthorizedusers,employstheP(Y)code,whichistransmittedonboththeL1andL2frequencies.TheStandardPositioningService,intendedforcivilusers,employstheC/Acode,whichistransmittedononlytheL1frequency.TheC/Acodeisalsousedforsatelliteacquisitionbyallusers.Thedeterminationofpositionmaybecharacterizedastheprocessoftriangulationusingpseudo-rangemeasurementsfromfourormoresatellites.ThemilitaryP(Y)codereceiverhasa95%horizontalpositionaccuracyofabout5m.Untilrecently,thecivilC/AcodewasintentionallydegradedbyatechniquecalledSelectiveAvailability(SA),whichintroducedpositionerrorsof50mto100mbyditheringthesatelliteclockdata.Thistechniquealsorestrictedtimetransfertoabout300nsinrealtime.However,on2May2000,underaUSpresidentialdirective,theSAfeatureoftheC/Acodewassettozero.Consequently,thecivilGPSaccuracyisnowabout10mto30minpositionand10nsto30nsintime.Differentialcorrectionsystems,wheretheyareavailable,canpermitpositiondeterminationtoanaccuracyoflessthanametre.AvarietyofGPSmodernizationinitiativesareunderway.WiththeadditionofanewL2civil(L2C)signalonGPSBlockIIR-Msatellitesin2003,thecivil95%horizontalpositionaccuracywillbecomeabout5mto10m.Also,in2000theWorldRadiocommunicationConference(Istanbul)approvedathirdcivilfrequency,knownasL5,tobecentredat1176.45MHzintheAeronauticalRadioNavigationServices(ARNS)band.Thisthirdfrequency,tobeavailableonGPSBlockIIFsatellitesin2005,wouldpermitthecreationoftwobeatfrequenciesthatwouldyieldsub-metrepositioningaccuracyinrealtime[117].AnewgenerationofGPSwithenhancedcapabilities,GPSIII,istobeimplementedbeginningin2010.TheorbitdeterminationprocessforGPS,likevirtuallyallotherEarth-orbitingsatellites,requirespreciseknowledgeof[UT1–UTC].ThecommonprocedureinvolvesintegrationoftheequationsofmotioninanEarth-CentredInertial(ECI)referenceframe.Thetrackingstations,however,arelocatedintheEarth-CentredEarth-Fixed(ECEF)referenceframeoftherotatingEarth.TheusualchoiceoftheinertialcoordinatesystemistheJ2000.0referenceframebasedontheFK5starcatalogue,whilethephysicalmodeloftheEarthistheWorldGeodeticSystem1984(WGS84)520Metrologia,2001,38,509-529 Theleapsecond:itshistoryandpossiblefuture [118,119].Thedatafromthetrackingstationsaretypicallytime-taggedwithaparticularrealizationofUTC.Moreover,theEarth’sgravitationalŽeldisalsorotatingwiththeEarthandtheperturbinggravitationalforcesmustbetransformed,viafourrotationmatrices,fromtheECEFframeintotheECIframeaspartoftheorbitdeterminationprocess.ThematricesaccountfortheEarth’spolarmotion,variablerotation,nutationandprecession.Nearreal-timeorbitdeterminationmustusepredictionsof[UT1–UTC].Today,thesepredictionsareexpressedintheformofapolynomialmodelthatisupdatedweekly[120].AsGPSTimedoesnotincludeleapseconds,theintroductionofaleapsecondintoUTCdoesnotaffectGPSusers.TheGPSoperationalcontrolsegment,however,mustcarefullyaccountfortheleapsecondstepin[UT1–UTC].Priortoaleapsecondevent,twosetsof“EarthOrientationParameters”areprovidedtotheGPScontrolsegment.Onesetisuseduptothetimealeapsecondisinsertedandasecondset,whichcontainsthenew1sstepin[UT1–UTC],isusedaftertheleapsecondisinserted.8.2GLONASSTheRussianGlobalNavigationSatelliteSystem(GLONASS)hasmanyfeaturesincommonwithGPS[121,122].Thenominalconstellationconsistsoftwenty-foursatellitesinthreeplanesinclinedat64.8 .Theorbitalradiusis25510kmandtheperiodis8/17siderealday(11h15min).TheŽrstsatellitewaslaunchedin1982.Thesystemwasfullydeployedinearly1996butcurrentlythereareonlynineoperationalsatellites.However,thereisacommitmenttorestorethecompletetwenty-foursatelliteconstellationby2004.IncontrasttoGPS,theGLONASSsatellitesalltransmitthesamecodesandaredistinguishedbyindividualL-bandcarrierfrequencies.Thus,whileGPSusesthespread-spectrumtechniqueofCodeDivisionMultipleAccess(CDMA),GLONASSusesFrequencyDivisionMultipleAccess(FDMA).TheGLONASSdesignusesMoscowTime,[UTC+3h],asitstimereferenceinsteadofitsowninternaltime.Thus,usersofthissystemaredirectlyaffectedbyleapseconds.Duringtheprocessofresettingthetimetoaccountforaleapsecond,thesystemisunavailablefornavigationservicebecausetheclocksarenotsynchronized.8.3UtilizationofsatellitesystemsCurrentCGPM,ITU-RandIAUrecommendationsaddresstheuseofsatellitesforspaceservices,frequencies,andtimetransfer.Thegrowingutilizationofsatellitesystemsandtheirinternaltimescalesmaygraduallybecometheprimarysourceoftimeformanypracticalapplications.LaboratoriesseparatedbyseveralthousandkilometrescanroutinelyperformtimecomparisonsusingGPScommon-viewtechniqueswithaprecisionofafewnanoseconds.GLONASScanprovidecontinentaltimetransferwithsomewhatlessprecision.AnothertechniquecomingintowideruseisTwo-WaySatelliteTimeTransfer(TWSTT)usinggeostationarycommunicationssatellites.Thistechniqueutilizesthewidebandcommunicationscapabilitytotransmitbidirectional,spread-spectrumrangingcodesthatpermittimecomparisonsatthesub-nanosecondlevel.Incomparison,theDUT1codeavailableinterrestrialradiosignalsthatdisseminateUTChasaresolutionof0.1s.Thecorrespondingpositionerrorontheequatorisabout50m.A1sresolutionbetweenUT1andUTCcorrespondstoapositionerrorusingcelestialmeasurementsof0.5km.Asaresult,satellitesystemsaresupersedingUTCradiosignalsasameansoftimedeterminationfornavigation.9.InternationalagreementsontimeNosingleinternationalagencybyitselfcouldassumecompleteresponsibilityforthedeŽnitionandrulesforthedisseminationoftime.ManyinternationalscientiŽcorganizations,listedbelow,havecombinedtheireffortsinthedevelopment,realizationanddisseminationofInternationalAtomicTime(TAI)andCoordinatedUniversalTime(UTC).Theirworkhasestablishedthelinkbetweenthetraditionalastronomicaldeterminationoftimeandthatbasedonfundamentalatomicphenomena.ThisessentialcooperationwasrequiredtosupportthenecessaryscientiŽcfoundation.(1)TheGeneralConferenceonWeightsandMeasures(ConfÂerenceGÂenÂeraledesPoidsetMesures,CGPM),whichhasresponsibilityfortheInter-nationalSystemofUnits(SystÁemeInternationald’UnitÂes,SI),wasestablishedbytheConventionoftheMetre(ConventionduMÁetre),signedinParisbyrepresentativesofseventeencountriesin1875andamendedin1921.TheConventionnowhasŽfty-onesignatories.UnderthetermsoftheConvention,theBureauInternationaldesPoidsetMesures(BIPM)operatesunderthesupervisionoftheInternationalCommitteeforWeightsandMeasures(ComitÂeInternationaldesPoidsetMesures,CIPM),whichitselfcomesundertheauthorityoftheCGPM[123,124].DuringtheperiodwhenTAIandUTCweredeveloped,theCIPMreceivedguidancefromtheComitÂeConsultatifpourlaDÂeŽnitiondelaSeconde(CCDS),setupin1956.ThiscommitteewasrenamedtheConsultativeCommitteeforTimeandFrequency(ComitÂeConsultatifduTempsetdesFrÂequences,CCTF)in1997.TheBIPMorganizesthetimelinksusedforcomputinganddisseminatingTAIandUTC.ItissuesamonthlyCircularTthatcontainstheinformationneededtoobtainthesetimescalesatthebestlevelofaccuracy.Metrologia,2001,38,509-529521 R.A.Nelsonetal. (2)TheInternationalRadioConsultativeCommittee(CCIR)oftheInternationalTelecommunicationUnion(ITU)wasestablishedin1927tocoordinatetechnicalstudies,testsandmeasurementsinthevariousŽeldsoftelecommunicationsandtoestablishinternationalstandards.RecommendationsforstandardizationofinternationalbroadcasttimeweredraftedattheCCIRXthPlenaryAssemblyinGenevain1963andXIthPlenaryAssemblyinOsloin1966.StudyGroup7wasformedin1959toincludespaceradiocommunicationandfrequenciesandwasresponsibleforthedeŽnitionofUTCasthestandardforfrequencyandtimedissemination.TheITUPlenipotentiaryConferenceof1992reorganizedtheCCIRintotheITU-R(RadiocommunicationSector).WorkingParty7AcontinuesastheresponsiblebodyforStandardFrequencyandTimeSignals.(3)TheInternationalAstronomicalUnion(IAU)wasestablishedduringtheConstitutiveAssemblyoftheInternationalResearchCouncil(IRC)heldinBrusselsin1919.TheIRCwassucceededbytheInternationalCouncilofScientiŽcUnions(ICSU)in1931(renamedtheInternationalCouncilforSciencein1998)[125,126].ThroughitsCommissions4(Ephemerides),19(RotationoftheEarth),and31(Time),theIAUstandardizedthedeŽnitionsofUniversalTime,EphemerisTime,andthevariousrelativistictimescalesanddeterminedtheirrelationshipstoInternationalAtomicTime.(4)TheInternationalUnionofGeodesyandGeo-physics(IUGG)isamemberoftheICSUandwasestablishedbytheIRCin1919.TheIUGGisdedicatedtothescientiŽcstudyoftheEarthanditsenvironmentinspaceandincludestheInternationalAssociationofGeodesy(IAG).(5)TheInternationalUnionofRadioScience(URSI)isamemberoftheICSUandwasestablishedbytheIRCin1919toencouragescientiŽcstudiesofradiotelegraphyandpromoteinternationalcooper-ation.ItspresentcharterincludesintercomparisonandstandardizationofthemeasuringinstrumentsusedinscientiŽcworkandscientiŽcaspectsoftelecommunications.URSImadetheoriginalrecommendationfortheworldwidebroadcastofoffsetatomictime.(6)TheBureauInternationaldel’Heure(BIH)wasestablishedattheParisObservatoryin1919bytheIRCConstitutiveAssemblytocoordinateinternationalradiotimesignals.Originally,theBIHwasunderthedirectionofIAUCommission31,butin1956itbecameaserviceoftheFederationofAstronomicalandGeophysicalDataAnalysisServices(FAGS)withtheIAU,IUGGandURSIasparentunions.TheBIHwasrequestedbytheCCIRin1963todeterminetheproperoffsetsbetweenUT2andbroadcastatomictimeandtocoordinatetheworldwidestandardfrequencyandtimesignalserviceprescribedbytheCCIR.TheBIHtransferredthisfunction,aswellastheestablishmentofInternationalAtomicTime,totheBIPMon1January1988,whileitsactivitiesontherotationoftheEarthweretakenoverbyanewservice,theInternationalEarthRotationService.(7)TheInternationalEarthRotationService(IERS)wasestablishedin1987bytheIAUandtheIUGGandbeganoperationon1January1988.Itsstructurewasreorganizedcommencingin2001.TheIERSisaninternationalconsortiumofnationallaboratoriesandobservatoriesthatprovidesoperationaldatarelatedtotheorientationoftheEarthinspace.IthastheresponsibilityfordecisionsregardingchangestoUTCbasedonobservationsoftheEarth’srotationanddetermineswhenleapsecondsshouldbeapplied.TheIERSpublishesfourbulletins.BulletinA(dailyandsemiweekly)isissuedbytheSub-BureauforRapidServiceandPredictionsatUSNOandcontainsrapiddeterminationsforEarthOrientationBulletinBcontainsmonthlyEarthOrientationParameters.BulletinC,containingannouncementsoftheleapsecondsinUTC,andBulletinD,containingannouncementsofthevalueofDUT1,aredistributedasrequired.Merelytoenumeratetheseagenciesandtheircommissions,studygroupsandsub-committeesistorealizethecomplexityoftheinternationalestablishmentinchargeoftime,andthedifŽcultyofmakingfundamentalchanges.ThepresentdeŽnitionofUTCistheresultoffar-reachingcompromisesamongthecommunitiesthattheseagenciesrepresent.Today’susercommunitieshavechangedsigniŽ-cantlyinthefewensuingdecades,justastheusesoftimehavechanged.Thetraditionalradiobroadcastoftimesignalsisbeingovertakenbysatellitesignalslinkeddirectlytoatomicstandards.Ensemblesofatomicstandardsinindividuallaboratoriesandhigh-speedcomputernetworksaresynchronizedtothesesamestandards.ThemanyanddiversepurposesthataninternationaltimescalemustservearenowpartofaninternationaltelecommunicationandcommercialinfrastructureinvolvingsigniŽcanteconomicinterestsinwhichchangesrepresentamajorŽnancialinvestment.ThisnewrelationshipcouldmakechangemoredifŽcult.Ifaneworrevisedinternationalstandardistorepresentallthelegitimateinterests,coordinationwithnon-traditionalagenciesandgroupsmaybenecessary.10.LegaltimeAnimportantconsiderationwiththecurrentdeŽnitionofUTCisthelegaldeŽnitionoftimeimpliedwithin522Metrologia,2001,38,509-529 Theleapsecond:itshistoryandpossiblefuture thedomesticlawsofindividualcountries[127].Thepurposeofstatutesgoverninglegaltimeistopromotecommerceandthepublicinterest.10.1StandardTimeTheadventoftherailroadsinthesecondquarterofthenineteenthcenturyintroducedaneraofhigh-speedtransportandmobility.EffortstocoordinateschedulesculminatedintheadoptionofregionalzonesofStandardTimeandthechoiceofGreenwichastheinternationalreferencefortheprimemeridian.GreenwichMeanTime(GMT)hasbeenthelegaltimeintheUKsince1880.IntheUSA,theStandardTimeActof19March1918,asamendedbytheUniformTimeActof1966,establishedeighttimezonesthatarebasedonmeansolartimeandarenominallyseparatedinlongitudebyintervalsof15 (1h)withrespecttotheGreenwichmeridian[128,129].ItalsoauthorizedtheInterstateCommerceCommissiontomodifythetimezoneboundaries.In1983thisresponsibilitywastransferredtotheDepartmentofThepublicationoftheBritishNauticalAlmanacbeginningwiththeyear1767bytheAstronomerRoyalNevilMaskelyne,whichenabledthedeterminationoflongitudeatseausingobservationsoftheMoon’spositionwithrespecttothestars,andthecontemporaneousdevelopmentofthemarinechronometerbyJohnHarrison,hadestablishedGreenwichasthedefactofundamentalreferenceforlongitudeandtimeforoveracentury[130,131].TheGreenwichmeridianwasformallyrecommendedasaworldwidestandardreferenceforlongitudeandtimeattheInternationalMeridianConference,heldinWashington,D.C.,inOctober1884attheinvitationoftheUnitedStatesGovernment,asaresultofdiscussionsthathadtakenplaceatseveralscientiŽcconferencesoverthepreviousdecade.Bythennearlythree-quartersoftheworld’scommercialshipsusedchartsbasedontheGreenwichmeridian.TheConferencealsorecommendedtheadoptionofaUniversalDay,deŽnedasameansolardaycountedfrom0upto24hours,thatwouldbeginatmidnightattheprimemeridian[132,133].TheideaoftimezoneswasŽrstproposedin1870byCharlesF.Dowd[134],anAmericancollegeprofessor,asamethodofregulatingtimefortherailroads.InDowd’splan,standardtimewouldbeusedbytherailroads,whileeachcityandtownwouldpreserveitsownlocaltime.Asimilarproposal,butonethatrecommendedadjustinglocaltimetorailroadtime,waslatersuccessfullypromotedbyWilliamF.Allen[135],editorofaprominentrailroadperiodicalandSecretaryoftheAmericanRailwayAssociation.ImportantcontributionswerealsomadebyClevelandAbbe[136]oftheUSSignalServiceandSandfordFleming[137]oftheCanadianPaciŽcRailway.Topermitamoreconvenientlocationoftimezoneboundaries,theGreenwichmeridianwaschosenastheprimaryreferenceratherthanWashington,D.C.“StandardRailwayTime”wasadoptedthroughoutNorthAmericaatnoononSunday,18November1883,reducingthenumberofrailroadtimesfromforty-ninetoŽve,andwassoonextendedtociviltime[138].Therapidgrowthoftherailroadscreatedademandfortimesynchronizationacrosslargedistancesandthecontinuingexpansionofthenetworkoftelegraphwiresalongtheirrightsofwayprovidedthemeansforachievingit.Towardstheendofthenineteenthcentury,theUSNavalObservatorywasdisseminatingadailytimesignalviatheWesternUnionTelegraphCompanytocitiesthroughouttheEast,SouthandMidwestoftheUSA[139].DaylightSavingTimewasconceivedbyWilliamWillett,asuccessfulLondonbuilder,in1907[140];itwasŽrstintroducedinEuropeandNorthAmericaduringtheFirstWorldWarasameansofconservingenergy[141].IntheUSA,theStandardTimeActof1918requiredtheobservanceofDaylightSavingTime,whichisadvanced1haheadofStandardTimeoversevenmonthsoftheyear,inadditiontoprovidingalegalbasisforŽvetimezones(extendedtoeightin1966tocoverallUSterritories).10.2GreenwichMeanTimeOriginally,GreenwichMeanTime(GMT)wasdeŽnedasmeansolartimeonthemeridianofGreenwichreckonedfrommeannoon.In1919,theBIHundertooktocoordinatetheemissionofradiotimesignalsonthebasisofGreenwichCivilTime(i.e.GMTplus12h),asrecommendedbytheInternationalMeridianTheastronomicalalmanacskeptGMTasthetimeargumentuntil1925.Beginningin1925,theBritishNauticalAlmanacandmanyothernationalephemeridesreckonedGMTfrommidnighttocoincidewiththecivilday,ratherthannoonashadbeenthetraditionalastronomicalpractice.TheredeŽnedGMTwasdesignatedUniversalTime(UT)bytheIAUin1928[142].However,thetermGMTpersistedinalmanacsandnavigationpublicationsandtheambiguityinitsintendedmeaningwasthecauseofsomeconfusion[143].10.3CoordinatedUniversalTimeTheterms“meansolartime”and“GMT”havecometoberecognizedasbeingsynonymouswithUTCinordinarylanguage.In1970,Commission31oftheIAUrecommendedthatclocksincommonusewouldindicateminutes,secondsandfractionsofUTCandthattheterm“GMT”wouldbeacceptedasthegeneralequivalentofUTCinnavigationandcommunications[144].The15thCGPMin1975adoptedthefollowingresolution[145]:Metrologia,2001,38,509-529523 R.A.Nelsonetal. “The15thConfÂerenceGÂenÂeraledesPoidsetMesures,thatthesystemcalled“CoordinatedUniversalTime”(UTC)iswidelyused,thatitisbroadcastinmostradiotransmissionsoftimesignals,thatthiswidediffusionmakesavailabletotheusersnotonlyfrequencystandardsbutalsoInternationalAtomicTimeandanapproximationtoUniversalTime(or,ifoneprefers,meansolartime),notesthatthisCoordinatedUniversalTimeprovidesthebasisofciviltime,theuseofwhichislegalinmostcountries,judgesthatthisusageisstronglyendorsed.”TheinternationaldiplomaticauthorityforthedecisionsoftheCGPManditsorgansisconveyedthroughtheConventionoftheMetreof1875.TheCCIRin1978andtheWorldAdministrativeRadioConference(Geneva)in1979recommendedthatUTCshouldbeusedtodesignatethetimeinallinternationaltelecommunicationactivities[146].TheITURadioRegulationsdeŽneUTCasthetimescale,basedontheSIsecond,asspeciŽedinRecommendationITU-RTF.460-5.ThedeŽnitionisaccompaniedbythefollowingNote[147]:“FormostpracticalpurposesassociatedwiththeRadioRegulations,UTCisequivalenttomeansolartimeattheprimemeridian(0 longitude),formerlyexpressedinGMT.”ThisdeŽnitioniscitedintheCodeofFederal,Title47,thatspeciŽestherulesoftheUSFederalCommunicationsCommission(FCC)[148].TherolethatUTCplaysinnationalandinternationalmonetaryexchange,telecommunicationsandrelatedformsofcommerceisnotclear.ShouldthedeŽnitionofUTCberevised,theeffectonlegalcodesmayneedtobeinvestigated.11.Futuredevelopments11.1OptionsforUTCThereexistavarietyofoptionsforthefutureofUTC.SomeoftheseoptionsareidentiŽedanddiscussedbelow.(1)Maintainthestatusquo.TheadvantageofmaintainingthepresentformofUTCisthatestablishedtimekeepingpracticeswillnotrequiremodiŽcation.Ontheotherhand,ifleapsecondswerecontinued,therequirednumberandfrequencycanonlyincrease,asshowninFigure6.By2100therewouldbeaneedfornearlytwoleapsecondsperyear.Thecurrentemergingproblemsandtheresultingdissatisfactionwithleapsecondswillonlycontinuetogrow.TheoperationalimpactandassociatedcostofmaintainingleapsecondsinFigure6.Projectedincreaseinleapsecondsversustime(afterMcCarthyandKlepczynski[149]).complextimekeepingsystemsmustbeconsideredinevaluatingtheircontinueduseinthefuture.(2)IncreasethetolerancebetweenUT1andUTC.AsmallincrementofseveralleapsecondscouldbeinsertedintoUTCeveryfewyearsor,alternatively,a“leapminute”inaboutŽftyyears.Theadvantageofthisapproachisthatitwouldberelativelyeasytoadopt.However,duetotheparabolicrateofdeparturebetweensolartimeandatomictime,thetolerancewouldhavetobecontinuallyincreasedandeventuallylargertimestepswouldberequired.(3)Periodicinsertionofleapseconds.AtimestepcouldbeinsertedintoUTCatawell-deŽnedinterval,suchason29Februaryeveryfouryears.Theadvantageisthatthedatewouldbepredictable.However,thenumberofleapsecondswouldnotbepredictableandlargetimestepswouldstillberequired.(4)Variableadjustmentsinfrequency.ThisalternativeissimilartotheoriginalformofUTCthatwasabandoned.IntroducingavariableatomicscaleinstepwithsolartimewouldcausesigniŽcantdisruptionstoequipmentandwouldnotdisseminatetheunitoftime,theSIsecond.(5)RedeŽnethesecond.Thisoptionwouldappeartobethemostfundamentalsolution.However,itwouldbeinconsistentwiththeusualpracticeinmetrology,whichistoadoptanewdeŽnitionofaunitonlywhenitsrealizationundertheolddeŽnitionbecomesthelimitingsourceofexperimentaluncertaintyandtomaintaincontinuitybetweentheoldandnewrealizations.ChangingthedeŽnitionofthesecondtobeclosertothecurrentrotationalsecondwouldalterthevalueofeveryphysicalmeasurementandrenderobsoleteeveryinstrumentrelatedtotime.Moreover,thesolutionwouldbeonlytemporaryastheEarthcontinuestodecelerate.524Metrologia,2001,38,509-529 Theleapsecond:itshistoryandpossiblefuture (6)SubstituteTAIforUTC.TAIisthefundamentalatomictimescale“inthebackground”fromwhichotherscalesofuniformtimearederived.TAIisrelatedtoUTCbytherelation[TAI] [UTC+ AT],where ATistheincrementtobeappliedtoUTCtogiveTAIandisequaltothetotalnumberofleapsecondsplus10s.In2001,thevalueof ATwas+32s.TheadvantageofTAIisthatitisacontinuous,atomictimescalewithoutsteps.However,TAIiscurrentlynoteasilyavailabletotheprecisetimeuserand,asTAIiscurrentlyaheadofUTCbyanoffsetof32s,aworldwideadjustmentofclockswouldberequiredifitwereadoptedasthescaleofciviltime.Promotionoftwoparalleltimescalesforciviltimekeeping,onewithleapsecondsandonewithout,wouldbepotentiallyconfusing.Inaddition,asUTCisrecognizedastheprimarybasisofciviltimeinresolutionsofvariousinternationaltreatyandscientiŽcorganizationsandbymanyconformingnationallegalcodes,aworldwidechangeinthelegaldeŽnitionoftimewouldberequiredifUTCwerereplacedbyTAI.(7)DiscontinueleapsecondsinUTC.ThisoptionwouldpermitcontinuitywiththeexistingUTCtimescaleandwouldeliminatetheneedforfutureadjustmentstocomplextimekeepingsystems.Figure7showstheprojecteddifferencebetweenUTCwithoutleapsecondsandUT1.IfthecurrentrateofdecelerationoftheEarth’srotationweretopersistandnoleapsecondswereadded,by2050thedifferencebetweenUTCandUT1wouldbeabout1min.Bytheendofthetwenty-Žrstcentury,theexpecteddifferencewouldbeabout2.5min[149].However,thesedifferencesareminorcomparedwiththedifferencebetweenapparentsolartimeandmeansolartime(upto16.5min),meansolartimeandclocktimewithinagiventimezone(nominallyupto30min),orDaylightSavingFigure7.ProjecteddifferencebetweenUTCandUT1ifleapsecondswerediscontinued(afterMcCarthyandKlepczynski[149]).TimeandStandardTime(1h).Itisthusunlikelythatthegrowingdifferencebetweenclocktimeandlevelsofdaylightwouldbenoticeablefortheforeseeablefuture.Also,certainreligiouscustomsdependontheactualobservationoftheSunortheMoonanddonotdependonclocktime.Therefore,theeliminationofleapsecondswouldhavenopracticaleffectonthecorrespondencebetweenciviltimeandsolartimeoroncontemporarysocialconventions.TheuseofUTCwithoutleapsecondswouldretainalltheadvantagesofTAI.ThetransitiontoacontinuousUTCsystemmightbeplannedforafuturedatesufŽcientlyfarinadvancethatchangestoexistinghardwareandsoftware,wherenecessary,couldbeaccommodatedwithinthenormalmaintenanceandreplacementschedules.11.2RequirementsofcelestialnavigationThereremainstheneedtomeettherequirementsofcelestialnavigation.ThreepossibleoptionsforaddressingthisneedifthecurrentUTCsystemwererevisedareconsidered.AdditionalalternativesmaybeidentiŽedastheissueisdebated.(1)Alternativetimescalefornavigation.Anewbroadcastscaleoftime,possiblydesignated“UT1C”,mightbedisseminatedbysupplementarycodedsignalsthatprovidetheapproximatedifferencebetweenthenewlydeŽnedUTCandUT1,justasDUT1codescurrentlygivethedifferencebetweenthepresentlydeŽnedUTCandUT1tothenearest0.1s.However,mosttimecodeformatswouldhavetobemodiŽedtoaccommodateadifferenceintimegreaterthan1s.AsabeneŽcialtrade-off,theresolutionmightbeincreasedintheprocess,forexampleto0.001s.Thetimedifference[UTC–UT1C]mightalsobeconvenientlydisseminatedinsatellitenavigationmessages,possiblyasacommercialservice.(2)GreateremphasisonUT1predictions.Thesere-quirementsmightalsobemetbypublishedpredic-tionsof[UT1–UTC].TheIERS/USNOprovidesdailyandsemiweeklypredictionsinBulletinA,availableontheInternetat http://www.iers.org .Theestimatedaccuraciesare0.0017sat10daysand0.0039sat30days.Forexample,theNationalImageryandMappingAgency(NIMA)providesEarthOrientationParameterPredictioncoefŽcientsbasedonIERS/USNOweeklypost-Žtvaluesthatareusedtogenerate[UT1–UTC]predictionsforGPSorbitdetermination.Inaddition,long-termprojectionsmightbeincludedinthenauticalephemerideswithlessprecision.Withtheusualyearlyscheduleofpublication,theextrapolationshouldnotbringerrorsexceeding1s(leadingtoapositionerrorof0.5kmatmost).Throughbothshort-termandlong-termUT1predictions,itMetrologia,2001,38,509-529525 R.A.Nelsonetal. wouldbepossibletocomplementtheinformationtonavigatorsbydisseminatingacorrectiontotheargumentoftheephemerides,asisdonecurrentlywithDUT1.(3)Greateremphasisonsatellitenavigationsystems.DuetotheavailabilityoftheGPSandGLONASSsatellitenavigationsystemsandthepossibilityofsimilarfuturesystems,suchasGalileo,theneedforcodedterrestrialradiotimesignalsislessthanitoncewas.Existinginternationalagreementsmightberecasttoredirectthefocusofthoseagreementstowardsincreaseduseofmodernsatellitenavigationalaids.12.ConclusionsThetransitionfromsolartimetoatomictime,madepossiblebythedevelopmentofatomicclocks,representsaparadigmshiftinthewaytimeitselfisperceivedthatisnotunlikethetransitionfromtheunequalhourtotheequalhourŽvehundredyearsago,broughtaboutbytheinventionofmechanicalclocks,orthetransitionfromapparenttimetomeansolartimesometwohundredyearsagothatwasmadepossiblebyimprovementstopendulumclocks.ThemostbasicissueinthefutureofUTCisthenatureofthesocialrequirementtoadjustanextremelyprecise,uniformtimescaletothetimedeterminedusingthevariablerotationoftheEarth.Commonpracticetodayhasalreadycompromisedthisrequirementtothepointthatwearecontentwithconventionalconstructionssuchasmeansolartime,zonetimeandDaylightSavingTime.Weshouldrealizethat,asaresultofthechangefromapparenttomeantime,thelocalmeannoonofourclockscansometimesbeabout15minbeforeoraftertheapparentnoonoftheSun;thustheafternoonsinNovemberarehalfanhourshorterthanthemornings,whileinFebruarythemorningsarehalfanhourshorterthantheafternoons.Thischangewasevenmorefundamentalthanthatfromlocalmeantimetozonetime[150].Alltheseconventionsintroducesubstantialdiffer-encesbetweenthecommonlyacceptedtimeandsolartimethatareordersofmagnitudelargerthanthedifferencebetweenauniformtimescaleandasolartimescale.Weanticipatethatthisdifferencewillgrowbyanadditional2minoverthenextcentury.Willwebewillingtoneglectthisdifferenceinciviltimescales?Theastronomicallydeterminedrotationanglewillbemeasuredwithimprovingaccuracyduringthatperiodandwillbemadeavailabletouserssooner.Willthisbeabletosatisfyuserneeds?Ineachstageoftheevolutionoftimekeeping,therehasbeenanincrementalstepawayfromtheSunasthemeasureoftimeinfavourofamoreuniform,accessible,orconvenientstandard.ThenextstageintheevolutionofUTCmaybeadeŽnitionofciviltimeintermsofacontinuousscaleofatomictimeandadisassociationofciviltimefromsolartimealtogether,accompaniedbytheadoptionofarepresentationofUT1forthoseuserswhoneedit.Throughoutthehistoryoftimemeasurement,fromsundialstoatomicclocks,timescaleshavealwaysbeenestablishedbytakingintoaccountprevailingtechnologyandneeds.SincetheUTCsystemofleapsecondswasintroducedthirtyyearsago,bothofthesefactorshavechanged.Therefore,weshouldperhapsnotbetoohesitantinadaptingtomoderntechnologyandmodernneeds.References1.NeugebauerO.,TheExactSciencesinAntiquity,2nded.,Providence,R.I.,BrownUniversityPress,1957;NewYork,DoverPublications,1969,81.2.HoyleF.,Astronomy,London,CrescentBooks,1962,81.3.WhitrowG.J.,TimeinHistory,NewYork,OxfordUniversityPress,1988,Chap.7.4.UsherA.P.,AHistoryofMechanicalInventions,rev.ed.,Cambridge,Mass.,HarvardUniversityPress,1954;NewYork,DoverPublications,1988,Chap.8.5.GerberE.A,SykesR.A.,Proc.IEEE,1966,54,103-116;reprintedinTimeandFrequency:Theoryand,Natl.Bur.Stand.(U.S.)Monograph140(EditedbyB.E.Blair),Washington,D.C.,U.S.Govt.PrintingOfŽce,1974,41-56.6.Natl.Bur.Stand.(U.S.)Tech.NewsBull.,1949,33(2),17-24.7.EssenL.,ParryJ.V.L.,Nature,1955,176,280-282.8.GoldenbergH.M.,KleppnerD.,RamseyN.F.,Phys.Rev.Lett.,1960,5,361-362.9.GuinotB.,HistoryoftheBureauInternationaldel’Heure,InPolarMotion:HistoricalandScientiŽcProblems,IAUColloquium178,ASPConferenceSeries,Vol.208(EditedbyS.Dick,D.McCarthyandB.Luzum),SanFrancisco,Astron.Soc.PaciŽc,2000,175-184.10.GuinotB.,1994/1995,31,431-440.11.KovalevskyJ.,Metrologia,1965,1,169-180.12.McCarthyD.D.,Proc.IEEE,1991,79,915-920.13.ExplanatorySupplementtotheAstronomicalAlmanac,rev.ed.(EditedbyP.K.Seidelmann),MillValley,Calif.,UniversityScienceBooks,1992,50,508.14.AokiS.,GuinotB.,KaplanG.H.,KinoshitaH.,McCarthyD.D.,SeidelmannP.K., 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Receivedon9July2001andinrevisedformon5September2001.Metrologia,2001,38,509-529529