地球科学概论第4讲地球形状及自转-4May-New

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讲地球形状及自转申文斌，邓洪涛，徐新禹，罗佳2014.5.41内容提要1历史2球形3椭球形4更复杂形状5地球自转6地球自转参数观测7地球自转应用举例21HistoryGreek(Homer,Thales,Pythagoras,Plato,Eratosthenes)Homer(800-1000BC?poet):theearthresemblingaflatdiscThales(624-546BC,Think,Sci,Phi):theearthisspherical(600B.C)Pythagoras(572-497BC,Math,Phi)andAristotels(384-322BC,Phi,Sci,Educ):sphere31HistoryGreekPlato(427-347BC):Earth’scircumferenceis400,000stadia(byspeculation)（62,800km-74,000km),andArchimedes(287-212BC):300,000stadia[Euclid:325-265BC]【1stadium=157.5m】Eratosthenes(276-194BC,Math,Georagr,Histo,Peot,Astro):earth’sradiusis6267km[39,377](bycalculation,240B.C)4AristotelsPlato1HistoryChina:orbicularskyandrectangularearth（天圆地方）51HistoryHan:张衡(78-139A.D,Astro,Math,Inventor,Geogra,Map,Liter)《浑天仪注》“天如鸡卵，地如卵黄”61History思考:WhatdoestheEarthlooklikefortheancientpeople?Ifyoulivein500B.C,couldyoufindanycluesindicatingthattheearthisspherical?Canyouproveyourviewpoint？Assumetheearthisspherical,howtocalculateitsradius?72SphereEuclideangeometry(Euclid,325-265BC,GreekMath)DrawandonlydrawonestraightlinefromonepointtoanotherpointProduce[extend]afinitestraightlinecontinuouslyintoastraightlineDetermineauniquecirclewithanycenterandadistance[radius]AllrightanglesareequalwitheachanotherTheparallelpostulate[Twoparallellineswillnevercrosseachother]82SphereEratosthenes’method:Onsummersolstice,heobservedthemiddaysunshonetothebottomofawellinthetownofSyeneAtthesametime,heobservedthesunwasnotdirectlyoverheadatAlexandriaItcastsashadowwiththeverticalequalto1/50thofacircle(7°12')ThedistancefromAlexandriatoSyeneis5000stadia(1stadium=157.5m)TheradiusoftheEarthis6267km(Erroronly2%)92SphereEratosthenes’smethod:10CitedfromBakiiz2010练习:

请验证2Sphere进一步思考:NoticethatthesunsourceisadistancefromtheEarth(notparallellightray),calculatetheradiusoftheEarthBasedontheMoonlightray,pleasepreciselymeasurethesphericalEarth’sradiusSupposetheEarthisarotationalellipsoid,howtomeasurethesemi-majorandminoraxes,basedonthesunray?【练习】112SphereIstheEarthasphere?No!Then,whichkindoffigure?Ellipsoid[firstapproxiamtion!]12TheoreticalinferencethattheEarthisanellipsoid

由于地球自转，地球必定是两极扁平、赤道隆起的（旋转）椭球【rotationalellipsoid

flattenedslightlyatthepolesandbulgessomewhatattheequator】

如何知道地球在自转？【后面讲述】3Ellipsoid2SphereTherotationofearth(evidence)Dayandnight?Regularmovementofcelestialbodies(N.Copernicus1473-1543)？？？Foucault(1819-1868)pendulum(1885)Geographicalphenomena?？？？Gravity?Whirlpool(differentdirectionsinnorthandsouthpoles)??Hair’srounddirection?143EllipsoidTheearthisrotationalellipsoid(flattenedslightlyatthepolesandbulgessomewhatattheequator)TheoreticalinferencethattheEarthisanellipsoid153EllipsoidHowtodeducerotationalellipsoidtheoretically?163EllipsoidArgumentsinhistoryIstheearthoblatespheroidoroliveellipsoid？Newton:accordingtomechanics,theearthshouldbeoblatespheroid.【如何利用观测证明？ThusThusthe1°meridianarclengthshouldincreaseswiththeincreaseofthelatitude】Cassini:theearthisoliveellipsoid,supportedbymeasurementresults——the1°meridianarclengthincreasewiththeincreaseofthelatitudeWhomademistakes?Whatmistakes?173EllipsoidTheproblemliesintwokindoflatitudes:geocentriclatitude(地心纬度)geodeticlatitude(大地纬度)18geocentriclatitudegeodeticlatitude3EllipsoidRelationshipbetweenMeridianarclengthandgeocentriclatitude【考察地心纬度变化】InPlane-Rectangularcoordinatesystem,wehaveellipticequation:193EllipsoidRelationshipbetweenMeridianarclengthandgeocentriclatitudeThenwehaveaccordingtodifferentialequation203EllipsoidRelationshipbetweenMeridianarclengthandgeocentriclatitudeThensubstituteparameter213EllipsoidRelationshipbetweenMeridianarclengthandgeocentriclatitude22随着地心纬度的增加而减小(Shenetal2011)

3EllipsoidRelationshipbetweenMeridianarclengthandgeodeticlatitude【地理纬度关系如何？】Thenegativevalueofco-tangentφcanbeexpressedbythetwocoordinatesofcorrespondingpointonellipsoid:Since233EllipsoidRelationshipbetweenMeridianarclengthandgeodeticlatitudeThen243EllipsoidRelationshipbetweenMeridianarclengthandgeodeticlatitude随着大地纬度（地理纬度）的增加而增大(Shenetal2011)

253EllipsoidPracticalmeasurements26与理论值比较(Shenetal2011)3EllipsoidFortheoblatespheroidalearth:the1°meridianarclengthincreaseswiththeincreaseofthegeodeticlatitudethe1°meridianarclengthdecreaseswiththeincreaseofthegeocentriclatitudeCassinimistakenlyregardedgeodeticlatitudeasgeocentriclatitude274Morecomplicatedfigure28sphericalearthellipsoidalearthpear-shapedearth5地球自转5.1概述5.2地球自转证据5.3欧拉方程5.4进动，章动和极移5.5日长变化5.6具有挑战性的问题295地球自转5.1概述－作用作用:

【不同学科纽带作用】Tiesofdifferentbranches[geophysics,astronomy,geodesy,geodynamics,oceanscience,meteorology，navigation,...]ReferencesystemInteriorofEarthGlobalclimatechange???305地球自转5.1概述简史Aristarchus（ca.BC300）:Earthmovesaroundsun1Copernicus(1473-1543)2Galileo(1564-1642)[ca.1582]3Huygens(1629-1695)[1657]4Hooke(1635-1703)[1660]5Newton(1642-1726)[1687]6Euler(1707-1783)7Kant(1724-1804)8…9Foucault(1819-1868)[1851]315地球自转5.2地球自转证据diurnalmotionofcelestialbody(天体周日运动)【能证明吗？】easterndeflectionofafallingbody(落体偏东)Foucaultpendulum(1851)(傅科摆)[巴黎国葬院，光滑悬挂摆长67米，摆锤重28公斤;θ=15tsinφ]32练习题：如何根据傅科摆确定地理纬度？5地球自转5.3欧拉方程欧拉角：33惯性坐标系地固坐标系自转角，进动角，章动角5地球自转5.3欧拉方程欧拉运动学方程：5地球自转5.3欧拉方程欧拉动力学方程：主惯性矩：5地球自转5.4进动，章动和极移Precession:precessionaroundeclipticpole(黄极),T=25800yrNutation:smallamplitudeTremor,T=18.6yrPrecessionandnutationarecausedbythegravitationaleffectsofSunandMoon5地球自转5.4进动，章动和极移ThemigrationofEarthpoleontheEarthsurface,notnecessarilythemigrationoftherotationaxis.Periodicmotion:12-month;14-month(Chandlerwobble)long-termdriftslowlong-termdriftCauseofpolarmigration:complex(interiormassmigration（postglacialrebound(冰后回弹),seasonvariations,…）375地球自转5.5日长变化日长变化原因:（1）由于潮汐摩擦，相对于地月连线，存在2.9度的超前角，因而存在反力矩；（2）反力矩使地球自转变慢，导致日长（LOD）变长，其变长量大约1-2ms/世纪（3）在不同尺度上的日长变化？385地球自转5.6具有挑战性的问题（1）InfluenceonglobalclimateduetotheEarth’sprecessionwithrespecttotheSun（2）Solutionofthree-layeredtriaxialEarthrotation（3）MechanismoftheLODvariationinten-yearscale（4）PrecisequantitativecomputationofthesecularvariationoftheLODcausedbytidalfriction（5）Polarwander(PW)causedbyoceanandatmosphere（6）InvestigationofpossibleinverseoftheEarth’srotationaxis(Shen2004)39自转参数观测进动角（岁差）：需要观测恒星【相对恒星定位，VLBI】

章动角（章动）：需要观测恒星【相对恒星定位,VLBI】

自转角（自转，日长）：需要一恒星为参考【相对恒星确定自转速率,时钟】

6地球自转参数观测6地球自转参数观测月掩星测量(LunarOccultation)光学天文测量(OpticalAstrometric)空间大地测量(Space-Geodetic)VLBI(Verylongbaselineinterferometry)GNSS(Globalnavigationsatellitesystem)SLR/LLR(Satelliteandlunarlaserranging)DORIS(Dopplerorbitographyandradiopositioningintegratedbysatellite)环形激光陀螺仪(RingLaserGyroscope)416地球自转参数观测月掩星测量(LunarOccultation)Jordi等在1994年对1830.0-1955.5年间5300个观测值分析，获得这些年4个月时间间隔的TT-UT1系列的值和中误差。（TT=TAI+32.1845s）随后，jordi等从BIH和IERS获取（UT1-TAI）的值将TT-UT1系列扩展到1992年后又对扩展的UT1系列通过有限差分和平滑处理获得1830-1987年间4个月时间间隔的LOD系列Gross在2001年结合月掩星测量数据和光学天文测量、空间大地测量技术，获得1832.5-1997.5年间以年为时间间隔的平滑的LOD系列426地球自转参数观测光学天文测量(OpticalAstrometric)ILS在全球建立七个观测站观测测站纬度变化，获得1899-1978年间月间隔的极移观测系列。随后有更多的其他非ILS测站和方法的光学天文测量经纬度变化，Li和Feissel利用136个非ILS测站的经纬度观测值获得UT1和极移观测系列，即BIH观测系列，时间从1962.1.5-1981.12.31，间隔为5天。利用包括ILS7个测站的数据，对板块运动、海洋负荷和潮汐变化进行了改正，采用更精确的Hipparcos星表，获得Hipparcos地球定向参数观测系列包含了1899.7-1992.0五天时间间隔的极移、章动数值和误差，1956年以后的UT1值。436地球自转参数观测空间大地测量(Space-Geodetic)VLBI：多基线VLBI（multibaselineVLBI）是唯一能独立确定所有EOP参数的技术。其他技术需要额外的外部限制或只能确定部分EOP参数。GNSS，SLR/LLR，DORIS：这几种技术只能确定极移和极移变化率。此外，由于UT1不能从卫星轨道元素中分离出来而不能确定，但UT1的变化率（与LOD有关）可以确定。446地球自转参数观测IERS：ICRF、ITRF、EOPJPLKalmanfilter/IERS/EN/Organization/TechniqueCentres/TC.html456地球自转参数观测46/IERS/EN/DataProducts/EarthOrientationData/eop.htmlhttp://hpiers.obspm.fr/eop-pc/Theseseriesarederivedfromthevariousastro-geodetictechniques(LLR,SLR,GPS,VLBIandDORIS).Bulletin

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