地球科學概論第4講地球形狀及自轉-4May-New

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講地球形狀及自轉申文斌，鄧洪濤，徐新禹，羅佳2014.5.41內(nèi)容提要1歷史2球形3橢球形4更復雜形狀5地球自轉6地球自轉參數(shù)觀測7地球自轉應用舉例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（天圓地方）51HistoryHan:張衡(78-139A.D,Astro,Math,Inventor,Geogra,Map,Liter)《渾天儀注》“天如雞卵，地如卵黃”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練習:

請驗證2Sphere進一步思考:NoticethatthesunsourceisadistancefromtheEarth(notparallellightray),calculatetheradiusoftheEarthBasedontheMoonlightray,pleasepreciselymeasurethesphericalEarth’sradiusSupposetheEarthisarotationalellipsoid,howtomeasurethesemi-majorandminoraxes,basedonthesunray?【練習】112SphereIstheEarthasphere?No!Then,whichkindoffigure?Ellipsoid[firstapproxiamtion!]12TheoreticalinferencethattheEarthisanellipsoid

由于地球自轉，地球必定是兩極扁平、赤道隆起的（旋轉）橢球【rotationalellipsoid

flattenedslightlyatthepolesandbulgessomewhatattheequator】

如何知道地球在自轉？【后面講述】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.【如何利用觀測證明？ThusThusthe1°meridianarclengthshouldincreaseswiththeincreaseofthelatitude】Cassini:theearthisoliveellipsoid,supportedbymeasurementresults——the1°meridianarclengthincreasewiththeincreaseofthelatitudeWhomademistakes?Whatmistakes?173EllipsoidTheproblemliesintwokindoflatitudes:geocentriclatitude(地心緯度)geodeticlatitude(大地緯度)18geocentriclatitudegeodeticlatitude3EllipsoidRelationshipbetweenMeridianarclengthandgeocentriclatitude【考察地心緯度變化】InPlane-Rectangularcoordinatesystem,wehaveellipticequation:193EllipsoidRelationshipbetweenMeridianarclengthandgeocentriclatitudeThenwehaveaccordingtodifferentialequation203EllipsoidRelationshipbetweenMeridianarclengthandgeocentriclatitudeThensubstituteparameter213EllipsoidRelationshipbetweenMeridianarclengthandgeocentriclatitude22隨著地心緯度的增加而減小(Shenetal2011)

3EllipsoidRelationshipbetweenMeridianarclengthandgeodeticlatitude【地理緯度關系如何？】Thenegativevalueofco-tangentφcanbeexpressedbythetwocoordinatesofcorrespondingpointonellipsoid:Since233EllipsoidRelationshipbetweenMeridianarclengthandgeodeticlatitudeThen243EllipsoidRelationshipbetweenMeridianarclengthandgeodeticlatitude隨著大地緯度（地理緯度）的增加而增大(Shenetal2011)

253EllipsoidPracticalmeasurements26與理論值比較(Shenetal2011)3EllipsoidFortheoblatespheroidalearth:the1°meridianarclengthincreaseswiththeincreaseofthegeodeticlatitudethe1°meridianarclengthdecreaseswiththeincreaseofthegeocentriclatitudeCassinimistakenlyregardedgeodeticlatitudeasgeocentriclatitude274Morecomplicatedfigure28sphericalearthellipsoidalearthpear-shapedearth5地球自轉5.1概述5.2地球自轉證據(jù)5.3歐拉方程5.4進動，章動和極移5.5日長變化5.6具有挑戰(zhàn)性的問題295地球自轉5.1概述－作用作用:

【不同學科紐帶作用】Tiesofdi?erentbranches[geophysics,astronomy,geodesy,geodynamics,oceanscience,meteorology，navigation,...]ReferencesystemInteriorofEarthGlobalclimatechange???305地球自轉5.1概述簡史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地球自轉5.2地球自轉證據(jù)diurnalmotionofcelestialbody(天體周日運動)【能證明嗎？】easternde?ectionofafallingbody(落體偏東)Foucaultpendulum(1851)(傅科擺)[巴黎國葬院，光滑懸掛擺長67米，擺錘重28公斤;θ=15tsinφ]32練習題：如何根據(jù)傅科擺確定地理緯度？5地球自轉5.3歐拉方程歐拉角：33慣性坐標系地固坐標系自轉角，進動角，章動角5地球自轉5.3歐拉方程歐拉運動學方程：5地球自轉5.3歐拉方程歐拉動力學方程：主慣性矩：5地球自轉5.4進動，章動和極移Precession:precessionaroundeclipticpole(黃極),T=25800yrNutation:smallamplitudeTremor,T=18.6yrPrecessionandnutationarecausedbythegravitationaleffectsofSunandMoon5地球自轉5.4進動，章動和極移ThemigrationofEarthpoleontheEarthsurface,notnecessarilythemigrationoftherotationaxis.Periodicmotion:12-month;14-month(Chandlerwobble)long-termdriftslowlong-termdriftCauseofpolarmigration:complex(interiormassmigration（postglacialrebound(冰后回彈),seasonvariations,…）375地球自轉5.5日長變化日長變化原因:（1）由于潮汐摩擦，相對于地月連線，存在2.9度的超前角，因而存在反力矩；（2）反力矩使地球自轉變慢，導致日長（LOD）變長，其變長量大約1-2ms/世紀（3）在不同尺度上的日長變化？385地球自轉5.6具有挑戰(zhàn)性的問題（1）InfluenceonglobalclimateduetotheEarth’sprecessionwithrespecttotheSun（2）Solutionofthree-layeredtriaxialEarthrotation（3）MechanismoftheLODvariationinten-yearscale（4）PrecisequantitativecomputationofthesecularvariationoftheLODcausedbytidalfriction（5）Polarwander(PW)causedbyoceanandatmosphere（6）InvestigationofpossibleinverseoftheEarth’srotationaxis(Shen2004)39自轉參數(shù)觀測進動角（歲差）：需要觀測恒星【相對恒星定位，VLBI】

章動角（章動）：需要觀測恒星【相對恒星定位,VLBI】

自轉角（自轉，日長）：需要一恒星為參考【相對恒星確定自轉速率,時鐘】

6地球自轉參數(shù)觀測6地球自轉參數(shù)觀測月掩星測量(LunarOccultation)光學天文測量(OpticalAstrometric)空間大地測量(Space-Geodetic)VLBI(Verylongbaselineinterferometry)GNSS(Globalnavigationsatellitesystem)SLR/LLR(Satelliteandlunarlaserranging)DORIS(Dopplerorbitographyandradiopositioningintegratedbysatellite)環(huán)形激光陀螺儀(RingLaserGyroscope)416地球自轉參數(shù)觀測月掩星測量(LunarOccultation)Jordi等在1994年對1830.0-1955.5年間5300個觀測值分析，獲得這些年4個月時間間隔的TT-UT1系列的值和中誤差。（TT=TAI+32.1845s）隨后，jordi等從BIH和IERS獲?。║T1-TAI）的值將TT-UT1系列擴展到1992年后又對擴展的UT1系列通過有限差分和平滑處理獲得1830-1987年間4個月時間間隔的LOD系列Gross在2001年結合月掩星測量數(shù)據(jù)和光學天文測量、空間大地測量技術，獲得1832.5-1997.5年間以年為時間間隔的平滑的LOD系列426地球自轉參數(shù)觀測光學天文測量(OpticalAstrometric)ILS在全球建立七個觀測站觀測測站緯度變化，獲得1899-1978年間月間隔的極移觀測系列。隨后有更多的其他非ILS測站和方法的光學天文測量經(jīng)緯度變化，Li和Feissel利用136個非ILS測站的經(jīng)緯度觀測值獲得UT1和極移觀測系列，即BIH觀測系列，時間從1962.1.5-1981.12.31，間隔為5天。利用包括ILS7個測站的數(shù)據(jù)，對板塊運動、海洋負荷和潮汐變化進行了改正，采用更精確的Hipparcos星表，獲得Hipparcos地球定向參數(shù)觀測系列包含了1899.7-1992.0五天時間間隔的極移、章動數(shù)值和誤差，1956年以后的UT1值。436地球自轉參數(shù)觀測空間大地測量(Space-Geodetic)VLBI：多基線VLBI（multibaselineVLBI）是唯一能獨立確定所有EOP參數(shù)的技術。其他技術需要額外的外部限制或只能確定部分EOP參數(shù)。GNSS，SLR/LLR，DORIS：這幾種技術只能確定極移和極移變化率。此外，由于UT1不能從衛(wèi)星軌道元素中分離出來而不能確定，但UT1的變化率（與LOD有關）可以確定。446地球自轉參數(shù)觀測IERS：ICRF、ITRF、EOPJPLKalmanfilter/IERS/EN/Organization/TechniqueCentres/TC.html456地球自轉參數(shù)觀測46/IERS/EN/DataProducts/EarthOrientationData/eop.htmlhttp://hpiers.obspm.fr/eop-pc/Theseseriesarederivedfromthevariousastro-geodetictechniques(LLR,SLR,GPS,VLBIandDORIS).Bulletin

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