地球科學(xué)概論第4講地球形狀及自轉(zhuǎn)-4May-New

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講地球形狀及自轉(zhuǎn)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(fù)雜形狀5地球自轉(zhuǎn)6地球自轉(zhuǎn)參數(shù)觀測(cè)7地球自轉(zhuǎn)應(yīng)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(xí):

請(qǐng)驗(yàn)證2Sphere進(jìn)一步思考:NoticethatthesunsourceisadistancefromtheEarth(notparallellightray),calculatetheradiusoftheEarthBasedontheMoonlightray,pleasepreciselymeasurethesphericalEarth’sradiusSupposetheEarthisarotationalellipsoid,howtomeasurethesemi-majorandminoraxes,basedonthesunray?【練習(xí)】112SphereIstheEarthasphere?No!Then,whichkindoffigure?Ellipsoid[firstapproxiamtion!]12TheoreticalinferencethattheEarthisanellipsoid

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

flattenedslightlyatthepolesandbulgessomewhatattheequator】

如何知道地球在自轉(zhuǎn)？【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(cè)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(guān)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(zhuǎn)5.1概述5.2地球自轉(zhuǎn)證據(jù)5.3歐拉方程5.4進(jìn)動(dòng)，章動(dòng)和極移5.5日長(zhǎng)變化5.6具有挑戰(zhàn)性的問(wèn)題295地球自轉(zhuǎn)5.1概述－作用作用:

【不同學(xué)科紐帶作用】Tiesofdi?erentbranches[geophysics,astronomy,geodesy,geodynamics,oceanscience,meteorology，navigation,...]ReferencesystemInteriorofEarthGlobalclimatechange???305地球自轉(zhuǎn)5.1概述簡(jiǎn)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(zhuǎn)5.2地球自轉(zhuǎn)證據(jù)diurnalmotionofcelestialbody(天體周日運(yùn)動(dòng))【能證明嗎？】easternde?ectionofafallingbody(落體偏東)Foucaultpendulum(1851)(傅科擺)[巴黎國(guó)葬院，光滑懸掛擺長(zhǎng)67米，擺錘重28公斤;θ=15tsinφ]32練習(xí)題：如何根據(jù)傅科擺確定地理緯度？5地球自轉(zhuǎn)5.3歐拉方程歐拉角：33慣性坐標(biāo)系地固坐標(biāo)系自轉(zhuǎn)角，進(jìn)動(dòng)角，章動(dòng)角5地球自轉(zhuǎn)5.3歐拉方程歐拉運(yùn)動(dòng)學(xué)方程：5地球自轉(zhuǎn)5.3歐拉方程歐拉動(dòng)力學(xué)方程：主慣性矩：5地球自轉(zhuǎn)5.4進(jìn)動(dòng)，章動(dòng)和極移Precession:precessionaroundeclipticpole(黃極),T=25800yrNutation:smallamplitudeTremor,T=18.6yrPrecessionandnutationarecausedbythegravitationaleffectsofSunandMoon5地球自轉(zhuǎn)5.4進(jìn)動(dòng)，章動(dòng)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(zhuǎn)5.5日長(zhǎng)變化日長(zhǎng)變化原因:（1）由于潮汐摩擦，相對(duì)于地月連線(xiàn)，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(zhuǎn)變慢，導(dǎo)致日長(zhǎng)（LOD）變長(zhǎng)，其變長(zhǎng)量大約1-2ms/世紀(jì)（3）在不同尺度上的日長(zhǎng)變化？385地球自轉(zhuǎn)5.6具有挑戰(zhàn)性的問(wèn)題（1）InfluenceonglobalclimateduetotheEarth’sprecessionwithrespecttotheSun（2）Solutionofthree-layeredtriaxialEarthrotation（3）MechanismoftheLODvariationinten-yearscale（4）PrecisequantitativecomputationofthesecularvariationoftheLODcausedbytidalfriction（5）Polarwander(PW)causedbyoceanandatmosphere（6）InvestigationofpossibleinverseoftheEarth’srotationaxis(Shen2004)39自轉(zhuǎn)參數(shù)觀測(cè)進(jìn)動(dòng)角（歲差）：需要觀測(cè)恒星【相對(duì)恒星定位，VLBI】

章動(dòng)角（章動(dòng)）：需要觀測(cè)恒星【相對(duì)恒星定位,VLBI】

自轉(zhuǎn)角（自轉(zhuǎn)，日長(zhǎng)）：需要一恒星為參考【相對(duì)恒星確定自轉(zhuǎn)速率,時(shí)鐘】

6地球自轉(zhuǎn)參數(shù)觀測(cè)6地球自轉(zhuǎn)參數(shù)觀測(cè)月掩星測(cè)量(LunarOccultation)光學(xué)天文測(cè)量(OpticalAstrometric)空間大地測(cè)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(zhuǎn)參數(shù)觀測(cè)月掩星測(cè)量(LunarOccultation)Jordi等在1994年對(duì)1830.0-1955.5年間5300個(gè)觀測(cè)值分析，獲得這些年4個(gè)月時(shí)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獲取（UT1-TAI）的值將TT-UT1系列擴(kuò)展到1992年后又對(duì)擴(kuò)展的UT1系列通過(guò)有限差分和平滑處理獲得1830-1987年間4個(gè)月時(shí)間間隔的LOD系列Gross在2001年結(jié)合月掩星測(cè)量數(shù)據(jù)和光學(xué)天文測(cè)量、空間大地測(cè)量技術(shù)，獲得1832.5-1997.5年間以年為時(shí)間間隔的平滑的LOD系列426地球自轉(zhuǎn)參數(shù)觀測(cè)光學(xué)天文測(cè)量(OpticalAstrometric)ILS在全球建立七個(gè)觀測(cè)站觀測(cè)測(cè)站緯度變化，獲得1899-1978年間月間隔的極移觀測(cè)系列。隨后有更多的其他非ILS測(cè)站和方法的光學(xué)天文測(cè)量經(jīng)緯度變化，Li和Feissel利用136個(gè)非ILS測(cè)站的經(jīng)緯度觀測(cè)值獲得UT1和極移觀測(cè)系列，即BIH觀測(cè)系列，時(shí)間從1962.1.5-1981.12.31，間隔為5天。利用包括ILS7個(gè)測(cè)站的數(shù)據(jù)，對(duì)板塊運(yùn)動(dòng)、海洋負(fù)荷和潮汐變化進(jìn)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(cè)系列包含了1899.7-1992.0五天時(shí)間間隔的極移、章動(dòng)數(shù)值和誤差，1956年以后的UT1值。436地球自轉(zhuǎn)參數(shù)觀測(cè)空間大地測(cè)量(Space-Geodetic)VLBI：多基線(xiàn)VLBI（multibaselineVLBI）是唯一能獨(dú)立確定所有EOP參數(shù)的技術(shù)。其他技術(shù)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(shù)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(lái)而不能確定，但UT1的變化率（與LOD有關(guān)）可以確定。446地球自轉(zhuǎn)參數(shù)觀測(cè)IERS：ICRF、ITRF、EOPJPLKalmanfilter/IERS/EN/Organization/TechniqueCentres/TC.html456地球自轉(zhuǎn)參數(shù)觀測(cè)46/IERS/EN/DataProducts/EarthOrientationData/eop.htmlhttp://hpiers.obspm.fr/eop-pc/Theseseriesarederivedfromthevariousastro-geodetictechniques(LLR,SLR,GPS,VLBIandDORIS).Bulletin

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