地球科学概论 第4讲 地球形状及自转-4May-New

1、第 4 讲地球形状及自转地球形状及自转申文斌，邓洪涛，徐新禹，罗佳申文斌，邓洪涛，徐新禹，罗佳2014.5.42014.5.41内容提要l 1 1 历史历史 l 2 2 球形球形l 3 3 椭球形椭球形l 4 4 更复杂形状更复杂形状l 5 5 地球自转地球自转l 6 6 地球自转参数观测地球自转参数观测l 7 7 地球自转应用举例地球自转应用举例21 Historyl Greek(Homer, Thales, Pythagoras, Plato, Greek(Homer, Thales, Pythagoras, Plato, Eratosthenes )Eratosthenes )p Hom

2、er (800-1000 BC ? poet): the earth resembling a flat disc p Thales (624-546BC,Think, Sci, Phi): the earth is spherical (600B.C)p Pythagoras (572-497 BC, Math, Phi) and Aristotels (384-322BC, Phi, Sci, Educ): sphere 31 Historyl GreekGreekp Plato (427-347BC): Earths circumference is 400,000 stadia (by

3、 speculation)（62,800 km - 74,000km), and Archimedes (287-212BC): 300,000stadia Euclid: 325-265BC【1 stadium = 157.5 m】p Eratosthenes (276-194BC, Math, Georagr, Histo, Peot, Astro): earths radius is 6267km39,377 (by calculation, 240B.C)4AristotelsPlato1 Historyl China: orbicular sky and rectangular ea

4、rth China: orbicular sky and rectangular earth （天圆地方）（天圆地方）51 Historyl Han:Han:张衡张衡(78-139 A.D, Astro, Math, Inventor, (78-139 A.D, Astro, Math, Inventor, Geogra, Map, Liter)Geogra, Map, Liter)浑天仪注浑天仪注“天如鸡卵，天如鸡卵，地如卵黄地如卵黄”61 Historyl 思考思考: :p What does the Earth look like for the ancient people?p If

5、you live in 500B.C, could you find any clues indicating that the earth is spherical?p Can you prove your viewpoint？p Assume the earth is spherical, how to calculate its radius?72 Spherel Euclidean geometry (Euclid, 325-265 BC, Euclidean geometry (Euclid, 325-265 BC, Greek Math)Greek Math)p Draw and

6、only draw one straight line from one point to another pointp Produce extend a finite straight line continuously into a straight linep Determine a unique circle with any center and a distance radiusp All right angles are equal with each anotherp The parallel postulate Two parallel lines will never cr

7、oss each other82 Spherel Eratosthenesmethod:Eratosthenesmethod:p On summer solstice, he observed the midday sun shone to the bottom of a well in the town of Syene p At the same time, he observed the sun was not directly overhead at Alexandria p It casts a shadow with the vertical equal to 1/50th of

8、a circle (7 12) p The distance from Alexandria to Syene is 5000 stadia (1 stadium = 157.5 m)p The radius of the Earth is 6267km (Error only 2%)92 Spherel Eratostheness method:Eratostheness method:10Cited from Baki iz 2010练习练习: 请验证请验证2 Spherel 进一步思考进一步思考: :p Notice that the sun source is a distance f

9、rom the Earth (not parallel light ray), calculate the radius of the Earthp Based on the Moon light ray, please precisely measure the spherical Earths radius p Suppose the Earth is a rotational ellipsoid, how to measure the semi-major and minor axes, based on the sun ray ?【练习】112 Spherel Is the Earth

10、 a sphere? Is the Earth a sphere? l No !No !l Then, which kind of figure? Then, which kind of figure? l Ellipsoid first approxiamtion!Ellipsoid first approxiamtion!12l Theoretical inference that the Earth is an ellipsoidp 由于地球自转，地球必定是两极扁平、赤道隆起的（旋转）椭球 【rotational ellipsoid flattened slightly at the p

11、oles and bulges somewhat at the equator】p 如何知道地球在自转？【后面讲述】3 Ellipsoid2 Spherel The rotation of earth (evidence)The rotation of earth (evidence)p Day and night ?p Regular movement of celestial bodies (N. Copernicus 1473-1543 )？p Foucault (1819-1868) pendulum (1885) p Geographical phenomena? ？p Gravit

12、y ?p Whirlpool (different directions in north and south poles) ?p Hairs round direction ? 143 Ellipsoidl The earth is rotational ellipsoid (flattened The earth is rotational ellipsoid (flattened slightly at the poles and bulges somewhat at slightly at the poles and bulges somewhat at the equator) th

13、e equator) l Theoretical inference that the Earth is an Theoretical inference that the Earth is an ellipsoidellipsoid153 Ellipsoidl How to deduce rotational ellipsoid How to deduce rotational ellipsoid theoretically? theoretically? 163 Ellipsoidl Arguments in history Arguments in historyp Is the ear

14、th oblate spheroid or olive ellipsoid？p Newton: according to mechanics, the earth should be oblate spheroid. 【如何利用观测证明？Thus Thus the 1 meridian arc length should increases with the increase of the latitude】p Cassini: the earth is olive ellipsoid, supported by measurement results the 1 meridian arc l

15、ength increase with the increase of the latitudep Who made mistakes? What mistakes?173 Ellipsoidl The problem lies in two kind of latitudes:The problem lies in two kind of latitudes:p geocentric latitude (地心纬度)p geodetic latitude (大地纬度)18fjgeocentric latitudegeodetic latitude3 Ellipsoidl Relationshi

16、p between Meridian arc length Relationship between Meridian arc length and geocentric latitude and geocentric latitude 【考察地心纬度变化考察地心纬度变化】p In Plane-Rectangular coordinate system, we have elliptic equation:19x=rcosfy=rsinfx2a2+y2b2=1r=a1-e21-e2cos2fe=a2-b2/a3 Ellipsoidl Relationship between Meridian

17、arc length Relationship between Meridian arc length and geocentric latitudeand geocentric latitudep Then we havep according to differential equation20 x=a1-e2cosf1-e2cos2fy=a1-e2sinf1-e2cos2fdxdf=-a1-e2sinf(1-e2cos2f)3/2dydf=a1-e2(1-e2)cosf(1-e2cos2f)3/2dl=dx2+dy23 Ellipsoidl Relationship between Me

18、ridian arc length Relationship between Meridian arc length and geocentric latitudeand geocentric latitudep Thenp substitute parameter21dl=a1-e2 1-2e2cos2f+e4cos2f1/2(1-e2cos2f)3/2dff(f)=dldf=a1-e21-2e2cos2f+e4cos2f1/2(1-e2cos2f)3/2a=6378137m, e2=0.00669438002293 Ellipsoidl Relationship between Merid

19、ian arc length and Relationship between Meridian arc length and geocentric latitudegeocentric latitude22110900 110950 111000 111050 111100 111150 111200 111250 111300 111350 0 10 20 30 40 50 60 70 80 90 100 f()/(m/) / 随着地心纬度的增加而减小(Shen et al 2011) 3 Ellipsoidl Relationship between Meridian arc lengt

20、h Relationship between Meridian arc length and geodetic latitude and geodetic latitude 【地理纬度关系如何？地理纬度关系如何？】p The negative value of co-tangent can be expressed by the two coordinates of corresponding point on ellipsoid:p Since 23dydx=-b2a2xyx2a2+y2b2=13 Ellipsoidl Relationship between Meridian arc le

21、ngth Relationship between Meridian arc length and geodetic latitudeand geodetic latitudep Then24x=a1-e2sin2jcosj, dx=-a(1-e2)sinj(1-e2sin2j)3/2djy=a(1-e2)1-e2sin2jsinj, dy=a(1-e2)cosj(1-e2sin2j)3/2djdl=a(1-e2)(1-e2sin2j)3/2djf(j)=dldj=a(1-e2)(1-e2sin2j)3/23 Ellipsoidl Relationship between Meridian a

22、rc length and Relationship between Meridian arc length and geodetic latitudegeodetic latitudel 随着大地纬度（地理纬度）的增加而增大随着大地纬度（地理纬度）的增加而增大(Shen et al 2011) 25110400 110600 110800 111000 111200 111400 111600 111800 0 10 20 30 40 50 60 70 80 90 100 f()/(m/) / 3 Ellipsoidl Practical measurementsPractical meas

23、urements26 不同纬度标准的 1子午线弧长及与法国科学院 18 世纪测量结果比较 地区 拉普兰 巴黎 秘鲁 纬度 地心纬度 66o11 45o8 1o31 大地纬度 66o20 45o20 1o31 归化纬度 66o15 45o14 1o31 1子午线弧长(m) 采用地心纬度 111007.18 111132.13 111319.23 采用大地纬度 111512.23 111138.29 110575.06 采用归化纬度 111259.08 111134.55 110946.52 法国 18 世纪测量值(m) 111918 111116 110604 理论值与18世纪测量值之差(m)

24、采用地心纬度 -911 +16 +715 采用大地纬度 -406 +22 -29 采用归化纬度 -659 +18 +342 与理论值比较(Shen et al 2011)3 Ellipsoidl For the oblate spheroidal earth:For the oblate spheroidal earth:p the 1 meridian arc length increases with the increase of the geodetic latitude p the 1 meridian arc length decreases with the increase o

25、f the geocentric latitude l Cassini mistakenly regarded geodetic Cassini mistakenly regarded geodetic latitude as geocentric latitude latitude as geocentric latitude 274 More complicated figure28spherical earth ellipsoidal earthpear-shaped earth5 地球自转l 5.1 5.1 概述概述l 5.2 5.2 地球自转证据地球自转证据l 5.3 5.3 欧拉方

26、程欧拉方程l 5.4 5.4 进动，章动和极移进动，章动和极移l 5.5 5.5 日长变化日长变化l 5.6 5.6 具有挑战性的问题具有挑战性的问题295 地球自转l 5.1 5.1 概述作用概述作用p 作用: p 【不同学科纽带作用】Ties of different branches geophysics, astronomy, geodesy, g e o d y n a m i c s , o c e a n s c i e n c e , meteorology， navigation, .p Reference system p Interior of Earth p Globa

27、l climate changep ?305 地球自转l 5.1 5.1 概述概述p 简史 Aristarchus （ca. BC 300）: Earth moves around sun 1 Copernicus (1473-1543) 2 Galileo (1564-1642) ca.1582 3 Huygens (1629-1695)1657 4 Hooke (1635-1703) 1660 5 Newton (1642-1726) 1687 6 Euler (1707-1783) 7 Kant (1724-1804) 8 9 Foucault (1819-1868)1851315 地球

28、自转l 5.2 5.2 地球自转证据地球自转证据p diurnal motion of celestial body(天体周日运动)【能证明吗？】p eastern deflection of a falling body(落体偏东)p Foucault pendulum(1851)(傅科摆) 巴黎国葬院，光滑悬挂 摆长 67 米，摆锤重 28 公斤; = 15t sin 32练习题：如何根据傅科摆确定地理纬度？5 地球自转l 5.3 5.3 欧拉方程欧拉方程p 欧拉角：33 O-xhz惯性坐标系 O-xyz地固坐标系 y,f,q自转角，进动角，章动角5 地球自转l 5.3 5.3 欧拉方程欧

29、拉方程p 欧拉运动学方程：5 地球自转l 5.3 5.3 欧拉方程欧拉方程p 欧拉动力学方程：主惯性矩：5 地球自转l 5.4 5.4 进动，章动进动，章动和极移和极移 Precession: precession around ecliptic pole(黄极), T = 25800 yr Nutation: small amplitude Tremor, T = 18.6 yr Precession and nutation a r e c a u s e d b y t h e gravitational effects of Sun and Moon5 地球自转l 5.4 5.4 进动

30、，章动和进动，章动和极移极移p The migration of Earth pole on the Earth surface, not necessarily the migration of the rotation axis.p Periodic motion: 12-month; 14-month (Chandler wobble)p long-term driftp slow long-term driftp Cause of polar migration: complex (interior mass migration（postglacial rebound (冰后回弹),

31、season variations,）375 地球自转l 5.5 5.5 日长变化日长变化p 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l 5.6 5.6 具有挑战性的问题具有挑战性的问题 （1）Influence on global climate due to the Earths precession with respect to the Sun （2）Solution of three-layered t

32、riaxial Earth rotation （3）Mechanism of the LOD variation in ten-year scale （4）Precise quantitative computation of the secular variation of the LOD caused by tidal friction （5）Polar wander (PW) caused by ocean and atmosphere （6）Investigation of possible inverse of the Earths rotation axis (Shen 2004)

33、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l 月掩星测量月掩星测量(Lunar Occultation)(Lunar Occultation)l 光学天文测量光学天文测量(Optical Astrometric)(Optical Astrometric)l 空间大地测量空间大地测量(Space-Geodetic )(Space-Geodetic )p VLBI(Very long baseline

34、 interferometry)p GNSS(Global navigation satellite system)p SLR/LLR(Satellite and lunar laser ranging)p DORIS(Doppler orbitography and radio positioning integrated by satellite)l 环形激光陀螺仪环形激光陀螺仪(Ring Laser Gyroscope)(Ring Laser Gyroscope)416 地球自转参数观测l 月掩星测量月掩星测量(Lunar Occultation)(Lunar Occultation)p

35、 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）p 随后，jordi等从BIH和IERS获取（UT1-TAI）的值将TT-UT1系列扩展到1992年p 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p 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l 光学天文测量光学天文测量(Optical Astromet

36、ric)(Optical Astrometric)p 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。p 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。p 利用包括ILS 7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，195

37、6年以后的UT1值。436 地球自转参数观测l 空间大地测量空间大地测量(Space-Geodetic )(Space-Geodetic )p VLBI：多基线VLBI（multibaseline VLBI）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。p 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l IERSIERS：ICRFICRF、ITRFITRF、EOPEOPl JPL Kalman fi

38、lterJPL Kalman filterl /IERS/EN/Organization/T/IERS/EN/Organization/TechniqueCentres/TC.htmlechniqueCentres/TC.html456 地球自转参数观测46l/IERS/EN/DataProducts/EarthOrientationData/eop.htmllhttp:/hpiers.obspm.fr/eop-pc/lThese series are derived from the various astro-geodetic techniques (LLR, SLR, GPS, VLBI and DORIS).p Bulletin A rapid data and predictionsp Bulletin B monthly earth ori