地球主惯性矩

©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.:100121595(2005)0120007207:P22:A(,710054)EarthsPrincipalMomentsofInertiaWEIZi2qing(XianResearchInstituteofSurveyingandMapping,Xian710054,China)Abstract:TheEarthsprincipalmomentsofinertiaarethegeodeticandastronomicalfundamentalEarthparame2ters.ThepaperisdevotedtotheEarthsprincipalmomentsofinertiaandtherelatedissues.Section1formulatestheEarthsprincipalmomentsofinertiaandtheEarthsflattening;Section2dealswiththecomputationofthesec2ond2degreeharmoniccoefficientsintheprincipalaxescoordinatesystem;Section3studiesthedirectionsoftheEarthsprincipalaxesofinertia,andSection4presentsthenumericalvaluesoftheEarthsprincipalmomentsofin2ertia,andoftheorientationsoftheEarthsprincipalaxesofinertia,andoftheEarthsflattening.Keywords:second2degreeharmoniccoefficients;earthsprincipalaxesofinertia;earthsprincipalmomentsofin2ertia;earthsfigure:;2;,:2004204216;:2004209210:(19372),,,,,:2;;;,,,;2,2,,,,,1,2V2©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=-GMa2r32m=0(J2mcosm+k2msinm)P2m(sin)(1),GM,a;r,,();P2m(sin);J2m,K2m,m=0,1,2,2m,([1](2238),(2239)(2240)):J20=J2=-1Ma2mr2p20(sin)dM(2a)J21=-13Ma2mr2cosp21(sin)dM(2b)K21=-13Ma2mr2sinp21(sin)dM(2c)J22=-112Ma2mr2cos2p22(sin)dM(2d)K22=-112Ma2mr2sin2p22(sin)dM(2e),M,a,,[1]J20J2=C-A+B2Ma2(3a)J21=K21=0(z)(3b)J22=A-B4Ma2(3c)K22=-D2Ma2(3d),A,B,Cx,y,z,Dx,y,:A=m(y2+z2)dMB=m(z2+x2)dMC=m(x2+y2)dM(4a)D=mxydM(4b)x,y,x,y,D=0,ABC,K22=0(3(d))(3a)J2=C-A+A-B2Ma2=C-AMa2+A-B2Ma2=C-AMa2+2J22C-AMa2=J2-2J22(5)C-BMa2C-AMa2+A-BMa2=J2-2J2+4J22=J2+2J22(6)2J2J22[1,2]H=C-A+B2C(7)A,B,C,(3a),(5)(7),CMa2=J2H(8)BMa2=J2H-(J2+2J22)(9)AMa2=J2H-(J2-2J22)(10)M(M=GM/G,GM,G),(8210)A,B,C(9),(10),J22,CBA3,3A,B,C,C,A[1]fp=32C-AMa2+m2(11),m=2a3GM,(5)(11),fp=32(J2-2J22)+m2(11),,C,Bfp=32C-BMa2+m2=32(J2+2J22)+m2(12)A,B()fe=32B-AMa2=-6J22(13)(13)m/2,AB222J2,J22834©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(320)(,EGM96JGM22)C2m,S2m,m=0,1,2,xyzC2m,S2mABCJ2,J22,2V2V2=GMa2r32m=0(C2mcosm+S2msinm)P2m(sin)(14),P2m(sin),,,,rx,y,z,(14)[3]:V2=152GMa2r5rTHr(15)r=(xyz)T(16)H=C22-C203S22C21S22-C22-C203S21C21S212C203(17),(15),(16),(17)V2=152GMa2r5„rT“H„r(18)„r=(‰x‰y‰z)T(19)“H=A22-A203000-A22-A2030002A203(20),A20,A222,„r,(15)(18)rTHrrQr=Q„r„r„rT“H„r,“H,(20)“H1,2,3H,1=A22-A2032=-A22-A2033=2A203(21),123(21)A20=332A22=1+A203=-2-A203(22)1,2,3,:|E-H|=0(23),E33(23),3+p+q=0(24)p=-C220-C221-S221-C222-S222(25)q=-2C32033-C203(C221+S221-2C222-2S222)-C22(C221-S221)-2C21S21S22(26)D=q22+p330,(24)3:1=2tsin3+32=-2tsin3=2tsin3-3(27)t=-p3(28)sin=-q2t3,-22(29)(22)A20,A22,J2=-A20=-5A20J22=-A22=-512A22(30)J2,J22(2a),J2sin2xyzABC,J2,xyz91:©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(J2)ABC=(J2)xyz=-5(C20)xyz(31)ABC,K22=0,(2e),=0,(2d)J22=-112Ma2mr2p22(sin)dM(32),dM(2d)(2e),xyzABC,(J22)ABC=-(J222)xyz+(k222)xyz=-512(C222)xyz+(S222)xyz(33)3x-,y-,z,HrTHr“H„rT“H„r,Qrr=Q„rQq-1,q-2,q-3,H1,2,31,A,B,Cx-,y-,z,QeA=q-1=(cos(A,x)cos(A,y)cos(A,z))TQeB=q-2=(cos(B,x)cos(B,y)cos(B,z))TQeC=q3=(cos(C,x)cos(C,y)cos(C,z))T(34),eA,eB,eC,A,B,C,,H1,2,31(15)V2=152GMa2r3LTHL(35)L=rr=(lmn)T(36)rx-,y-,zrTHr(),99LLT(E-H)L=2LT(E-H)=0(E-H)L=0(37),:-C22+C203l-S22m-C21n=0-S22l++C22+C203m-S21n=0-C21l-S21m+-2C203n=0(38)H2,(38),l2+m2+n2=1(39),l,m,n,(38)(39)n=1+u2+S21u-+2C20/3C212-12m=unl=-2C203-S21unC21(40)u=C21S21+S22-2C203S21S22+C21+C22+C203(41)l,m,n,x-,y-,ziA,B,C,ix-,y-,zli,mi,ni,ix-,y-,zi,x=arccoslii,y=arccosmii,z=arccosni(42)iii,i=arctanmilii=arcsinmil2i+m2ii=arctannil2i+m2i(43)A,[9]tan2A=K22J22=S22C22(44),A0,(2d)(2e),,A0134©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(EGM96)=6378136.3m[4]GM(EGM96)=(398600441.50.8)106m3s-2[4,6]G=(6.67420.0010)10-11m3kg-1s-2[8]H=0.0032737634470.0000000032,ÛH=(-7.8640.270)10-11a-1,=1997.0[5]EGM9621[3,4]1EMG962Tab.1Second2degreeharmoniccoefficientsandtheirtemporalvariationsfortheEGM9610-610-1110-11a-1C20-484.1653717363.56106351.16275534C21-0.000186987635955-0.32S210.001195280120311.62C222.439143523985.3739154-0.494731439S22-1.400166836545.4353269-0.203385232:,2000.0C20=-484.16520895010-63.561063510-11C21=-2.3178763595510-10S21=1.4220801203110-9C22=2.4390742615810-65.373915410-11S22=-1.4001953104710-65.435326910-11JGM22(ITRF94)[4](22):A20=-484.16520895210-63.561063510-11A22=2.8124064706810-65.389202610-11J2=1.0826263195610-37.962780110-11J22=-1.8154005706210-63.478715310-11C-AMa2=(1086.257120.00011)10-6C-BMa2=(1078.995520.00011)10-6B-AMa2=(7.261600.00014)10-6H(2000.0)=0.0032737632110.0000000032,:AMa2=0.329611550.00000032BMa2=0.329618810.00000032CMa2=0.330697810.00000032GMGM=(5.97230.0009)1024kgMa2=(2.42960.0004)1038kgm2(2000.0):A=(8.00810.0012)1037kgm2B=(8.00830.0012)1037kgm2C=(8.03450.0012)1037kgm2C-BA=(3273.53670.4905)10-6C-AB=(3295.49490.4938)10-6B-AC=(21.95840.0033)10-6111:©1994-2010ChinaAcademicJourn