Table Of ContentSeeber · Satellite Geodesy
Günter Seeber
Satellite Geodesy
2nd completely revised and extended edition
≥
Walter de Gruyter · Berlin · New York 2003
Author
Günter Seeber, Univ. Prof. Dr.-Ing.
Institut für Erdmessung
Universität Hannover
Schneiderberg 50
30167 Hannover
Germany
1stedition1993
Thisbookcontains281figuresand64tables.
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Seeber,Günter,1941(cid:1)
[Satellitengeodäsie.English]
Satellitegeodesy:foundations,methods,andapplications/Gün-
terSeeber.(cid:1)2ndcompletelyrev.andextendeded.
p. cm.
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ISBN3-11-017549-5(alk.paper)
1.Satellitegeodesy. I.Title.
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To the memory of my grandson
Johannes
Preface
Methodsofsatellitegeodesyareincreasinglyusedingeodesy,surveyingengineering,
and related disciplines. In particular, the modern development of precise and opera-
tionalsatellitebasedpositioningandnavigationtechniqueshaveenteredallfieldsof
geosciences and engineering. A growing demand is also evident for fine-structured
gravityfieldmodelsfromnewandforthcomingsatellitemissionsandforthemonitor-
ingofEarth’srotationinspace. FormanyyearsIhavehadthefeelingthatthereisa
definiteneedforasystematictextbookcoveringthewholesubject,includingbothits
foundations and its applications. It is my intention that this book should, at least in
part,helptofulfillthisrequirement.
ThematerialpresentedhereispartlybasedoncoursestaughtattheUniversityof
Hannoversince1973andonguestlecturesgivenabroad. Itismyhopethatthismate-
rialcanbeusedatotheruniversitiesforsimilarcourses. Thisbookisintendedtoserve
as a text for advanced undergraduates and for graduates, mainly in geodesy, survey-
ingengineering,photogrammetry,cartographyandgeomatics. Itisalsointendedasa
sourceofinformationforprofessionalswhohaveaninterestinthemethodsandresults
ofsatellitegeodesyandwhoneedtoacquaintthemselveswithnewdevelopments. In
addition, this book is aimed at students, teachers, professionals and scientists from
relatedfieldsofengineeringandgeosciences,suchasterrestrialandspacenavigation,
hydrography, civil engineering, traffic control, GIS technology, geography, geology,
geophysics and oceanography. In line with this objective, the character of the book
fallssomewherebetweenthatofatextbookandthatofahandbook. Thebackground
requiredisanundergraduatelevelofmathematicsandelementarymathematicalstatis-
tics. Becauseofrapidandcontinuousdevelopmentsinthisfield,ithasbeennecessary
to be selective, and to give greater weight to some topics than to others. Particular
importancehasbeenattachedtothefundamentalsandtotheapplications,especially
totheuseofartificialsatellitesforthedeterminationofprecisepositions. Acompre-
hensive list of references has been added for further reading to facilitate deeper and
advancedstudies.
Thefirsteditionofthisbookwaspublishedin1993asanEnglishtranslationand
updateofthebook“Satellitengeodäsie”, thatwasprintedintheGermanlanguagein
1989. Thepresenteditionhasbeencompletelyrevisedandsignificantlyextended. The
fundamentalstructureofthefirsteditionhasbeenmaintainedtofacilitatecontinuity
ofteaching;however,outdatedmaterialhasbeenremovedandnewmaterialhasbeen
included. Allchaptershavebeenupdatedandsomehavebeenre-written. Theoverall
status is autumn 2002 but some of the most recent technological developments to
March2003havebeenincluded.
Extensionsandupdatesmainlypertaintoreferencecoordinatesystemsandrefer-
enceframes[2.2],signalpropagation[2.3],directionswithCCDtechnology[5.2],the
Global Positioning System (GPS) and GNSS [7], satellite laser ranging [8], satellite
viii Preface
altimetry[9],gravityfieldmissions[10]andapplications[12]. Inparticular,thechap-
teronGPSandGNSS[7]hasbeenalmostcompletelyre-writtenandnowcoversabout
200 pages. Together with chapters [2], [3], and [12], it forms a comprehensive GPS
manual on its own. New technological developments of the space and user segment
areincluded,asisthecurrentstateofdataanalysisanderrorbudget. DifferentialGPS
andpermanentreferencenetworksarenowtreatedinacomprehensivesectionoftheir
own[7.5]. GLONASSandtheforthcomingGALILEOareincludedinanewsection
onGNSS[7.7].
GravityfieldmissionslikeCHAMP,GRACEandGOCE,becauseoftheirincreas-
ing importance, are dealt with in a new chapter [10]. VLBI, together with the new
inclusionofinterferometricSAR,formanothernewchapter[11]. Coverageofhistor-
icaltechniqueslikephotographiccameraobservations[5]andTransitDoppler[6]has
beenconsiderablyreduced. Thebasicprinciples,however,arestillincludedbecause
of their historical importance and because they are shared by new technologies like
CCDcameras[5.2]andDORIS[6.7]. ThegeodetichistoryofTransitDopplertech-
niques, in addition, is an excellent source for understanding the evolution and basic
concepts of the GPS. The chapter on applications, now renumbered [12], has been
updated to include modern developments and a new section on the combination of
geodeticspacetechniques[12.5]. Internationalservicesofinteresttosatellitegeodesy
have been included, namely the IGS [7.8.1], the ILRS [8.5.1], the IVS [11.1.3], and
theIERS[12.4].
The bibliography has been updated and expanded considerably by adding an in-
creasednumberofEnglishlanguagereferences. Thetotalnumberofreferencesisnow
reaching760,abouthalfofwhicharenewinthisedition.
Many of the examples within this book are based on field projects and research
workcarriedoutincollaborationwithmygraduatestudents,doctoratecandidatesand
scientificcolleaguesattheUniversityofHannoverovermorethan20years. Iwould
like to thank all these individuals for their long standing cooperation and the many
fruitfuldiscussionsIhavehadwiththem. Inaddition,thehelpofthestaffattheInstitut
fürErdmessungisgratefullyacknowledged. Mostfigureshavebeenredrawnbycand.
geod.AnkeDaubnerandDipl.-Ing.WolfgangPaech.
My sincere thanks for checking and correcting the English language go to
Dr. Graeme Eagles of theAlfred Wegener Institut für Polar- und Meeresforschung,
Bremerhaven. Ishouldalsoliketothankthemanycolleaguesfromallovertheworld
whohelpedtoimprovethebookthroughtheircommentsonthefirstedition,andthe
individualsandorganizationswhoprovidedillustrations.
FinallymygratitudegoestomywifeGiselaforherneverendingsupportandunder-
standing. Thepublisherremainedexcellentlycooperativethroughoutthepreparation
of this book. My cordial thanks go to Dr. Manfred Karbe, Dr. Irene Zimmermann,
andthestaffatWalterdeGruyter.
Hannover,May2003 GünterSeeber
Contents
Preface vii
Abbreviations xvii
1 Introduction 1
1.1 SubjectofSatelliteGeodesy . . . . . . . . . . . . . . . . . . . . . . 1
1.2 ClassificationandBasicConceptsofSatelliteGeodesy . . . . . . . . 3
1.3 HistoricalDevelopmentofSatelliteGeodesy . . . . . . . . . . . . . . 5
1.4 ApplicationsofSatelliteGeodesy. . . . . . . . . . . . . . . . . . . . 7
1.5 StructureandObjectiveoftheBook . . . . . . . . . . . . . . . . . . 9
2 Fundamentals 10
2.1 ReferenceCoordinateSystems . . . . . . . . . . . . . . . . . . . . . 10
2.1.1 CartesianCoordinateSystemsandCoordinateTransformations 10
2.1.2 ReferenceCoordinateSystemsandFramesinSatelliteGeodesy 12
2.1.2.1 ConventionalInertialSystemsandFrames . . . . . 13
2.1.2.2 ConventionalTerrestrialSystemsandFrames. . . . 15
2.1.2.3 RelationshipbetweenCISandCTS . . . . . . . . . 17
2.1.3 ReferenceCoordinateSystemsintheGravityFieldofEarth . 21
2.1.4 EllipsoidalReferenceCoordinateSystems . . . . . . . . . . . 23
2.1.5 Ellipsoid,GeoidandGeodeticDatum . . . . . . . . . . . . . 25
2.1.6 WorldGeodeticSystem1984(WGS84) . . . . . . . . . . . . 28
2.1.7 Three-dimensionalEccentricityComputation . . . . . . . . . 30
2.2 Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.2.1 BasicConsiderations . . . . . . . . . . . . . . . . . . . . . . 31
2.2.2 SiderealTimeandUniversalTime . . . . . . . . . . . . . . . 32
2.2.3 AtomicTime . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.2.4 EphemerisTime,DynamicalTime,TerrestrialTime . . . . . . 37
2.2.5 ClocksandFrequencyStandards . . . . . . . . . . . . . . . . 39
2.3 SignalPropagation . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.3.1 SomeFundamentalsofWavePropagation . . . . . . . . . . . 43
2.3.1.1 BasicRelationsandDefinitions . . . . . . . . . . . 43
2.3.1.2 Dispersion,PhaseVelocityandGroupVelocity . . . 45
2.3.1.3 FrequencyDomains . . . . . . . . . . . . . . . . . 46
2.3.2 StructureandSubdivisionoftheAtmosphere . . . . . . . . . 48
2.3.3 SignalPropagationthroughtheIonosphereandtheTroposphere 52
2.3.3.1 IonosphericRefraction . . . . . . . . . . . . . . . 54
2.3.3.2 TroposphericRefraction . . . . . . . . . . . . . . . 56
x Contents
3 SatelliteOrbitalMotion 62
3.1 FundamentalsofCelestialMechanics,Two-BodyProblem . . . . . . 62
3.1.1 KeplerianMotion . . . . . . . . . . . . . . . . . . . . . . . . 63
3.1.2 NewtonianMechanics,Two-BodyProblem . . . . . . . . . . 66
3.1.2.1 EquationofMotion . . . . . . . . . . . . . . . . . 66
3.1.2.2 ElementaryIntegration . . . . . . . . . . . . . . . 69
3.1.2.3 VectorialIntegration . . . . . . . . . . . . . . . . . 74
3.1.3 OrbitGeometryandOrbitalMotion . . . . . . . . . . . . . . 77
3.2 PerturbedSatelliteMotion . . . . . . . . . . . . . . . . . . . . . . . 82
3.2.1 RepresentationofthePerturbedOrbitalMotion . . . . . . . . 84
3.2.1.1 OsculatingandMeanOrbitalElements . . . . . . . 84
3.2.1.2 Lagrange’sPerturbationEquations . . . . . . . . . 85
3.2.1.3 GaussianFormofPerturbationEquation . . . . . . 87
3.2.2 DisturbedMotionduetoEarth’sAnomalousGravityField . . 88
3.2.2.1 PerturbationEquationandGeopotential . . . . . . 89
3.2.2.2 PerturbationsoftheElements . . . . . . . . . . . . 94
3.2.2.3 PerturbationsCausedbytheZonalCoefficientsJn . 96
3.2.3 OtherPerturbations . . . . . . . . . . . . . . . . . . . . . . . 98
3.2.3.1 PerturbingForcesCausedbytheSunandMoon . . 98
3.2.3.2 SolidEarthTidesandOceanTides . . . . . . . . . 101
3.2.3.3 AtmosphericDrag . . . . . . . . . . . . . . . . . . 102
3.2.3.4 DirectandIndirectSolarRadiationPressure . . . . 104
3.2.3.5 FurtherPerturbations . . . . . . . . . . . . . . . . 105
3.2.3.6 Resonances . . . . . . . . . . . . . . . . . . . . . 107
3.2.4 ImplicationsofPerturbationsonSelectedSatelliteOrbits . . . 108
3.3 OrbitDetermination . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
3.3.1 IntegrationoftheUndisturbedOrbit . . . . . . . . . . . . . . 110
3.3.2 IntegrationofthePerturbedOrbit . . . . . . . . . . . . . . . 114
3.3.2.1 AnalyticalMethodsofOrbitIntegration . . . . . . 114
3.3.2.2 NumericalMethodsofOrbitIntegration . . . . . . 116
3.3.2.3 PreciseOrbitDeterminationwithSpaceborneGPS . 119
3.3.3 OrbitRepresentation . . . . . . . . . . . . . . . . . . . . . . 120
3.3.3.1 EphemerisRepresentationforNavigationSatellites 121
3.3.3.2 PolynomialApproximation . . . . . . . . . . . . . 122
3.3.3.3 SimplifiedShortArcRepresentation . . . . . . . . 124
3.4 SatelliteOrbitsandConstellations . . . . . . . . . . . . . . . . . . . 126
3.4.1 BasicAspects . . . . . . . . . . . . . . . . . . . . . . . . . . 126
3.4.2 OrbitsandConstellations . . . . . . . . . . . . . . . . . . . . 128
3.4.3 Sun-synchronous,Geostationary,andTransferOrbits . . . . . 131
