Theory of satellite geodesy and gravity field determination:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York ; London, Paris ; Tokyo ; Hong
Springer
1989
|
| Series: | Lecture notes in earth sciences
25 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XII, 491 S. graph. Darst., Kt. |
| ISBN: | 3540515283 0387515283 |
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| 245 | 1 | 0 | |a Theory of satellite geodesy and gravity field determination |c F. Sansò ; R. Rummel (eds.) |
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Record in the Search Index
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| adam_text | Lecture Notes in
Earth Sciences
Edited by Somdev Bhattacharji, Gerald M Friedman,
Horst J Neugebauer and Adolf Seilacher
F Sansd R Rummel (Eds )
Theory of
Satellite Geodesy and
Gravity Field Determination
Springer-Verlag
Berlin Heidelberg New York London Paris Tokyo Hong Kong
CONTENTS
Introduction
J Adam
LECTURES
Introduction to Classical Mechanics
H Moritz
Introduction 9
Lecture 1 NEWTON 11
1 1 Motion of a Mass Point 11
1 2 Central Forces 14
1 3 Planetary Motion 15
1 4 Free Motion 15
1 5 The Many-Body Problem 16
1 6 Motion of a Rigid Body 17
1 7 Inertial Navigation and Surveying 19
1 8 Error Propagation 20
1 9 Unstable Convergence in Integration 20
j-Lecture 2 LAGRANGE 23
;21 Statics; Principle of Virtual Displacements 23
2 2 Mass Point in Equilibrium on a Surface 25
2 3 D Alembert s Principle 27
2 4 Lagrange s Equations of First Kind 28
,25 Lagrange s Equations of Second Kind 29
2 6 Geometrical Interpretations 31
2 7 The Principle of Least Action 34
Lecture 3 HAMILTON 36
3 1 The Legendre Transformation 36
3 2 Hamilton s Canonical Equations 38
3 3 Canonical Transformations 41
3 4 Symplectic Geometry 42
3 5 Cyclical Variables 46
3 6 Perturbation Theory 48
3 7 Keplerian Motion 49
jLecture 4 POINCARE 55
4 1 Liouvilie s Theorem, Measure-Preserving Transformations and
Stochasti c Processes 55
4 2 The Kolmogorov-Arnold-Moser Theorem 59
4 3 The Example of H6non and Heiles 60
4 4 Chaos and Order 61
Suggested Additional Reading 66
i
Lectures in Celestial Mechanics
!J Kovalevsky
|1 General Introduction 69
2 The Two Body Probl em 70
2 1 Elliptical Solution of the Two Body Problem 70
2 2 Kepler s Equation 72
2 3 Expansions in Mean Anomaly 74| 2 4 Orbital Elements 76
i
VIII
3 Equations of Perturbed Motion 78
3 1 The Disturbing Function 78
3 2 Osculating Elements 79
3 3 Lagrange PIanetary Equati ons 80
3 4 Gauss Equations 80
3 5 Canonical Osculating Elements 81
4 General Perturbation Techniques 82
4 1 Development of the Disturbing Function 82
4 2 Artificial Satellite Disturbed by the Sun 83
4 3 Method of Solution 85
4 4 Solution in Canonical Variables 87
4 5 Form of the Solution 89
5 Motion of an Artificial Satellite 89
5 1 Earth s Gravitational Potential 89
5 2 Development of the Disturbing Function - 92
5 3 First Order Solution 93
5 4 Second Order Solution , 96
5 5 Effects of Other Zonal Harmonics 96
5 6 Treatment of Tesseral Harmonics 97
5 7 Other Perturbations 98
6 Resonances 99
6 1 General Presentati on 99
62A Simplified Resonance Problem 101
6 3 Applications to Artificial Satellites 103
6 4 The Critical Inclination 104
7 Numerical Methods 104
7 1 Semi-Numerical General Analytical Theories 105
7 2 Secular Semi-Numerical Theories 108
7 3 Numerical Integration ; ; 108
7 4 Single Step Methods 109
7 5 Multistep Methods 110
7 6 Discussion of Numerical Integration Methods 113
General Bibliography 114
Four Lectures on Special and General Relativity
E W Grafarend
Lecture I Flat spacetime, pseudo-Euclidean space, the Lorentz transformation
Summary 115
1 Flat spacetime, pseudo-Euclidean space, the Lorentz transformation 115
2 Examples 122
3 Exercises 127
3 1 Lorentz transformation in spinor notation 127
3 2 The Sagnac effect 128
Lecture II-IV Curved spacetime, pseudo-Riemann space, the affine
transformation 129
Summary 129
1 Curved Spacetime, pseudo-Riemann space, the affine transformation 129
2 Examples 137
3 Exercises 148
3 1 The Kerr metric 148
3 2 Schwarzschild metric in isotropic coordinates 149
Literature 150
Reference Coordinate Systems: An Update
I I Mueller
1 Introduction 153
2 Conventional Inertial Systems (CIS) of Reference 156
IX
2 1 Basic Considerations 156
2 2 Inertial Systems in Practice 159
2 21 Extragalactic Radio Source System 159
2 22 Stellar System 161
2 23 Dynamical Systems 163
2 3 Conclusions 166
3 Conventional Terrestrial Systems (CTS) of Reference 167
3 1 Brief History of the Past Decade 169
3 2 The New CTS 170
3 3 Reference Frame Ties 172
3 31 Ties Between the CIS Frames 172
3 32 Ties Between the CTS Frames 174
4 Modeling the Deformable Earth 175
4 1 Precession (P) 177
4 2 Nutation (N) 177
4 3 Earth Rotation (S) 180
4 4 Deformations (L1) 181
4 41 Tidal Deformations 182
4 42 Plate Tectonic Mass Transfer 182
4 43 Other Deformations 183
4 44 Current (1988) Practice 183
4 5 Recent Developments 184
4 51 Expected Changes in the Adopted Series of Nutation 184
4 52 Expected Change in the Constant of Precession 185
4 53 Intermediate Reference Frame Issues 185
5 The International Earth Rotation Service 186
5 1 The MERIT-COTES Programs 186
5 2 The International Earth Rotation Service 187
References 189
Appendix 1 Principal Recommendations of the MERIT and COTES
Working Group 194
Appendix 2 Resolution of International Astronomical Union (1985) 196
Appendix 3 Resolution 1 of the International Union of Geodesy and Geophysics,
XIX General Assembly, Vancouver, 21 August 1987 196
Gravity Field Recovery from Satellite Tracking Data
C Reigber
1 Introduction 197
2 Principles of Gravity Parameter Determination 199
2 1 Li near Observati on Equati ons 203
3 Gravity Induced Linear Orbit Perturbations 206
3 1 Secular Perturbations 210
3 2 Periodic Perturbations 211
4 Adjustment Procedures 217
4 1 Single Arc Solution 217
4 2 Solution from Combined Normal Equations 218
4 3 Constraint Equations 219
4 4 Light Constraint Solutions 220
4 5 Parameters Considered for Adjustment 221
5 Tracking Data 222
5 1 Existing Data 222
5 2 Data Selection • 223
6 Processi ng Steps 224
7 Special Topics 228
8 Global Gravity Field Models 230
8 1 Recent Gravity Field Models 230
8 2 New Gravity Model Developments 232
References 234
Fundamentals of Orbit Determination
B D Tapley
Introduction 235
The Orbit Determination Problem 235
Linearization of the Orbit Determination Process 238
The Least Squares Solution 239
The Minimum Norm Solution 240
Weighted Least Squares Solution 241
The Minimum Variance Estimate 242:
Propagation of the Estimate 244j
Minimum Variance Estimate With A Priori Information 244;
The Sequential Estimation Algorithm 246
The Extended Sequential Estimation Algorithm 247
State Noi se Compensati on Algori thm 247
Batch and Sequential Estimation Compared 248
Error Sources 249
Solution Methods for the Orbit Determination Problem 250
Cholesky Decomposition 251 ,
Least Squares Solution via Orthogonal Transformation 251
Appendix A The Primary Forces on a Near-Earth Satellite 255
Gravi tati onal Perturbations 255
Gravitational Potential for the Earth 255
Sol id Earth Tides 256
N-Body 256
Ocean Tides 257
General Relativity 258
Nongravitational Perturbations 258
Atmospheri c Drag 258
Solar Radiation Pressure 259
Earth Radiation Pressure 259
References 260
Combination of Satellite, Altimetric and Terrestrial Gravity Data
R H Rapp
1 0 Introduction 261
2 0 Representation of the Gravitational Potential 262
2 1 Spherical Harmonics 262
211 Spherical Potential Coefficients and Gravity Anomalies 263
212 Spherical Harmonics and Orthogonality Relationships 266
2 2 Ellipsoidal Harmonics 267
221 Ellipsoidal Harmonics and Gravity Anomalies 268
3 0 Data Definition 269
3 1 Satellite Data 269
3 2 Terrestrial Gravity Data 269
4 0 Data Combination 271
4 1 General Principles 271
4 2 Least Squares Principles 271
4 3 Optimal Estimation 274
5 0 Observati on Equati on Formati on 275
5 1 Combination Procedure - Method A 275
5 2 Combi nati on Procedure - Method B 276
5 3 Comment 278
6 0 The Development of High Degree Potential Coefficient Models 279
7 0 The Role of Satellite Altimeter Data 279
8 0 Comparisons of Satellite and Terrestrial Gravity Anomaly Fields 281
9 0 Conclusion 283
References 283
XI
I
i
Summer School Lectures on Satellite Altimetry
;CA Wagner
Lecture 1 Purposes and Motivation, The Altimetric Equation, Radial
Perturbations 285
Lecture 2 Frequency Classification and Observability of Radial
Variations 302
Lecture 3 Determination of Permanent Sea Topography From Altimetry 1:
Removal of Orbit Error 312
Lecture 4 Determination of PST from Altimetry 2: Simulation of a
Subtraction Method 315
Lecture 5 Determination of PST from Altimetry 3: Simulation of a
Simultaneous Solution for the Geoid 323
A Footnote on New Results from the Subtraction Method 329
References 332
Advanced Techniques for High-Resolution Mapping of the
Gravitational Field
0 Colombo
1 Basic Techniques for Gathering Data on a Global Basis 335
Why use a gradiometer? 335
Fundamental problems 336
Accuracy required 337
Problems limiting the accuracy 337
The null-point principle 338
Every-day examples 7 338
The precision balance used in laboratories 338
Some basic relationships : 341
Which way is up in freee fall? 341
Prospecting in the Asteroids 342
Dealing with orbit error and attitude / Rotation to estimate
gravitation 343
a) The orbit error 343
b) Dealing with attitude and rotation errors 346
2 Global Data Analysis 349
3 Mission Error Analysis for a 10 2EU, Full-Tensor Instrument 352
3 1 Time series representation of the second gradients for a circular,
polar, repeating orbit 353
3 2 The general element of the normal matrix H for the full-tensor
gradi ometer 356
3 3 Rescaling for different altitude accuracies and mission lengths 357
3 4 Calculating global RMS errors of area mean anomalies 357
4 Implications for the Study of the Earth of the Results of a Global
Error Analysis of a Full-Tensor Gradiometer Mission 359
References 368
SEMINARS
The Integrated Approach to Satel l i te Geodesy
B Betti, F Sansd
i
1 Introduction 373
2 The Typical Form of Satellite Observation Equations 374
3 The Spherical Field-Circular Motion approximation 380
4 The Solution of Hill s Equation in the Circular Motion Approximation 386
5 The Covariance Function and the Integrated Scheme 395
6 Sub-Optimal Solutions 401
XII
Appendi x 405
References 416
Determination of a Local Geodetic Network by Multi-Arc Processing
of Satellite Laser Ranges
A Milani, E Melchioni
1 Introduction and summary 417
2 Choice of the arc length 419
3 Symmetri es and rank defi ci ency 422
4 The multi-arc algori thm 430
5 Experimental results 435
References 444
Boundary Value Problems and Invariants of the Gravitational
Tensor in Satellite Gradiometry
P Hoiota
Summary 447
1 Introducti on 447
2 Differential Accelerometry 448
3 Invariants of the Gravitational Tensor 450
4 Reduction and Linearization 452
5 Separation of the Field and Orbit Perturbations 454
References 457
A Possible Application of the Space VLBI Observations for
Establishment of a New Connection of Reference Frames
J Adam
Summary 459
1 Introduction 460
2 The role of space VLBI in reference frames tie 462
3 Rank deficiencies within a space VLBI network 465
4 Conclusi ons 473
References 474
Optimization of the Reordering Algorithm for Least Squares Problems
Relevant to Space Geodesy
M Crespi, G Forlani, L Mussio
Summary 477
1 The Problem 477
2 The Method 478
3 The Program 480
4 The Test 481
5 The Example 481
6 Remarks 484
References • 491
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| id | DE-604.BV001877529 |
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| indexdate | 2024-07-09T15:36:54Z |
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| spelling | Theory of satellite geodesy and gravity field determination F. Sansò ; R. Rummel (eds.) Berlin ; Heidelberg ; New York ; London, Paris ; Tokyo ; Hong Springer 1989 XII, 491 S. graph. Darst., Kt. txt rdacontent n rdamedia nc rdacarrier Lecture notes in earth sciences 25 Literaturangaben Satellitengeodäsie (DE-588)4051744-5 gnd rswk-swf Gravitationsfeld (DE-588)4072014-7 gnd rswk-swf Schwerefeld (DE-588)4192182-3 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1988 Assisi gnd-content Satellitengeodäsie (DE-588)4051744-5 s Schwerefeld (DE-588)4192182-3 s DE-604 Gravitationsfeld (DE-588)4072014-7 s Sansò, Fernando 1945- Sonstige (DE-588)1082398675 oth Lecture notes in earth sciences 25 (DE-604)BV023550940 25 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001238700&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Theory of satellite geodesy and gravity field determination Lecture notes in earth sciences Satellitengeodäsie (DE-588)4051744-5 gnd Gravitationsfeld (DE-588)4072014-7 gnd Schwerefeld (DE-588)4192182-3 gnd |
| subject_GND | (DE-588)4051744-5 (DE-588)4072014-7 (DE-588)4192182-3 (DE-588)1071861417 |
| title | Theory of satellite geodesy and gravity field determination |
| title_auth | Theory of satellite geodesy and gravity field determination |
| title_exact_search | Theory of satellite geodesy and gravity field determination |
| title_full | Theory of satellite geodesy and gravity field determination F. Sansò ; R. Rummel (eds.) |
| title_fullStr | Theory of satellite geodesy and gravity field determination F. Sansò ; R. Rummel (eds.) |
| title_full_unstemmed | Theory of satellite geodesy and gravity field determination F. Sansò ; R. Rummel (eds.) |
| title_short | Theory of satellite geodesy and gravity field determination |
| title_sort | theory of satellite geodesy and gravity field determination |
| topic | Satellitengeodäsie (DE-588)4051744-5 gnd Gravitationsfeld (DE-588)4072014-7 gnd Schwerefeld (DE-588)4192182-3 gnd |
| topic_facet | Satellitengeodäsie Gravitationsfeld Schwerefeld Konferenzschrift 1988 Assisi |
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