Relativistic celestial mechanics of the solar system:
Gespeichert in:
| Hauptverfasser: | , , |
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| Format: | Buch |
| Sprache: | English |
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Weinheim
Wiley-VCH
2011
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| Beschreibung: | XXXI, 860 S. graph. Darst. |
| ISBN: | 9783527408566 9783527634569 |
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| 100 | 1 | |a Kopeikin, Sergei |d 1956- |e Verfasser |0 (DE-588)1014871883 |4 aut | |
| 245 | 1 | 0 | |a Relativistic celestial mechanics of the solar system |c Sergei Kopeikin, Michael Efroimsky, and George Kaplan |
| 264 | 1 | |a Weinheim |b Wiley-VCH |c 2011 | |
| 300 | |a XXXI, 860 S. |b graph. Darst. | ||
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| 700 | 1 | |a Kaplan, George |e Verfasser |0 (DE-588)1014893453 |4 aut | |
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IMAGE 1
CONTENTS
PREFACE XVII
SYMBOLS AND ABBREVIATIONS XXIII REFERENCES XXXI
1 NEWTONIAN CELESTIAL MECHANICS 1 1.1 PROLEGOMENA - CLASSICAL MECHANICS
IN A NUTSHELL 1 1.1.1 KEPLER'S LAWS 1
1.1.2 FUNDAMENTAL LAWS OF MOTION - FROM DESCARTES, NEWTON, AND LEIBNIZ
TO POINCARE AND EINSTEIN 2 1.1.3 NEWTON'S LAW OF GRAVITY 7 1.2 THE
N-BODY PROBLEM 10
1.2.1 GRAVITATIONAL POTENTIAL 11 1.2.2 GRAVITATIONAL MULTIPOLES 13 1.2.3
EQUATIONS OF MOTION 15 1.2.4 THE INTEGRALS OF MOTION 19 1.2.5 THE
EQUATIONS OF RELATIVE MOTION WITH PERTURBING POTENTIAL 21 1.2.6 THE
TIDAL POTENTIAL AND FORCE 22 1.3 THE REDUCED TWO-BODY PROBLEM 24 1.3.1
INTEGRALS OF MOTION AND KEPLER'S SECOND LAW 24 1.3.2 THE EQUATIONS OF
MOTION AND KEPLER'S FIRST LAW 27 1.3.3 THE MEAN AND ECCENTRIC ANOMALIES
- KEPLER'S THIRD LAW 31 1.3.4 THE LAPLACE-RUNGE-LENZ VECTOR 35 1.3.5
PARAMETERIZATIONS OF THE REDUCED TWO-BODY PROBLEM 37 1.3.5.1 A KEPLERIAN
ORBIT IN THE EUCLIDEAN SPACE 37 1.3.5.2 A KEPLERIAN ORBIT IN THE
PROJECTIVE SPACE 39 1.3.6 THE FREEDOM OF CHOICE OF THE ANOMALY 43 1.4 A
PERTURBED TWO-BODY PROBLEM 45 1.4.1 PREFATORY NOTES 45 1.4.2 VARIATION
OF CONSTANTS - OSCULATING CONIES 47 1.4.3 THE LAGRANGE AND POISSON
BRACKETS 49 1.4.4 EQUATIONS OF PERTURBED MOTION FOR OSCULATING ELEMENTS
51 1.4.5 EQUATIONS FOR OSCULATING ELEMENTS IN THE EULER-GAUSS FORM 53
1.4.6 THE PLANETARY EQUATIONS IN THE FORM OF LAGRANGE 55
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1002408172
DIGITALISIERT DURCH
IMAGE 2
VI I CONTENTS
1.4.7 THE PLANETARY EQUATIONS IN THE FORM OF DELAUNAY 56
1.4.8 MARKING A MINEFIELD 57 1.5 RE-EXAMINING THE OBVIOUS 58 1.5.1 WHY
DID LAGRANGE IMPOSE HIS CONSTRAINT? CAN IT BE RELAXED? 58 1.5.2 EXAMPLE
- THE GAUGE FREEDOM OF A HARMONIC OSCILLATOR 59
1.5.3 RELAXING THE LAGRANGE CONSTRAINT IN CELESTIAL MECHANICS 62 1.5.3.1
THE GAUGE FREEDOM 62 1.5.3.2 THE GAUGE TRANSFORMATIONS 64
1.5.4 THE GAUGE-INVARIANT PERTURBATION EQUATION IN TERMS OF THE
DISTURBING FORCE 66 1.5.5 THE GAUGE-INVARIANT PERTURBATION EQUATION IN
TERMS OF THE DISTURBING FUNCTION 67 1.5.6 THE DELAUNAY EQUATIONS WITHOUT
THE LAGRANGE CONSTRAINT 69 1.5.7 CONTACT ORBITAL ELEMENTS 72 1.5.8
OSCULATION AND NONOSCULATION IN ROTATIONAL DYNAMICS 75
1.6 EPILOGUE TO THE CHAPTER 76 REFERENCES 77
2 INTRODUCTION TO SPECIAL RELATIVITY 81 2.1 FROM NEWTONIAN MECHANICS TO
SPECIAL RELATIVITY 81 2.1.1 THE NEWTONIAN SPACETIME 81 2.1.2 THE
NEWTONIAN TRANSFORMATIONS 84
2.1.3 THE GALILEAN TRANSFORMATIONS 85 2.1.4 FORM-INVARIANCE OF THE
NEWTONIAN EQUATIONS OF MOTION 88 2.1.5 THE MAXWELL EQUATIONS AND THE
LORENTZ TRANSFORMATIONS 89 2.2 BUILDING THE SPECIAL RELATIVITY 94
2.2.1 BASIC REQUIREMENTS TO A NEW THEORY OF SPACE AND TIME 94 2.2.2 ON
THE "SINGLE-POSTULATE" APPROACH TO SPECIAL RELATIVITY 96 2.2.3 THE
DIFFERENCE IN THE INTERPRETATION OF SPECIAL RELATIVITY BY EINSTEIN,
POINCARE AND LORENTZ 97
2.2.4 FROM EINSTEIN'S POSTULATES TO MINKOWSKI'S SPACETIME OF EVENTS 99
2.2.4.1 DIMENSION OF THE MINKOWSKI SPACETIME 99 2.2.4.2 HOMOGENEITY AND
ISOTROPY OF THE MINKOWSKI SPACETIME 99 2.2.4.3 COORDINATES AND REFERENCE
FRAMES 100
2.2 A A SPACETIME INTERVAL 100 2.2.4.5 THE NULL CONE 101 2.2.4.6 THE
PROPER TIME 102 2.2.4.7 THE PROPER DISTANCE 103 2.2.4.8 CAUSAL
RELATIONSHIP 103
2.3 MINKOWSKI SPACETIME AS A PSEUDO-EUCLIDEAN VECTOR SPACE 103 2.3.1
AXIOMS OF VECTOR SPACE 103 2.3.2 DOT-PRODUCTS AND NORMS 105 2.3.2.1
EUCLIDEAN SPACE 106
2.3.2.2 PSEUDO-EUCLIDEAN SPACE 107 2.3.3 THE VECTOR BASIS 108
IMAGE 3
CONTENTS I VIL
2.3.4 THE METRIC TENSOR 111
2.3.5 THE LORENTZ GROUP 113 2.3.5.1 GENERAL PROPERTIES 113 2.3.5.2
PARAMETRIZATION OF THE LORENTZ GROUP 115 2.3.6 THE POINCARE GROUP 118
2.4 TENSOR ALGEBRA 120
2.4.1 WARMING UP IN THREE DIMENSIONS - SCALARS, VECTORS, WHAT NEXT? 120
2.4.2 COVECTORS 123
2.4.2.1 AXIOMS OF COVECTOR SPACE 123 2.4.2.2 THE BASIS IN THE COVECTOR
SPACE 125 2.4.2.3 DUALITY OF COVECTORS AND VECTORS 126 2.4.2.4 THE
TRANSFORMATION LAW OF COVECTORS 127 2.4.3 BILINEAR FORMS 128 2.4.4
TENSORS 129
2.4.4.1 DEFINITION OF TENSORS AS LINEAR MAPPINGS 129 2.4.4.2
TRANSFORMATIONS OF TENSORS UNDER A CHANGE OF THE BASIS 130 2.4.4.3
RISING AND LOWERING INDICES OF TENSORS 131 2.4.4.4 CONTRACTION OF TENSOR
INDICES 132 2.4.4.5 TENSOR EQUATIONS 133 2.5 KINEMATICS 134
2.5.1 THE PROPER FRAME OF OBSERVER 134 2.5.2 FOUR-VELOCITY AND
FOUR-ACCELERATION 136 2.5.3 TRANSFORMATION OF VELOCITY 138 2.5.4
TRANSFORMATION OF ACCELERATION 140 2.5.5 DILATION OF TIME 142 2.5.6
SIMULTANEITY AND SYNCHRONIZATION OF CLOCKS 143 2.5.7 CONTRACTION OF
LENGTH 146 2.5.8 ABERRATION OF LIGHT 148 2.5.9 THE DOPPLER EFFECT 150
2.6 ACCELERATED FRAMES 152
2.6.1 WORLDLINE OF A UNIFORMLY-ACCELERATED OBSERVER 155 2.6.2 A TETRAD
COMOVING WITH A UNIFORMLY-ACCELERATED OBSERVER 157 2.6.3 THE RINDLER
COORDINATES 158 2.6.4 THE RADAR COORDINATES 162
2.7 RELATIVISTIC DYNAMICS 166 2.7.1 LINEAR MOMENTUM AND ENERGY 166
2.7.2 RELATIVISTIC FORCE AND EQUATIONS OF MOTION 169 2.7.3 THE
RELATIVISTIC TRANSFORMATION OF THE MINKOWSKI FORCE 172 2.7 A THE LORENTZ
FORCE AND TRANSFORMATION OF ELECTROMAGNETIC FIELD 174 2.7.5 THE
ABERRATION OF THE MINKOWSKI FORCE 176 2.7.6 THE CENTER-OF-MOMENTUM FRAME
178 2.7.7 THE CENTER-OF-MASS FRAME 182 2.8 ENERGY-MOMENTUM TENSOR 184
2.8.1 NONINTERACTING PARTICLES 184 2.8.2 PERFECT FLUID 188
IMAGE 4
VIII I CONTENTS
2.8.3 NONPERFECT FLUID AND SOLIDS 189
2.8.4 ELECTROMAGNETIC FIELD 190 2.8.5 SCALAR FIELD 191
REFERENCES 194
3 GENERAL RELATIVITY 199
3.1 THE PRINCIPLE OF EQUIVALENCE 199 3.1.1 THE INERTIAL AND
GRAVITATIONAL MASSES 199 3.1.2 THE WEAK EQUIVALENCE PRINCIPLE 201 3.1.3
THE EINSTEIN EQUIVALENCE PRINCIPLE 202
3.1.4 THE STRONG EQUIVALENCE PRINCIPLE 203 3.1.5 THE MACH PRINCIPLE 204
3.2 THE PRINCIPLE OF COVARIANCE 207 3.2.1 LORENTZ COVARIANCE IN SPECIAL
RELATIVITY 208
3.2.2 LORENTZ COVARIANCE IN ARBITRARY COORDINATES 209 3.2.2.1 COVARIANT
DERIVATIVE AND THE CHRISTOFFEL SYMBOLS IN SPECIAL RELATIVITY 211 3.2.2.2
RELATIONSHIP BETWEEN THE CHRISTOFFEL SYMBOLS AND THE METRIC
TENSOR 212
3.2.2.3 COVARIANT DERIVATIVE OF THE METRIC TENSOR 213 3.2.3 FROM LORENTZ
TO GENERAL COVARIANCE 214 3.2.4 TWO APPROACHES TO GRAVITATION IN GENERAL
RELATIVITY 215 3.3 A DIFFERENTIABLE MANIFOLD 217 3.3.1 TOPOLOGY OF
MANIFOLD 217
3.3.2 LOCAL CHARTS AND ATLAS 218 3.3.3 FUNCTIONS 218
3.3.4 TANGENT VECTORS 219 3.3.5 TANGENT SPACE 220 3.3.6 COVECTORS AND
COTANGENT SPACE 222 3.3.7 TENSORS 224
3.3.8 THE METRIC TENSOR 224 3.3.8.1 OPERATION OF RISING AND LOWERING
INDICES 225 3.3.8.2 MAGNITUDE OF A VECTOR A N D AN ANGLE BETWEEN VECTORS
226 3.3.8.3 THE RIEMANN NORMAL COORDINATES 226
3.4 AFFINE CONNECTION ON MANIFOLD 229 3.4.1 AXIOMATIC DEFINITION OF THE
AFFINE CONNECTION 230 3.4.2 COMPONENTS OF THE CONNECTION 232 3.4.3
COVARIANT DERIVATIVE OF TENSORS 233
3.4.4 PARALLEL TRANSPORT OF TENSORS 234 3.4.4.1 EQUATION OF THE PARALLEL
TRANSPORT 234 3.4.4.2 GEODESIES 235 3.4.5 TRANSFORMATION LAW FOR
CONNECTION COMPONENTS 237
3.5 THE LEVI-CIVITA CONNECTION 238 3.5.1 COMMUTATOR OF TWO VECTOR FIELDS
238 3.5.2 TORSION TENSOR 240
IMAGE 5
CONTENTS I IX
3.5.3 NONMETRICITY TENSOR 242
3.5.4 LINKING THE CONNECTION WITH THE METRIC STRUCTURE 243 3.6 LIE
DERIVATIVE 245
3.6.1 A VECTOR FLOW 245 3.6.2 THE DIRECTIONAL DERIVATIVE OF A FUNCTION
246 3.6.3 GEOMETRIC INTERPRETATION OF THE COMMUTATOR OF TWO VECTOR
FIELDS 247 3.6.4 DEFINITION OF THE LIE DERIVATIVE 249 3.6.5 LIE
TRANSPORT OF TENSORS 251 3.7 THE RIEMANN TENSOR AND CURVATURE OF
MANIFOLD 253 3.7.1 NONCOMMUTATION OF COVARIANT DERIVATIVES 253 3.7.2 THE
DEPENDENCE OF THE PARALLEL TRANSPORT ON THE PATH 255 3.7.3 THE HOLONOMY
OF A CONNECTION 256 3.7 A THE RIEMANN TENSOR AS A MEASURE OF FLATNESS
258 3.7.5 THE JACOBI EQUATION AND THE GEODESIES DEVIATION 261 3.7.6
PROPERTIES OF THE RIEMANN TENSOR 262 3.7.6.1 ALGEBRAIC SYMMETRIES 262
3.7.6.2 THE WEYL TENSOR AND THE RICCI DECOMPOSITION 264 3.7.6.3 THE
BIANCHI IDENTITIES 265 3.8 MATHEMATICAL AND PHYSICAL FOUNDATIONS OF
GENERAL RELATIVITY 266 3.8.1 GENERAL COVARIANCE ON CURVED MANIFOLDS 267
3.8.2 GENERAL RELATIVITY PRINCIPLE LINKS GRAVITY TO GEOMETRY 269 3.8.3
THE EQUATIONS OF MOTION OF TEST PARTICLES 273 3.8.4 THE CORRESPONDENCE
PRINCIPLE - THE INTERACTION OF MATTER AND
GEOMETRY 277
3.8.4.1 THE NEWTONIAN GRAVITATIONAL POTENTIAL AND THE METRIC TENSOR 277
3.8.4.2 THE NEWTONIAN GRAVITY AND THE EINSTEIN FIELD EQUATIONS 279 3.8.5
THE PRINCIPLE OF THE GAUGE INVARIANCE 282 3.8.6 PRINCIPLES OF
MEASUREMENT OF GRAVITATIONAL FIELD 286 3.8.6.1 CLOCKS AND RULERS 286
3.8.6.2 TIME MEASUREMENTS 289
3.8.6.3 SPACE MEASUREMENTS 290 3.8.6.4 ARE COORDINATES MEASURABLE? 294
3.8.7 EXPERIMENTAL TESTING OF GENERAL RELATIVITY 297
3.9 VARIATIONAL PRINCIPLE IN GENERAL RELATIVITY 300 3.9.1 THE ACTION
FUNCTIONAL 300 3.9.2 VARIATIONAL EQUATIONS 303 3.9.2.1 VARIATIONAL
EQUATIONS FOR MATTER 303 3.9.2.2 VARIATIONAL EQUATIONS FOR GRAVITATIONAL
FIELD 307 3.9.3 THE HUBERT ACTION AND THE EINSTEIN EQUATIONS 307 3.9.3.1
THE HUBERT LAGRANGIAN 307 3.9.3.2 THE EINSTEIN LAGRANGIAN 309 3.9.3.3
THE EINSTEIN TENSOR 310 3.9.3.4 THE GENERALIZATIONS OF THE HILBERT
LAGRANGIAN 313 3.9.4 THE NOETHER THEOREM AND CONSERVED CURRENTS 316
3.9.4.1 THE ANATOMY OF THE INFINITESIMAL VARIATION 316
IMAGE 6
X I CONTENTS
3.9.4.2 EXAMPLES OF THE GAUGE TRANSFORMATIONS 319
3.9.4.3 PROOF OF THE NOETHER THEOREM 320 3.9.5 THE METRICAL
ENERGY-MOMENTUM TENSOR 322 3.9.5.1 HARDCORE OF THE METRICAL
ENERGY-MOMENTUM TENSOR 322 3.9.5.2 GAUGE INVARIANCE OF THE METRICAL
ENERGY MOMENTUM TENSOR 324
3.9.5.3 ELECTROMAGNETIC ENERGY-MOMENTUM TENSOR 325 3.9.5.4
ENERGY-MOMENTUM TENSOR OF A PERFECT FLUID 326 3.9.5.5 ENERGY-MOMENTUM
TENSOR OF A SCALAR FIELD 329 3.9.6 THE CANONICAL ENERGY-MOMENTUM TENSOR
329
3.9.6.1 DEFINITION 329 3.9.6.2 RELATIONSHIP TO THE METRICAL
ENERGY-MOMENTUM TENSOR 331 3.9.6.3 KILLING VECTORS AND THE GLOBAL LAWS
OF CONSERVATION 332 3.9.6.4 THE CANONICAL ENERGY-MOMENTUM TENSOR FOR
ELECTROMAGNETIC
FIELD 333
3.9.6.5 THE CANONICAL ENERGY-MOMENTUM TENSOR FOR PERFECT FLUID 334 3.9.7
PSEUDOTENSOR OF LANDAU AND LIFSHITZ 336 3.10 GRAVITATIONAL WAVES 339
3.10.1 THE POST-MINKOWSKIAN APPROXIMATIONS 340 3.10.2 MULTIPOLAR
EXPANSION OF A RETARDED POTENTIAL 344
3.10.3 MULTIPOLAR EXPANSION OF GRAVITATIONAL FIELD 345 3.10.4
GRAVITATIONAL FIELD IN TRANSVERSE-TRACELESS GAUGE 350 3.10.5
GRAVITATIONAL RADIATION AND DETECTION OF GRAVITATIONAL WAVES 352
REFERENCES 358
4 RELATIVISTIC REFERENCE FRAMES 371 4.1 HISTORICAL BACKGROUND 371 4.2
ISOLATED ASTRONOMICAL SYSTEMS 378 4.2.1 FIELD EQUATIONS IN THE
SCALAR-TENSOR THEORY OF GRAVITY 378
4.2.2 THE ENERGY-MOMENTUM TENSOR 380 4.2.3 BASIC PRINCIPLES OF THE
POST-NEWTONIAN APPROXIMATIONS 382 4.2.4 GAUGE CONDITIONS AND RESIDUAL
GAUGE FREEDOM 387 4.2.5 THE REDUCED FIELD EQUATIONS 389
4.3 GLOBAL ASTRONOMICAL COORDINATES 391 4.3.1 DYNAMIC AND KINEMATIC
PROPERTIES OF THE GLOBAL COORDINATES 391 4.3.2 THE METRIC TENSOR AND
SCALAR FIELD IN THE GLOBAL COORDINATES 395 4.4 GRAVITATIONAL MULTIPOLES
IN THE GLOBAL COORDINATES 396 4.4.1 GENERAL DESCRIPTION OF MULTIPOLE
MOMENTS 396
4.4.2 ACTIVE MULTIPOLE MOMENTS 399 4.4.3 SCALAR MULTIPOLE MOMENTS 401
4.4A CONFORMAI MULTIPOLE MOMENTS 402 4.4.5 POST-NEWTONIAN CONSERVATION
LAWS 404
4.5 LOCAL ASTRONOMICAL COORDINATES 406 4.5.1 DYNAMIC AND KINEMATIC
PROPERTIES OF THE LOCAL COORDINATES 406 4.5.2 THE METRIC TENSOR AND
SCALAR FIELD IN THE LOCAL COORDINATES 409 4.5.2.1 THE SCALAR FIELD:
INTERNAL AND EXTERNAL SOLUTIONS 410
IMAGE 7
CONTENTS I XI
4.5.2.2 THE METRIC TENSOR: INTERNAL SOLUTION 411
4.5.2.3 THE METRIC TENSOR: EXTERNAL SOLUTION 412 4.5.2.4 THE METRIC
TENSOR: THE COUPLING TERMS 419 4.5.3 MULTIPOLAR EXPANSION OF
GRAVITATIONAL FIELD IN THE LOCAL COORDINATES 420
REFERENCES 423
5 POST-NEWTONIAN COORDINATE TRANSFORMATIONS 429 5.1 THE TRANSFORMATION
FROM THE LOCAL TO GLOBAL COORDINATES 429 5.1.1 PRELIMINARIES 429 5.1.2
GENERAL STRUCTURE OF THE COORDINATE TRANSFORMATION 431 5.1.3
TRANSFORMATION OF THE COORDINATE BASIS 434 5.2 MATCHING TRANSFORMATION
OF THE METRIC TENSOR AND SCALAR FIELD 436 5.2.1 HISTORICAL BACKGROUND
436 5.2.2 METHOD OF THE MATCHED ASYMPTOTIC EXPANSIONS IN THE PPN
FORMALISM 439
5.2.3 TRANSFORMATION OF GRAVITATIONAL POTENTIALS FROM THE LOCAL TO
GLOBAL COORDINATES 442 5.2.3.1 TRANSFORMATION OF THE INTERNAL POTENTIALS
442 5.2.3.2 TRANSFORMATION OF THE EXTERNAL POTENTIALS 446 5.2.4 MATCHING
FOR THE SCALAR FIELD 447 5.2.5 MATCHING FOR THE METRIC TENSOR 447
5.2.5.1 MATCHING GOO(T *) AND G A SS(U, W) IN THE NEWTONIAN
APPROXIMATION 447 5.2.5.2 MATCHING GJ(T, X) AND G A SS(U,W) 450 5.2.5.3
MATCHING GO; (T, X) AND G A SS(U, W) 451 5.2.5.4 MATCHING GOO(T, *) AND G
A SS(U, W) IN THE POST-NEWTONIAN
APPROXIMATION 453 5.2.6 FINAL FORM OF THE PPN COORDINATE TRANSFORMATION
457 REFERENCES 458
6 RELATIVISTIC CELESTIAL MECHANICS 463 6.1 POST-NEWTONIAN EQUATIONS OF
ORBITAL MOTION 463 6.1.1 INTRODUCTION 463
6.1.2 MACROSCOPIC POST-NEWTONIAN EQUATIONS OF MOTION 467 6.1.3 MASS AND
THE LINEAR MOMENTUM OF A SELF-GRAVITATING BODY 468 6.1.4 TRANSLATIONAL
EQUATION OF MOTION IN THE LOCAL COORDINATES 473 6.1.5 ORBITAL EQUATION
OF MOTION IN THE GLOBAL COORDINATES 477 6.2 ROTATIONAL EQUATIONS OF
MOTION OF EXTENDED BODIES 479 6.2.1 THE ANGULAR MOMENTUM OF A
SELF-GRAVITATING BODY 479 6.2.2 EQUATIONS OF ROTATIONAL MOTION IN THE
LOCAL COORDINATES 480 6.3 MOTION OF SPHERICALLY-SYMMETRIC AND
RIGIDLY-ROTATING BODIES 483 6.3.1 DEFINITION OF A SPHERICALLY-SYMMETRIC
AND RIGIDLY-ROTATING BODY 483 6.3.2 COORDINATE TRANSFORMATION OF THE
MULTIPOLE MOMENTS 487 6.3.3 GRAVITATIONAL MULTIPOLES IN THE GLOBAL
COORDINATES 490 6.3.4 ORBITAL POST-NEWTONIAN EQUATIONS OF MOTION 492
6.3.5 ROTATIONAL EQUATIONS OF MOTION 500
IMAGE 8
XII1 CONTENTS
6.4 POST-NEWTONIAN TWO-BODY PROBLEM 501
6 A.I INTRODUCTION 501 6.4.2 PERTURBING POST-NEWTONIAN FORCE 503 6.4.3
ORBITAL SOLUTION IN THE TWO-BODY PROBLEM 505 6.4.3.1 OSCULATING ELEMENTS
PARAMETRIZATION 505 6.4.3.2 THE DAMOUR-DERUELLE PARAMETRIZATION 508
6.4.3.3 THE EPSTEIN-HAUGAN PARAMETRIZATION 511 6.4.3.4 THE BRUMBERG
PARAMETRIZATION 512 REFERENCES 513
7 RELATIVISTIC ASTROMETRY 519 7.1 INTRODUCTION 519 7.2 GRAVITATIONAL
LIENARD-WIECHERT POTENTIALS 524
7.3 MATHEMATICAL TECHNIQUE FOR INTEGRATING EQUATIONS OF PROPAGATION OF
PHOTONS 529 7.4 GRAVITATIONAL PERTURBATIONS OF PHOTON'S TRAJECTORY 538
7.5 OBSERVABLE RELATIVISTIC EFFECTS 541
7.5.1 GRAVITATIONAL TIME DELAY 541 7.5.2 GRAVITATIONAL BENDING AND THE
DEFLECTION ANGLE OF LIGHT 547 7.5.3 GRAVITATIONAL SHIFT OF
ELECTROMAGNETIC-WAVE FREQUENCY 552 7.6 APPLICATIONS TO RELATIVISTIC
ASTROPHYSICS AND ASTROMETRY 557
7.6.1 GRAVITATIONAL TIME DELAY IN BINARY PULSARS 557 7.6.1.1 PULSARS -
ROTATING RADIO BEACONS 557 7.6.1.2 THE APPROXIMATION SCHEME 560 7.6.1.3
POST-NEWTONIAN VERSUS POST-MINKOWSKI CALCULATIONS OF TIME DELAY IN
BINARY SYSTEMS 565 7.6.1.4 TIME DELAY IN THE PARAMETERIZED
POST-KEPLERIAN FORMALISM 567 7.6.2 MOVING GRAVITATIONAL LENSES 572
7.6.2.1 GRAVITATIONAL LENS EQUATION 572 7.6.2.2 GRAVITATIONAL SHIFT OF
FREQUENCY BY MOVING BODIES 580
7.7 RELATIVISTIC ASTROMETRY IN THE SOLAR SYSTEM 584 7.7.1 NEAR-ZONE AND
FAR-ZONE ASTROMETRY 584 7.7.2 PULSAR TIMING 590 7.7.3 VERY LONG BASELINE
INTERFEROMETRY 593
7.7A RELATIVISTIC SPACE ASTROMETRY 600 7.8 DOPPLER TRACKING OF
INTERPLANETARY SPACECRAFTS 604 7.8.1 DEFINITION AND CALCULATION OF THE
DOPPLER SHIFT 607 7.8.2 THE NULL CONE PARTIAL DERIVATIVES 609
7.8.3 DOPPLER EFFECT IN SPACECRAFT-PLANETARY CONJUNCTIONS 611 7.8.4 THE
DOPPLER EFFECT REVISITED 613 7.8.5 THE EXPLICIT DOPPLER TRACKING FORMULA
617 7.9 ASTROMETRIC EXPERIMENTS WITH THE SOLAR SYSTEM PLANETS 619 7.9.1
MOTIVATIONS 619
7.9.2 THE UNPERTURBED LIGHT-RAY TRAJECTORY 624 7.9.3 THE GRAVITATIONAL
FIELD 626
IMAGE 9
CONTENTS | XIII
7.9.3.1 THE FIELD EQUATIONS 626
7.9.3.2 THE PLANET'S GRAVITATIONAL MULTIPOLES 628 7.9.4 THE LIGHT-RAY
GRAVITATIONAL PERTURBATIONS 631 7.9.4.1 THE LIGHT-RAY PROPAGATION
EQUATION 631 7.9.4.2 THE NULL CONE INTEGRATION TECHNIQUE 632 7.9.4.3 THE
SPEED OF GRAVITY, CAUSALITY, AND THE PRINCIPLE OF EQUIVALENCE 636 7.9.5
LIGHT-RAY DEFLECTION PATTERNS 640 7.9.5.1 THE DEFLECTION ANGLE 640
7.9.5.2 SNAPSHOT PATTERNS 642 7.9.5.3 DYNAMIC PATTERNS OF THE LIGHT
DEFLECTION 646 7.9.6 TESTING RELATIVITY AND REFERENCE FRAMES 650 7.9.6.1
THE MONOPOLAR DEFLECTION 652 7.9.6.2 THE DIPOLAR DEFLECTION 653 7.9.6.3
THE QUADRUPOLAR DEFLECTION 655
REFERENCES 656
8 RELATIVISTIC GEODESY 671 8.1 INTRODUCTION 671
8.2 BASIC EQUATIONS 676
8.3 GEOCENTRIC REFERENCE FRAME 681 8.4 TOPOCENTRIC REFERENCE FRAME 684
8.5 RELATIONSHIP BETWEEN THE GEOCENTRIC AND TOPOCENTRIC FRAMES 687 8.6
POST-NEWTONIAN GRAVIMETRY 689 8.7 POST-NEWTONIAN GRADIOMETRY 694 8.8
RELATIVISTIC GEOID 703
8.8.1 DEFINITION OF A GEOID IN THE POST-NEWTONIAN GRAVITY 703 8.8.2
POST-NEWTONIAN U-GEOID 704 8.8.3 POST-NEWTONIAN O-GEOID 705 8.8.4
POST-NEWTONIAN LEVEL SURFACE 706 8.8.5 POST-NEWTONIAN CLAIRAUT'S
EQUATION 707
REFERENCES 709
9 RELATIVITY IN IAU RESOLUTIONS 715 9.1 INTRODUCTION 715
9.1.1 OVERVIEW OF THE RESOLUTIONS 716 9.1.2 ABOUT THIS CHAPTER 718 9.1.3
OTHER RESOURCES 719 9.2 RELATIVITY 720
9.2.1 BACKGROUND 720 9.2.2 THE BCRS AND THE GCRS 722 9.2.3 COMPUTING
OBSERVABLES 724
9.2.4 OTHER CONSIDERATIONS 727 9.3 TIME SCALES 728
9.3.1 DIFFERENT FLAVORS OF TIME 729 9.3.2 TIME SCALES BASED ON THE SI
SECOND 730 9.3.3 TIME SCALES BASED ON THE ROTATION OF THE EARTH 733
IMAGE 10
XIV I CONTENTS
9.3.4 COORDINATED UNIVERSAL TIME (UTC) 735
9.3.5 TO LEAP OR NOT TO LEAP 735 9.3.6 FORMULAS 737 9.3.6.1 FORMULAS FOR
TIME SCALES BASED ON THE SI SECOND 737 9.3.6.2 FORMULAS FOR TIME SCALES
BASED ON THE ROTATION OF THE EARTH 740
9.4 THE FUNDAMENTAL CELESTIAL REFERENCE SYSTEM 743 9A.I THE ICRS, ICRF,
AND THE HCRF 744 9.4.2 BACKGROUND: REFERENCE SYSTEMS AND REFERENCE
FRAMES 746 9.4.3 THE EFFECT OF CATALOGUE ERRORS ON REFERENCE FRAMES 748
9.4.4 LATE TWENTIETH CENTURY DEVELOPMENTS 750 9.4.5 ICRS IMPLEMENTATION
752 9.4.5.1 THE DEFINING EXTRAGALACTIC FRAME 752 9.4.5.2 THE FRAME AT
OPTICAL WAVELENGTHS 753
9.4.6 STANDARD ALGORITHMS 753 9.4.7 RELATIONSHIP TO OTHER SYSTEMS 754
9.4.8 DATA IN THE ICRS 755 9.4.9 FORMULAS 757
9.5 EPHEMERIDES OF THE MAJOR SOLAR SYSTEM BODIES 758 9.5.1 THE JPL
EPHEMERIDES 759 9.5.2 DE405 760 9.5.3 RECENT EPHEMERIS DEVELOPMENT 761
9.5.4 SIZES, SHAPES, AND ROTATIONAL DATA 762 9.6 PRECESSION AND NUTATION
763 9.6.1 ASPECTS OF EARTH ROTATION 764 9.6.2 WHICH POLE? 765
9.6.3 THE NEW MODELS 768 9.6.4 FORMULAS 771 9.6.5 FORMULAS FOR
PRECESSION 774 9.6.6 FORMULAS FOR NUTATION 778 9.6.7 ALTERNATIVE
COMBINED TRANSFORMATION 781 9.6.8 OBSERVATIONAL CORRECTIONS TO
PRECESSION-NUTATION 782
9.6.9 SAMPLE NUTATION TERMS 783 9.7 MODELING THE EARTH'S ROTATION 786
9.7.1 A MESSY BUSINESS 786 9.7.2 NONROTATING ORIGINS 788 9.7.3 THE PATH
OF THE CIO ON THE SKY 790
9.7.4 TRANSFORMING VECTORS BETWEEN REFERENCE SYSTEMS 791 9.7.5 FORMULAS
794 9.7.5.1 LOCATION OF CARDINAL POINTS 795 9.7.5.2 CIO LOCATION
RELATIVE TO THE EQUINOX 795 9.7.5.3 CIO LOCATION FROM NUMERICAL
INTEGRATION 797
9.7.5 A CIO LOCATION FROM THE ARC-DIFFERENCE S 798 9.7.5.5 GEODETIC
POSITION VECTORS AND POLAR MOTION 799 9.7.5.6 COMPLETE TERRESTRIAL TO
CELESTIAL TRANSFORMATION 801 9.7.5.7 HOUR ANGLE 802
REFERENCES 805
IMAGE 11
CONTENTS I XV
APPENDIX A FUNDAMENTAL SOLUTION OF THE LAPLACE EQUATION 813
REFERENCES 817
APPENDIX B ASTRONOMICAL CONSTANTS 819 REFERENCES 823
APPENDIXC TEXT OF IAU RESOLUTIONS 825 C.I TEXT OF IAU RESOLUTIONS OF
1997 ADOPTED AT THE XXIIIRD GENERAL ASSEMBLY, KYOTO 825 C.2 TEXT OF IAU
RESOLUTIONS OF 2000 ADOPTED AT THE XXIVTH GENERAL
ASSEMBLY, MANCHESTER 829 C.3 TEXT OF IAU RESOLUTIONS OF 2006 ADOPTED AT
THE XXVITH GENERAL ASSEMBLY, PRAGUE 841 C.4 TEXT OF IAU RESOLUTIONS OF
2009 ADOPTED AT THE XXVI ITH GENERAL
ASSEMBLY, RIO DE JANEIRO 847
INDEX 851 |
| any_adam_object | 1 |
| author | Kopeikin, Sergei 1956- Efroimsky, Michael Kaplan, George |
| author_GND | (DE-588)1014871883 (DE-588)101498260X (DE-588)1014893453 |
| author_facet | Kopeikin, Sergei 1956- Efroimsky, Michael Kaplan, George |
| author_role | aut aut aut |
| author_sort | Kopeikin, Sergei 1956- |
| author_variant | s k sk m e me g k gk |
| building | Verbundindex |
| bvnumber | BV037255120 |
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| ctrlnum | (OCoLC)754700514 (DE-599)DNB1002408172 |
| dewey-full | 521 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 521 - Celestial mechanics |
| dewey-raw | 521 |
| dewey-search | 521 |
| dewey-sort | 3521 |
| dewey-tens | 520 - Astronomy and allied sciences |
| discipline | Physik Geographie |
| format | Book |
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| genre_facet | Lehrbuch |
| id | DE-604.BV037255120 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T11:00:20Z |
| institution | BVB |
| isbn | 9783527408566 9783527634569 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-021168361 |
| oclc_num | 754700514 |
| open_access_boolean | |
| owner | DE-11 DE-703 DE-706 |
| owner_facet | DE-11 DE-703 DE-706 |
| physical | XXXI, 860 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Wiley-VCH |
| record_format | marc |
| spelling | Kopeikin, Sergei 1956- Verfasser (DE-588)1014871883 aut Relativistic celestial mechanics of the solar system Sergei Kopeikin, Michael Efroimsky, and George Kaplan Weinheim Wiley-VCH 2011 XXXI, 860 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Relativistische Korrektur (DE-588)4310201-3 gnd rswk-swf Himmelsmechanik (DE-588)4127484-2 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Himmelsmechanik (DE-588)4127484-2 s Relativistische Korrektur (DE-588)4310201-3 s DE-604 Efroimsky, Michael Verfasser (DE-588)101498260X aut Kaplan, George Verfasser (DE-588)1014893453 aut Erscheint auch als Online-Ausgabe, EPUB 978-3-527-63457-6 Erscheint auch als Online-Ausgabe, MOBI 978-3-527-63459-0 Erscheint auch als Online-Ausgabe, PDF 978-3-527-63458-3 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3474326&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021168361&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kopeikin, Sergei 1956- Efroimsky, Michael Kaplan, George Relativistic celestial mechanics of the solar system Relativistische Korrektur (DE-588)4310201-3 gnd Himmelsmechanik (DE-588)4127484-2 gnd |
| subject_GND | (DE-588)4310201-3 (DE-588)4127484-2 (DE-588)4123623-3 |
| title | Relativistic celestial mechanics of the solar system |
| title_auth | Relativistic celestial mechanics of the solar system |
| title_exact_search | Relativistic celestial mechanics of the solar system |
| title_full | Relativistic celestial mechanics of the solar system Sergei Kopeikin, Michael Efroimsky, and George Kaplan |
| title_fullStr | Relativistic celestial mechanics of the solar system Sergei Kopeikin, Michael Efroimsky, and George Kaplan |
| title_full_unstemmed | Relativistic celestial mechanics of the solar system Sergei Kopeikin, Michael Efroimsky, and George Kaplan |
| title_short | Relativistic celestial mechanics of the solar system |
| title_sort | relativistic celestial mechanics of the solar system |
| topic | Relativistische Korrektur (DE-588)4310201-3 gnd Himmelsmechanik (DE-588)4127484-2 gnd |
| topic_facet | Relativistische Korrektur Himmelsmechanik Lehrbuch |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3474326&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021168361&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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