Analytical and numerical methods of celestial mechanics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
American Elsevier
1967
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| Schriftenreihe: | Modern analytic and computational methods in science and mathematics
9 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 319 - 325 |
| Beschreibung: | XVIII, 331 S. graph. Darst. |
Internformat
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| 100 | 1 | |a Čebotarev, Gleb A. |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Analytičeskie i čislennye metody nebesnoj mechaniki |
| 245 | 1 | 0 | |a Analytical and numerical methods of celestial mechanics |c by G. A. Chebotarev. Transl. Ed.: Ludwig Oster |
| 264 | 1 | |a New York |b American Elsevier |c 1967 | |
| 300 | |a XVIII, 331 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Modern analytic and computational methods in science and mathematics |v 9 | |
| 500 | |a Literaturverz. S. 319 - 325 | ||
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Datensatz im Suchindex
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|---|---|
| adam_text |
CONTENTS
A NOTE FROM THE AUTHOR v
A NOTE FROM THE EDITOR vii
INTRODUCTION: Celestial Mechanics and Its Problems xv
1 ASTRONOMICAL COORDINATES AND TIME 1
1. Coordinates and Time 1
1. The different coordinate systems 1
2. Coordinates and time 2
3. Ephemeris time 3
4. Tropical year 4
2. Topocentric and Geocentric Coordinate Systems 5
1. Equatorial topocentric coordinate system 5
2. Transition to the geocentric equatorial system 5
3. Parallax reduction of observations 8
4. Computation of rectangular geocentric equatorial
coordinates from orbital elements 9
5. Rotating coordinate systems 9
6. Geodesic coordinates 10
7. Transition from the equatorial to the ecliptical
coordinate system 11
3. Heliocentric Coordinate Systems 12
1. Ecliptical heliocentric coordinate system 12
2. Equatorial heliocentric coordinate system 14
3. Transition from the equatorial heliocentric to the
equatorial geocentric coordinate system 15
4. Transition from the equatorial heliocentric to the
equatorial barycentric system 16
5. Ecliptical and equatorial orbital elements 17
IX
X CONTENTS
6. Transition from the ecliptical heliocentric to the
ecliptical geocentric system 18
4. The Influence of Precession on Coordinates and
Orbital Elements 19
1. Transformation of rectangular coordinates at one
epoch into coordinates at another epoch 19
2. Transformation of elements from one to another epoch 20
3. Transformation of equatorial spherical coordinates
from one epoch to another 21
5. Lunocentric Coordinates 22
2 THEORY OF MAJOR PLANETS 27
1. Laplace Newcomb Method 27
1. The basic concern of celestial mechanics 27
2. Equations of motion in cylindrical coordinates 28
3. Gaussian constant 31
4. The equations of motion in polar coordinates 32
5. Perturbations of the logarithm of the planetary radius
vector 33
6. Perturbations of the planetary longitude 36
7. Perturbations of the nodes and of the inclination of
the planetary orbit 37
8. Determination of the constants of integration 38
9. Computation of heliocentric longitude and latitude
of a planet 39
2. Series Expansion of the Disturbing Function 40
1. Disturbing function 40
2. Laplace coefficients 43
3. Expansion in powers of the inclination 44
4. Expansion in powers of the eccentricity 47
5. Calculation of Newcomb's operators 53
6. The second term of the disturbing function 54
3. Theory of Pluto's Motion 55
1. Introduction 55
2. Perturbations of Pluto owing to Jupiter 56
3. Improved values for Pluto's orbit 59
4. Theory of Major Planets 65
1. Fundamental results 65
2. Relativistic corrections in the theory of major planets 68
CONTENTS XI
3 THE THEORY OF MINOR PLANETS 72
1. The Ring of Minor Planets and Its Structure 72
1. The discovery of the ring of minor planets 72
2. Structure of the ring of minor planets 74
3. Orbits of minor planets 76
4. Groups of minor planets of particular interest 77
5. Minor planet service 80
6. Artificial asteroids 81
7. Minor planets and celestial mechanics 81
2. Hill's Method 82
1. Introduction 82
2. Basic equations 83
3. Expressions for the disturbing force 86
4. The relation between the true anomalies of the minor
planet and of Jupiter in unperturbed motion 89
5. Integration of the differential equations for Srand Sz 90
6. Computation of the perturbation of the third coordinate z 91
7. Computation of the perturbation of the radius vector 91
8. Computation of the perturbation in longitude 92
9. Relation between the arbitrary constants of integration 92
10. Determination of the constants 93
11. Fourier expansion of the derivatives of the disturbing
function 95
12. Computation of the perturbations 96
13. The first order perturbations of Ceres owing to Jupiter 97
14. Comparison of theory and observation 102
3. The Application of Periodic Orbits to the Study of
Minor Planets 105
1. Poincare"' s periodic orbits 105
2. Poincard's periodic orbits: continued 108
3. Numerical methods to treat periodic orbits 114
4. Variational equations 115
5. Integration of the variational equations 120
6. The derivatives of the disturbing function 123
7. Commensurability 1:3 127
8. Comparison of theory and observation 130
4 SATELLITE THEORY 135
1. Satellites of Major Planets 135
1. Satellites of Mars 135
2. Satellites of Jupiter 136
XII CONTENTS
3. Satellites of Saturn 138
4. Saturn's ring 140
5. Satellites of Uranus 141
6. Satellites of Neptune 142
7. Sizes and masses of the satellites of the major planets 142
2. Perturbations of the Satellite Motion Owing to
Planetary Flattening 143
1. The two body problem 143
2. The method of variation of arbitrary constants 146
3. Expansion of the disturbing function 150
4. First order perturbations 152
5. Firsi order secular perturbations 157
6. Example for the calculation of first order perturbations 159
7. Examples for secular perturbations 161
3. Satellite Motion in Orbits with Small Eccentricity 162
1. Transformation of Lagrange's equations 162
2. Transformation of the disturbing function 164
3. Firsl order perturbations 165
4. Computation of the coordinates of the satellite 167
4. True Anomaly as Independent Variable in Lagrange's
Equations 167
1. The anomaly as independent variable in Lagrange's
equations 167
2. The longitude in the orbit as independent variable in
Lagrange's equations 172
3. Disturbing function 173
4. Periodic perturbations 174
5. Secular perturbations 175
5. The Gravitational Field of the Earth 176
1. The general expression for the earth's gravitational
potential 176
2. The rotationally symmetric Earth potential 177
5 LUNAR THEORY 180
1. Hill's Method: First Approximation 180
1. Earth and Moon as twin planets 180
2. The differential equations of motion 181
3. Variational curve 187
2. Hill's Method: Second Approximation 192
1. Orbits that are infinitely close to the variational curve 192
CONTENTS XIII
2. Transformation of Eq. (5.56) 196
3. Hill's equation, 205
4. Integration of the equations for 8p and 5s 209
5. Introduction of the third coordinate 216
3. Comparison with Observation 219
1. Brown's tables 219
2. Empirical terms in the theory of motion of the Moon 222
4. Stability of Lunar Motion According to Hill 223
1. Jacobi's constant 223
2. The surface of zero velocity 225
3. Particular points on the surface of zero velocity 226
4. Stability according to Hill 229
6 THE THEORY OF COMETARY MOTION 232
1. The Comets in the Solar System 232
1. Three types of cometary orbits 232
2. General characteristics of cometary orbits 233
3. Short period comets 233
4. Comet Encke 236
5. Comet Oterma 3 239
6. Long period comets 241
7. Transition to the barycentric coordinate system 242
8. Initial and future orbits of long period comets 241
9. Numerical" methods for the computation of perturbations 245
2. Cowell's Method 246
1. The equations of motion 246
2. Differences and sums 247
3. Cowell's first method 249
4. Cowell's second method 253
5. Cowell's second method: continued 256
6. Cowell's method: numerical example 258
3. The Gravitational Spheres of the Major Planets,
of the Moon, and of the Sun 266
1. The equations of motion 266
2. The activity sphere of a planet 268
3. The sphere of attraction of the planets 270
4. Hill's gravitational sphere 271
5. The gravitational spheres of the Moon 272
6. The gravitational spheres of the Sun 274
XIV CONTENTS
APPENDIXES 275
1. Elements of the Elliptical Orbit 276
2. Mean Elements of the Inner Planets 280
3. Mean Elements of Outer Planets 282
4. Osculating Elements of the Outer Planets 283
5. Mean Orbital Elements of the Moon 286
6. Fundamental Astronomical Constants (de Sitter, 1938) 288
7. Fundamental Astronomical Constants (Clemence, 1948) 289
8. Astronomical Constants (IAU, 1964) 290
9. Table of Minor Planets Used to Determine the Constants
of Faint Star Catalogues 302
10. Table of Minor Planets with Large Daily Motion 303
11. Orbital Elements of the Trojans 304
12. Orbital Elements of Some Short Period Comets 305
13. Orbital Elements of Some Periodic Comets with Large
Aphelion Distances (Q) 307
14. Trigonometric Functions 308
15. Formulas of Spherical Trigonometry 312
16. Expansion of the Coordinates of Elliptic Motion 315
17. Conversion Tables for Anglo American and International
Units 318
REFERENCES 319
Translated List of Sources Cited by Author 319
Editor's List of Relevant Works in English 325
INDEX 327 |
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| indexdate | 2024-09-24T18:01:55Z |
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| language | English |
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| physical | XVIII, 331 S. graph. Darst. |
| publishDate | 1967 |
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| publisher | American Elsevier |
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| series | Modern analytic and computational methods in science and mathematics |
| series2 | Modern analytic and computational methods in science and mathematics |
| spelling | Čebotarev, Gleb A. Verfasser aut Analytičeskie i čislennye metody nebesnoj mechaniki Analytical and numerical methods of celestial mechanics by G. A. Chebotarev. Transl. Ed.: Ludwig Oster New York American Elsevier 1967 XVIII, 331 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Modern analytic and computational methods in science and mathematics 9 Literaturverz. S. 319 - 325 Himmelsmechanik (DE-588)4127484-2 gnd rswk-swf Himmelsmechanik (DE-588)4127484-2 s DE-604 Oster, Ludwig Sonstige oth Modern analytic and computational methods in science and mathematics 9 (DE-604)BV001888148 9 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001260194&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Čebotarev, Gleb A. Analytical and numerical methods of celestial mechanics Modern analytic and computational methods in science and mathematics Himmelsmechanik (DE-588)4127484-2 gnd |
| subject_GND | (DE-588)4127484-2 |
| title | Analytical and numerical methods of celestial mechanics |
| title_alt | Analytičeskie i čislennye metody nebesnoj mechaniki |
| title_auth | Analytical and numerical methods of celestial mechanics |
| title_exact_search | Analytical and numerical methods of celestial mechanics |
| title_full | Analytical and numerical methods of celestial mechanics by G. A. Chebotarev. Transl. Ed.: Ludwig Oster |
| title_fullStr | Analytical and numerical methods of celestial mechanics by G. A. Chebotarev. Transl. Ed.: Ludwig Oster |
| title_full_unstemmed | Analytical and numerical methods of celestial mechanics by G. A. Chebotarev. Transl. Ed.: Ludwig Oster |
| title_short | Analytical and numerical methods of celestial mechanics |
| title_sort | analytical and numerical methods of celestial mechanics |
| topic | Himmelsmechanik (DE-588)4127484-2 gnd |
| topic_facet | Himmelsmechanik |
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