Orbital Motion, Fourth Edition

Front Cover
CRC Press, Dec 31, 2004 - Science - 544 pages
3 Reviews
Long established as one of the premier references in the fields of astronomy, planetary science, and physics, the fourth edition of Orbital Motion continues to offer comprehensive coverage of the analytical methods of classical celestial mechanics while introducing the recent numerical experiments on the orbital evolution of gravitating masses and the astrodynamics of artificial satellites and interplanetary probes.

Following detailed reviews of earlier editions by distinguished lecturers in the USA and Europe, the author has carefully revised and updated this edition. Each chapter provides a thorough introduction to prepare you for more complex concepts, reflecting a consistent perspective and cohesive organization that is used throughout the book. A noted expert in the field, the author not only discusses fundamental concepts, but also offers analyses of more complex topics, such as modern galactic studies and dynamical parallaxes.

New to the Fourth Edition:

•††††††††† Numerous updates and reorganization of all chapters to encompass new methods

•††††††††† New results from recent work in areas such as satellite dynamics

•††††††††† New chapter on the Caledonian symmetrical n-body problem

Extending its coverage to meet a growing need for this subject in satellite and aerospace engineering, Orbital Motion, Fourth Edition remains a top reference for postgraduate and advanced undergraduate students, professionals such as engineers, and serious amateur astronomers.

 

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Contents

93 Planetary Ephemerides
266
95 Rings Shepherds Tadpoles Horseshoes and CoOrbitals
269
952 Small satellites of Jupiter and Saturn
270
953 Spirig and Waldvogels analysis
273
954 Satellitering interactions
281
96 NearCommensurable Satellite Orbits
284
97 LargeScale Numerical Integrations
286
973 Does Plutos perihelion librate or circulate?
287

15 Conclusion
15
Coordinate and TimeKeeping Systems
16
23 The Horizontal System
18
24 The Equatorial System
20
25 The Ecliptic System
21
26 Elements of the Orbit in Space
22
27 Rectangular Coordinate Systems
24
29 Transformation of Systems
25
292 Examples in the transformation of systems
28
210 Galactic Coordinate System
35
211 Time Measurement
36
2112 Mean solar time
39
2113 The Julian date
41
Problems
42
Bibliography
43
The Reduction of Observational Data
44
33 Refraction
47
34 Precession and Nutation
48
35 Aberration
53
36 Proper Motion
55
38 Geocentric Parallax
56
39 Review of Procedures
60
Problems
61
The TwoBody Problem
62
43 Newtons Law of Gravitation
63
44 The Solution to the TwoBody Problem
64
45 The Elliptic Orbit
67
451 Measurement of a planets mass
69
452 Velocity in an elliptic orbit
70
453 The angle between velocity and radius vectors
73
454 The mean eccentric and true anomalies
74
455 The solution of Keplers equation
76
456 The equation of the centre
78
46 The Parabolic Orbit
80
47 The Hyperbolic Orbit
83
471 Velocity in a hyperbolic orbit
84
472 Position in the hyperbolic orbit
85
48 The Rectilinear Orbit
87
49 Barycentric Orbits
89
410 Classification of Orbits with Respect to the Energy Constant
90
411 The Orbit in Space
91
412 The f and g Series
95
413 The Use of Recurrence Relations
97
414 Universal Variables
98
Problems
99
Bibliography
100
The ManyBody Problem
101
52 The Equations of Motion in the ManyBody Problem
102
53 The Ten Known Integrals and Their Meanings
103
54 The Force Function
105
55 The Virial Theorem
108
57 The Mirror Theorem
111
58 Reassessment of the ManyBody Problem
112
510 General Remarks on the Lagrange Solutions
117
511 The Circular Restricted ThreeBody Problem
118
5112 Tisserands criterion
121
5113 Surfaces of zero velocity
122
5114 The stability of the libration points
126
5115 Periodic orbits
130
5116 The search for symmetric periodic orbits
132
5117 Examples of some families of periodic orbits
134
5118 Stability of periodic orbits
136
5119 The surface of section
138
51110 The stability matrix
139
512 The General ThreeBody Problem
140
5121 The case C 0
141
5122 The case for C 0
142
5123 Jacobian coordinates
143
513 Jacobian Coordinates for the ManyBody Problem
144
5131 The equations of motion of the simple 𝙣body HDS
145
5132 The equations of motion of the general 𝙣body HDS
147
5133 An unambiguous nomenclature for a general mis
151
Problems
152
The Caledonian Symmetric NBody Problem
154
63 Sundmans Inequality
157
64 Boundaries of Real and Imaginary Motion in the Caledonian Symmetrical TVBody Problem
162
65 The Caledonian Symmetric Model for 𝙣 1
164
66 The Caledonian Symmetric Model for 𝙣 2
168
661 The Szebehely Ladder and Szebehelys Constant2
173
662 Regions of real motion in the pi P2 pu space
174
663 Climbing the rungs of Szebehelys Ladder
177
664 The case when E₀ 0
182
666 Szebehelys Constant
183
667 Loks and Sergysels study of the general fourbody problem
184
67 The Caledonian Symmetric Problem for 𝙣 3
185
68 The Caledonian Symmetric NBody Problem for Odd N
191
Bibliography
193
General Perturbations
194
72 The Equations of Relative Motion
195
73 The Disturbing Function
197
74 The Sphere of Influence
198
75 The Potential of a Body of Arbitrary Shape
201
76 Potential at a Point Within a Sphere
206
77 The Method of the Variation of Parameters
208
771 Modification of the mean longitude at the epoch
212
772 The solution of Lagranges planetary equations
214
773 Short and longperiod inequalities
217
11 A The resolution of the disturbing force
220
78 Lagranges Equations of Motion
223
79 Hamiltons Canonic Equations
226
710 Derivation of Lagranges Planetary Equations from Hamiltons Canonic Equations
231
Problems
232
Bibliography
233
Special Perturbations
234
82 Factors in Special Perturbation Problems
235
83 Cowells Method
236
84 Enckes Method
237
85 The Use of Perturbational Equations
239
851 Derivation of the perturbation equations case h 0
241
852 The relations between the perturbation variables the rectangular coordinates and velocity components and the usual conicsection elements
244
853 Numerical integration procedure
246
854 Rectilinear or almost rectilinear orbits
249
86 Regularization Methods
251
87 Numerical Integration Methods
253
871 Recurrence relations
255
873 Multistep methods
256
Problems
261
The Stability and Evolution of the Solar System
263
92 Chaos and Resonance
264
974 The outer planets for 10 yearsand longer
288
975 The analytical approach against the numerical approach
290
976 The whole planetary system
291
99 Conclusions
295
Bibliography
296
Lunar Theory
299
103 The Saros
301
104 Measurement of the Moons Distance Mass and Size
303
105 The Moons Rotation
304
106 Selenographic Coordinates
306
108 The Main Lunar Problem
307
109 The Suns Orbit in the Main Lunar Problem
309
1010 The Orbit of the Moon
310
1011 Lunar Theories
311
1012 The Secular Acceleration of the Moon
313
Bibliography
314
Artificial Satellites
315
1121 The Earths shape
317
1122 Clairauts formula
318
1123 The Earths interior
321
1125 The Earths atmosphere
322
1126 Solarterrestrial relationships
324
113 Forces Acting on an Artificial Earth Satellite
326
114 The Orbit of a Satellite About an Oblate Planet
327
1141 The shortperiod perturbations of the first order
330
1142 The secular perturbations of the first order
333
1144 Secular perturbations of the secondorder and longperiod perturbations
334
115 The Use of HamiltonJacobi Theory in the Artificial Satellite Problem
335
116 The Effect of Atmospheric Drag on an Artificial Satellite
337
117 Tesseral and Sectorial Harmonics in the Earths Gravitational Field
342
Problems
343
Rocket Dynamics and Transfer Orbits
345
1221 Motion of a rocket in a gravitational field
346
1222 Motion of a rocket in an atmosphere
347
1223 Step rockets
348
1224 Alternative forms of rocket
350
1231 Transfer between circular coplanar orbits
351
1232 Parabolic and hyperbolic transfer orbits
354
1233 Changes in the orbital elements due to a small impulse
355
1234 Changes in the orbital elements due to a large impulse
357
1235 Variation of fuel consumption with transfer time
358
1236 Sensitivity of transfer orbits to small errors in position and velocity at cutoff
360
1237 Transfer between particles orbiting in a central force field
364
124 Transfer Orbits in Two or More Force Fields
368
1242 Entry into orbit about the second body
370
1243 The hyperbolic capture
372
1244 Accuracy of previous analysis and the effect of error
373
1245 The flypast as a velocity amplifier
376
Problems
378
Bibliography
379
Interplanetary and Lunar Trajectories
380
133 Feasibility and Precision Study Methods
381
134 The Use of Jacobis Integral
382
136 The Use of TwoBody Solutions
383
137 Artificial Lunar Satellites
386
1371 Relative sizes of lunar satellite perturbations due to different causes
387
1372 Jacobis integral for a close lunar satellite
390
138 Interplanetary Trajectories
391
139 The Solar System as a Central Force Field
393
1310 MinimumEnergy Interplanetary Transfer Orbits
394
1311 The Use of Parking Orbits in Interplanetary Missions
399
1312 The Effect of Errors in Interplanetary Orbits
405
Problems
406
Bibliography
407
Orbit Determination and Interplanetary Navigation
408
142 The Theory of Orbit Determination
409
143 Laplaces Method
411
144 Gausss Method
413
145 Olberss Method for Parabolic Orbits
415
146 Orbit Determination with Additional Observational Data
417
147 The Improvement of Orbits
421
148 Interplanetary Navigation
424
1482 Navigation by onboard optical equipment
426
1483 Observational methods and probable accuracies
428
Bibliography
429
Binary and Other FewBody Systems
430
152 Visual Binaries
432
153 The MassLuminosity Relation
435
154 Dynamical Parallaxes
436
155 Eclipsing Binaries
437
156 Spectroscopic Binaries
442
157 Combination of Deduced Data
445
159 The Period of a Binary
447
1511 Forces Acting on a Binary System
448
1513 The Inadequacy of Newtons Law of Gravitation
451
1514 The Figures of Stars in Binary Systems
452
1515 The Roche Limits
453
1516 Circumstellar Matter
454
1517 The Origin of Binary Systems
456
Problems
457
ManyBody Stellar Systems
458
163 The Binary Encounter
459
164 The Cumulative Effect of Small Encounters
462
165 Some Fundamental Concepts
464
166 The Fundamental Theorems of Stellar Dynamics
465
1661 Jeanss theorem
467
167 Some Special Cases for a Stellar System in a Steady State
468
168 Galactic Rotation
469
1681 Oorts constants
470
1682 The period of rotation and angular velocity of the galaxy
472
1683 The mass of the Galaxy
473
1684 The mode of rotation of the Galaxy
475
1685 The gravitational potential of the Galaxy
479
1686 Galactic stellar orbits
480
1687 The highvelocity stars
484
169 Spherical Stellar Systems
485
1691 Application of the virial theorem to a spherical system
486
1692 Stellar orbits in a spherical system
487
1693 The distribution of orbits within a spherical system
489
Problems
492
Bibliography
493
Answers to Problems
494
Astronomical and Related Constants
502
The Earths Gravitational Field
506
Approximate Elements of the Ten Largest Asteroids
509
Ring Systems
511
Satellite Elements and Dimensions
512
Index
514
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Satellite Geodesy
GŁnter Seeber
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