Orbital Motion, Fourth Edition

Front Cover
CRC Press, Dec 31, 2004 - Science - 544 pages
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

The Restless Universe
11
121 Keplers laws
11
123 Commensurabilities in mean motion
11
124 Comets the EdgeworthKuiper Belt and meteors
11
125 Conclusions
11
131 Binary systems
11
133 Globular clusters
11
134 Galactic or open clusters
12
93 Planetary Ephemerides
264
95 Rings Shepherds Tadpoles Horseshoes and CoOrbitals
267
952 Small satellites of Jupiter and Saturn
268
953 Spirig and Waldvogels analysis
271
954 Satellitering interactions
279
96 NearCommensurable Satellite Orbits
282
97 LargeScale Numerical Integrations
284
973 Does Plutos perihelion librate or circulate?
285

15 Conclusion
13
Coordinate and TimeKeeping Systems
14
23 The Horizontal System
16
24 The Equatorial System
18
25 The Ecliptic System
19
26 Elements of the Orbit in Space
20
27 Rectangular Coordinate Systems
22
29 Transformation of Systems
23
292 Examples in the transformation of systems
26
210 Galactic Coordinate System
33
211 Time Measurement
34
2112 Mean solar time
37
2113 The Julian date
39
Problems
40
Bibliography
41
The Reduction of Observational Data
42
33 Refraction
45
34 Precession and Nutation
46
35 Aberration
51
36 Proper Motion
53
38 Geocentric Parallax
54
39 Review of Procedures
58
Problems
59
The TwoBody Problem
60
43 Newtons Law of Gravitation
61
44 The Solution to the TwoBody Problem
62
45 The Elliptic Orbit
65
451 Measurement of a planets mass
67
452 Velocity in an elliptic orbit
68
453 The angle between velocity and radius vectors
71
454 The mean eccentric and true anomalies
72
455 The solution of Keplers equation
74
456 The equation of the centre
76
46 The Parabolic Orbit
78
47 The Hyperbolic Orbit
81
471 Velocity in a hyperbolic orbit
82
472 Position in the hyperbolic orbit
83
48 The Rectilinear Orbit
85
49 Barycentric Orbits
87
410 Classification of Orbits with Respect to the Energy Constant
88
411 The Orbit in Space
89
412 The f and g Series
93
413 The Use of Recurrence Relations
95
414 Universal Variables
96
Problems
97
Bibliography
98
The ManyBody Problem
99
52 The Equations of Motion in the ManyBody Problem
100
53 The Ten Known Integrals and Their Meanings
101
54 The Force Function
103
55 The Virial Theorem
106
57 The Mirror Theorem
109
58 Reassessment of the ManyBody Problem
110
510 General Remarks on the Lagrange Solutions
115
511 The Circular Restricted ThreeBody Problem
116
5112 Tisserands criterion
119
5113 Surfaces of zero velocity
120
5114 The stability of the libration points
124
5115 Periodic orbits
128
5116 The search for symmetric periodic orbits
130
5117 Examples of some families of periodic orbits
132
5118 Stability of periodic orbits
134
5119 The surface of section
136
51110 The stability matrix
137
512 The General ThreeBody Problem
138
5121 The case C 0
139
5122 The case for C 0
140
5123 Jacobian coordinates
141
513 Jacobian Coordinates for the ManyBody Problem
142
5131 The equations of motion of the simple 𝙣body HDS
143
5132 The equations of motion of the general 𝙣body HDS
145
5133 An unambiguous nomenclature for a general mis
149
Problems
150
The Caledonian Symmetric NBody Problem
152
63 Sundmans Inequality
155
64 Boundaries of Real and Imaginary Motion in the Caledonian Symmetrical TVBody Problem
160
65 The Caledonian Symmetric Model for 𝙣 1
162
66 The Caledonian Symmetric Model for 𝙣 2
166
661 The Szebehely Ladder and Szebehelys Constant2
171
662 Regions of real motion in the pi P2 pu space
172
663 Climbing the rungs of Szebehelys Ladder
175
664 The case when E₀ 0
180
666 Szebehelys Constant
181
667 Loks and Sergysels study of the general fourbody problem
182
67 The Caledonian Symmetric Problem for 𝙣 3
183
68 The Caledonian Symmetric NBody Problem for Odd N
189
Bibliography
191
General Perturbations
192
72 The Equations of Relative Motion
193
73 The Disturbing Function
195
74 The Sphere of Influence
196
75 The Potential of a Body of Arbitrary Shape
199
76 Potential at a Point Within a Sphere
204
77 The Method of the Variation of Parameters
206
771 Modification of the mean longitude at the epoch
210
772 The solution of Lagranges planetary equations
212
773 Short and longperiod inequalities
215
11 A The resolution of the disturbing force
218
78 Lagranges Equations of Motion
221
79 Hamiltons Canonic Equations
224
710 Derivation of Lagranges Planetary Equations from Hamiltons Canonic Equations
229
Problems
230
Bibliography
231
Special Perturbations
232
82 Factors in Special Perturbation Problems
233
83 Cowells Method
234
84 Enckes Method
235
85 The Use of Perturbational Equations
237
851 Derivation of the perturbation equations case h 0
239
852 The relations between the perturbation variables the rectangular coordinates and velocity components and the usual conicsection elements
242
853 Numerical integration procedure
244
854 Rectilinear or almost rectilinear orbits
247
86 Regularization Methods
249
87 Numerical Integration Methods
251
871 Recurrence relations
253
873 Multistep methods
254
Problems
259
The Stability and Evolution of the Solar System
261
92 Chaos and Resonance
262
974 The outer planets for 10 yearsand longer
286
975 The analytical approach against the numerical approach
288
976 The whole planetary system
289
99 Conclusions
293
Bibliography
294
Lunar Theory
297
103 The Saros
299
104 Measurement of the Moons Distance Mass and Size
301
105 The Moons Rotation
302
106 Selenographic Coordinates
304
108 The Main Lunar Problem
305
109 The Suns Orbit in the Main Lunar Problem
307
1010 The Orbit of the Moon
308
1011 Lunar Theories
309
1012 The Secular Acceleration of the Moon
311
Bibliography
312
Artificial Satellites
313
1121 The Earths shape
315
1122 Clairauts formula
316
1123 The Earths interior
319
1125 The Earths atmosphere
320
1126 Solarterrestrial relationships
322
113 Forces Acting on an Artificial Earth Satellite
324
114 The Orbit of a Satellite About an Oblate Planet
325
1141 The shortperiod perturbations of the first order
328
1142 The secular perturbations of the first order
331
1144 Secular perturbations of the secondorder and longperiod perturbations
332
115 The Use of HamiltonJacobi Theory in the Artificial Satellite Problem
333
116 The Effect of Atmospheric Drag on an Artificial Satellite
335
117 Tesseral and Sectorial Harmonics in the Earths Gravitational Field
340
Problems
341
Rocket Dynamics and Transfer Orbits
343
1221 Motion of a rocket in a gravitational field
344
1222 Motion of a rocket in an atmosphere
345
1223 Step rockets
346
1224 Alternative forms of rocket
348
1231 Transfer between circular coplanar orbits
349
1232 Parabolic and hyperbolic transfer orbits
352
1233 Changes in the orbital elements due to a small impulse
353
1234 Changes in the orbital elements due to a large impulse
355
1235 Variation of fuel consumption with transfer time
356
1236 Sensitivity of transfer orbits to small errors in position and velocity at cutoff
358
1237 Transfer between particles orbiting in a central force field
362
124 Transfer Orbits in Two or More Force Fields
366
1242 Entry into orbit about the second body
368
1243 The hyperbolic capture
370
1244 Accuracy of previous analysis and the effect of error
371
1245 The flypast as a velocity amplifier
374
Problems
376
Bibliography
377
Interplanetary and Lunar Trajectories
378
133 Feasibility and Precision Study Methods
379
134 The Use of Jacobis Integral
380
136 The Use of TwoBody Solutions
381
137 Artificial Lunar Satellites
384
1371 Relative sizes of lunar satellite perturbations due to different causes
385
1372 Jacobis integral for a close lunar satellite
388
138 Interplanetary Trajectories
389
139 The Solar System as a Central Force Field
391
1310 MinimumEnergy Interplanetary Transfer Orbits
392
1311 The Use of Parking Orbits in Interplanetary Missions
397
1312 The Effect of Errors in Interplanetary Orbits
403
Problems
404
Bibliography
405
Orbit Determination and Interplanetary Navigation
406
142 The Theory of Orbit Determination
407
143 Laplaces Method
409
144 Gausss Method
411
145 Olberss Method for Parabolic Orbits
413
146 Orbit Determination with Additional Observational Data
415
147 The Improvement of Orbits
419
148 Interplanetary Navigation
422
1482 Navigation by onboard optical equipment
424
1483 Observational methods and probable accuracies
426
Bibliography
427
Binary and Other FewBody Systems
428
152 Visual Binaries
430
153 The MassLuminosity Relation
433
154 Dynamical Parallaxes
434
155 Eclipsing Binaries
435
156 Spectroscopic Binaries
440
157 Combination of Deduced Data
443
159 The Period of a Binary
445
1511 Forces Acting on a Binary System
446
1513 The Inadequacy of Newtons Law of Gravitation
449
1514 The Figures of Stars in Binary Systems
450
1515 The Roche Limits
451
1516 Circumstellar Matter
452
1517 The Origin of Binary Systems
454
Problems
455
ManyBody Stellar Systems
456
163 The Binary Encounter
457
164 The Cumulative Effect of Small Encounters
460
165 Some Fundamental Concepts
462
166 The Fundamental Theorems of Stellar Dynamics
463
1661 Jeanss theorem
465
167 Some Special Cases for a Stellar System in a Steady State
466
168 Galactic Rotation
467
1681 Oorts constants
468
1682 The period of rotation and angular velocity of the galaxy
470
1683 The mass of the Galaxy
471
1684 The mode of rotation of the Galaxy
473
1685 The gravitational potential of the Galaxy
477
1686 Galactic stellar orbits
478
1687 The highvelocity stars
482
169 Spherical Stellar Systems
483
1691 Application of the virial theorem to a spherical system
484
1692 Stellar orbits in a spherical system
485
1693 The distribution of orbits within a spherical system
487
Problems
490
Bibliography
491
Answers to Problems
492
Astronomical and Related Constants
500
The Earths Gravitational Field
504
Approximate Elements of the Ten Largest Asteroids
507
Ring Systems
509
Satellite Elements and Dimensions
510
Index
512
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