Orbital Mechanics

Front Matter......Page 1
Foreword......Page 3
About the Authors......Page 6
Preface......Page 5
Table of Contents......Page 0
Table of Contents......Page 7
1.1 A Historical Perspective......Page 12
1.2 Velocity and Acceleration......Page 16
Problems......Page 20
Selected Solutions......Page 21
2.1 Coordinate Systems......Page 22
2.2 Time Systems......Page 28
References......Page 31
3.2 General and Restricted Two-Body Problem......Page 32
3.3 Conservation of Mechanical Energy......Page 34
3.4 Conservation of Angular Momentum......Page 35
3.5 Orbital Parameters of a Satellite......Page 36
3.6 Orbital Elements......Page 39
Problems......Page 42
Selected Solutions......Page 44
4.1 General Relationships......Page 45
4.2 Solving Kepler\'s Equation......Page 50
4.3 A Universal Approach......Page 65
4.4 Expressions with f and g......Page 69
4.5 Summary of the Universal Approach......Page 70
4.6 The Classical Element Set......Page 71
4.8 Modified Classical to Cartesian Transformation......Page 72
4.9 Rectangular to Modified Classical Elements Transformation......Page 76
4.10 The Spherical (ADBARV) Coordinate System......Page 77
4.11 Rectangular to Spherical Transformation......Page 78
4.12 Spherical to Rectangular Transformation......Page 79
4.13 The Earth-Relative Spherical (LDBARV) Coordinate System......Page 80
4.14 Geodetic and Geocentric Altitudes......Page 81
4.15 Converting from Perigee/Apogee Radii to Perigee/Apogee Altitudes......Page 86
4.16 Converting from Perigee/Apogee Altitudes to Perigee/Apogee Radii......Page 87
References......Page 92
Problems......Page 93
Selected Solutions......Page 95
5.1 Orbital Energy......Page 96
5.2 Single-Impulse Maneuvers......Page 98
5.3 Single- and Two-Impulse Transfer Comparison for Coplanar Transfers Between Elliptic Orbits That Differ Only in Their Apsidal Orientation......Page 101
5.4 Hohmann Transfer......Page 103
5.5 The Bi-elliptic Transfer......Page 105
5.6 Restricted Three-Impulse Plane Change Maneuver for Circular Orbits......Page 108
5.7 General Three-Impulse Plane Change Maneuver for Circular Orbit......Page 112
5.8 Hohmann Transfer with Split-Plane Change......Page 113
5.10 Transfer Between Coplanar Elliptic Orbits......Page 116
Problems......Page 118
Selected Solutions......Page 124
6.2 Fixed-Impulse Transfers......Page 126
6.3 Finite-Duration Bums: Gravity Losses......Page 135
6.4 Very Low Thrust Transfers......Page 139
Problems......Page 141
Selected Solutions......Page 143
7.1 Space Rendezvous......Page 144
7.2 Terminal Rendezvous......Page 164
7.3 Applications of Rendezvous Equations......Page 171
7.4 An Exact Analytical Solution for Two-Dimensional Relative Motion......Page 181
7.5 Optimal Multiple-Impulse Rendezvous......Page 186
References......Page 190
Problems......Page 191
Selected Solutions......Page 192
8.1 A General Overview of Orbit Perturbations......Page 194
8.2 Earth Gravity Harmonics......Page 195
8.3 Lunisolar Gravitational Attractions......Page 196
8.4 Radiation Pressure Effects......Page 197
8.5 Atmospheric Drag......Page 198
8.6 Tidal Friction Effects and Mutual Gravitational Attraction......Page 199
References......Page 201
9.1 Equations of Motion......Page 202
9.2 Methods of Solution......Page 204
9.3 Potential Theory......Page 211
9.4 More Definitions of Gravity Harmonics......Page 213
9.5 Perturbations Due to Oblateness (J_2)......Page 216
9.6 Integration of the Equations of Variation......Page 218
References......Page 222
10.1 Earth\'s Oblateness (J_2) Effects......Page 223
10.2 Critical Inclination......Page 225
10.3 Sun-Synchronous Orbits......Page 226
10.4 J_3 Effects and Frozen Orbits......Page 228
10.5 Earth\'s Triaxiality Effects and East-West Stationkeeping......Page 229
10.6 Third-Body Perturbations and North/South Stationkeeping......Page 230
10.7 Solar-Radiation-Pressure Effects......Page 231
10.8 Atmospheric Drag Effects......Page 235
10.9 Tidal Friction Effects......Page 238
10.10 Long-Term Inclination Variations......Page 241
References......Page 245
Problems......Page 246
Selected Solutions......Page 248
11.1 Launch Window Considerations......Page 249
11.2 Time of Event Occurrence......Page 261
11.3 Ground-Trace Considerations......Page 262
11.4 Highly Eccentric, Critically Inclined Q = 2 Orbits (Molniya)......Page 264
11.5 Frozen Orbits......Page 267
References......Page 271
12.1 Introduction......Page 273
12.2 Historical Background......Page 274
12.3 Important Concepts......Page 282
12.4 Lunar Trajectories......Page 287
12.5 Analytical Approximations......Page 288
12.7 Interplanetary Trajectories......Page 295
12.8 Galileo Mission......Page 302
12.9 Cassini-Huygens Mission to Saturn and Titan......Page 304
12.10 Mars Odyssey Mission......Page 306
Problems......Page 307
Selected Solutions......Page 308
13.1 Introduction......Page 309
13.2 Space Debris Environment: Low Earth Orbit......Page 310
13.3 Debris Measurements......Page 311
13.4 Space Debris Environment: Geosynchronous Equatorial Orbit......Page 315
13.5 Spatial Density......Page 318
13.6 Collision Hazard Assessment Methods......Page 323
13.7 Collision Hazards Associated with Orbit Operations......Page 328
13.8 Debris Cloud Modeling......Page 330
13.9 Lifetime of Nontrackable Debris......Page 335
13.10 Methods of Debris Control......Page 336
13.11 Shielding......Page 337
13.12 Collision Avoidance......Page 338
References......Page 340
14.2 The Edelbaum Low-Thrust Orbit-Transfer Problem......Page 343
14.3 The Full Six-State Formulation Using Nonsingular Equinoctial Orbit Elements......Page 362
14.4 Orbit Transfer with Continuous Constant Acceleration......Page 380
14.5 Orbit Transfer with Variable Specific Impulse......Page 397
Appendix: The Partials of the M Matrix......Page 407
References......Page 417
15.1 Coverage from a Single Satellite......Page 419
15.2 Design of Optimal Satellite Constellations for Continuous Zonal and Global Coverage......Page 437
15.3 Considerations in Selecting Satellite Constellations......Page 447
15.4 Nontypical Coverage Patterns......Page 450
References......Page 454
Problems......Page 456
Selected Solutions......Page 458
I......Page 461
S......Page 462
Z......Page 463