Preface |
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About the Authors |
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xi | |
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Chapter 1 Two-Body Orbital Mechanics |
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1 | (40) |
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1.1 Historical Background and Basic Laws |
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1 | (3) |
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4 | (5) |
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9 | (3) |
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12 | (4) |
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1.5 The Trajectory Equation |
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16 | (6) |
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1.6 Relating E and h to the Geometry of an Orbit |
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22 | (3) |
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25 | (3) |
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28 | (1) |
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29 | (2) |
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1.10 The Hyperbolic Orbit |
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31 | (3) |
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34 | (7) |
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Chapter 2 Orbit Determination from Observations |
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41 | (82) |
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2.1 Historical Background |
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41 | (2) |
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43 | (3) |
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2.3 Classical Orbital Elements |
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46 | (3) |
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2.4 Determining the Orbital Elements from r and v |
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49 | (8) |
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2.5 Determining r and v from the Orbital Elements |
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57 | (2) |
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2.6 Coordinate Transformations |
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59 | (8) |
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2.7 Orbit Determination from a Singular Radar Observation |
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67 | (7) |
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2.8 SEZ to UK Transformation Using an Ellipsoid Earth Model |
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74 | (7) |
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2.9 The Measurement of Time |
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81 | (10) |
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2.10 Orbit Determination from Three Position Vectors |
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91 | (6) |
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2.11 Orbit Determination from Optical Sightings |
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97 | (5) |
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2.12 Improving a Preliminary Orbit by Differential Correction |
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102 | (7) |
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109 | (4) |
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2.14 Ground Track of a Satellite |
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113 | (10) |
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Chapter 3 Basic Orbital Maneuvers |
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123 | (20) |
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3.1 Historical Background |
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123 | (1) |
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3.2 Low-Altitude Earth Orbits |
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124 | (6) |
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3.3 High-Altitude Earth Orbits |
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130 | (1) |
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3.4 In-Plane Orbit Changes |
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131 | (7) |
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3.5 Out-of-Plane Orbit Changes |
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138 | (5) |
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Chapter 4 Position and Velocity as a Function of Time |
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143 | (48) |
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4.1 Historical Background |
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143 | (4) |
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4.2 Time of Flight as a Function of Eccentric Anomaly |
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147 | (8) |
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4.3 A Universal Formulation for Time of Flight |
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155 | (3) |
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4.4 The Prediction Problem |
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158 | (9) |
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4.5 Implementing the Universal Variable Formulation |
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167 | (8) |
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4.6 Classical Formulations of the Kepler Problem |
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175 | (16) |
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Chapter 5 Orbit Determination from Two Positions and Time |
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191 | (42) |
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5.1 Historical Background |
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191 | (1) |
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5.2 The Gauss Problem--General Methods of Solution |
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192 | (3) |
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5.3 Solutions of the Gauss Problem via Universal Variables |
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195 | (8) |
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5.4 The p-Iteration Method |
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203 | (9) |
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5.5 The Gauss Problem Using the f and g Series |
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212 | (5) |
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5.6 The Original Gauss Method |
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217 | (6) |
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5.7 Practical Applications of the Gauss Problem--Intercept and Rendezvous |
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223 | (5) |
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5.8 Determination of Orbit from Sighting Directions at Station |
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228 | (5) |
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Chapter 6 Ballistic Missile Trajectories |
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233 | (36) |
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6.1 Historical Background |
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233 | (2) |
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6.2 The General Ballistic Missile Problem |
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235 | (14) |
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6.3 Effect of Launching Errors on Range |
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249 | (8) |
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6.4 The Effect of Earth Rotation |
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257 | (12) |
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Chapter 7 Lunar Trajectories |
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269 | (28) |
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7.1 Historical Background |
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269 | (1) |
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7.2 The Earth-Moon System |
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270 | (4) |
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7.3 Simple Earth-Moon Trajectories |
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274 | (5) |
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7.4 The Patched-Conic Approximation |
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279 | (9) |
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7.5 Noncoplanar Lunar Trajectories |
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288 | (9) |
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Chapter 8 Interplanetary Trajectories |
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297 | (28) |
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8.1 Historical Background |
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297 | (1) |
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298 | (2) |
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8.3 The Patched-Conic Approximation |
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300 | (15) |
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8.4 Noncoplanar Interplanetary Trajectories |
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315 | (1) |
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316 | (9) |
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325 | (36) |
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9.1 Historical Background |
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325 | (2) |
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327 | (2) |
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329 | (4) |
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9.4 Variation of Parameters or Elements |
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333 | (13) |
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9.5 Comments on Integration Schemes and Errors |
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346 | (2) |
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9.6 Numerical Integration Methods |
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348 | (4) |
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9.7 Analytic Formulations of Perturbative Accelerations |
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352 | (9) |
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Chapter 10 Special Topics |
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361 | (22) |
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10.1 Historical Background |
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361 | (1) |
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10.2 General Perturbation Models |
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361 | (2) |
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10.3 NORAD Propagators and Two-Line Element Sets |
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363 | (8) |
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10.4 Relative Motion of Satellites |
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371 | (16) |
Appendix A Astrodynamic Constants |
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383 | (4) |
Appendix B Vector Review |
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387 | (8) |
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387 | (2) |
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389 | (4) |
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393 | (2) |
Appendix C Gauss Problem |
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395 | (6) |
Appendix D Proposed Three-Line Element Set Definition |
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401 | (6) |
Index |
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407 | |