Other versions by this Author
| Preface | p. xiii |
| Acknowledgments | p. xvii |
| Overview | p. 1 |
| Introduction | p. 1 |
| Spacecraft Encounters | p. 2 |
| The Encounter Region | p. 2 |
| The Isotropic Problem | p. 3 |
| Analytical Expressions for Short-Term Encounters | p. 4 |
| International Space Station Collision Probability | p. 5 |
| Maneuvers to Mitigate Potential Collision Threats | p. 6 |
| Analytical Expressions for Long-Term Encounters | p. 7 |
| Short-Term vs. Long-Term Spacecraft Encounters | p. 7 |
| Formation Flying | p. 8 |
| Maximum Probability of Collision | p. 9 |
| Close Encounters with Multiple Satellites | p. 9 |
| Instantaneous Probability of Collision | p. 10 |
| Spherical Error Probability Computation | p. 11 |
| References | p. 12 |
| Spacecraft Encounters | p. 13 |
| Covariance Ellipsoids | p. 13 |
| Combined Covariance Ellipsoids | p. 15 |
| Encounter Coordinate System | p. 27 |
| Minimum Separation at Conjunction | p. 30 |
| Additional Discussion on the Combined Covariance | p. 37 |
| Effects of Correlation on Combined Covariance | p. 42 |
| Discussion | p. 43 |
| Conclusion | p. 44 |
| Summary | p. 44 |
| Reference | p. 45 |
| The Encounter Region | p. 47 |
| The Three-Dimensional Collision Integral | p. 47 |
| Requisite Path Length for Integration | p. 49 |
| Rectilinear Motion Approximation | p. 49 |
| Extent of the Encounter Region | p. 54 |
| Discussion | p. 56 |
| Conclusion | p. 60 |
| Summary | p. 60 |
| References | p. 61 |
| The Isotropic Problem | p. 63 |
| The Rician Distribution | p. 63 |
| Analytical Expressions for the Rician Integral | p. 66 |
| Error Bounds | p. 68 |
| Recursive Algorithms for Computing the Rician Distribution | p. 70 |
| Discussion | p. 71 |
| Conclusion | p. 73 |
| Summary | p. 74 |
| References | p. 75 |
| Analytical Expressions for Short-Term Encounters | p. 77 |
| Nonisotropic Probability Density Function | p. 77 |
| Transformation to an Isotropic Density Function | p. 79 |
| Approximation of Cross Section by a Circle | p. 80 |
| Improved Analytical Expressions | p. 81 |
| Comparison with Other Models | p. 83 |
| Generalization to More Complex Cross Sections | p. 89 |
| Discussion | p. 92 |
| Conclusion | p. 95 |
| Summary | p. 96 |
| References | p. 97 |
| International Space Station Collision Probability | p. 99 |
| The Method of Equivalent Cross Section Area | p. 99 |
| Geometric Specifications of the ISS | p. 108 |
| Transformation from Inertial to ISS Body System | p. 118 |
| Computation of the Sun Vector | p. 120 |
| Sample Orbit of the ISS | p. 124 |
| Annual Variation of the Sun Vector in the ISS Body System | p. 126 |
| Case Study I: Head-On Collision Probability | p. 128 |
| Case Study II: Broadside Collision Probability | p. 131 |
| Case Study III: Overhead Collision Probability | p. 133 |
| Comparison with the Spherical Model | p. 134 |
| Discussion | p. 136 |
| Conclusion | p. 136 |
| Summary | p. 136 |
| References | p. 137 |
| Maneuvers to Mitigate Potential Collision Threats | p. 139 |
| Intrack Thrusting | p. 139 |
| General Thrusting | p. 144 |
| Discussion | p. 150 |
| Conclusion | p. 151 |
| Summary | p. 151 |
| References | p. 151 |
| Analytical Expressions for Long-Term Encounters | p. 153 |
| Choice of Random Variables | p. 153 |
| Transformation of a Sphere | p. 155 |
| Motion of a Sphere in Physical Space | p. 157 |
| Volume of Integration | p. 158 |
| Examples of Volumes V and V* | p. 161 |
| Probability of Collision | p. 165 |
| Discussion | p. 170 |
| Conclusion | p. 170 |
| Summary | p. 170 |
| References | p. 171 |
| Short-Term vs. Long-Term Spacecraft Encounters | p. 173 |
| Distance of Closest Approach | p. 173 |
| Short-Term Encounters | p. 176 |
| Long-Term Encounters | p. 177 |
| Case Study I: Concentric Ellipses, Primary at Center | p. 179 |
| Case Study II: Fixed-Size Ellipses, Variable Apsidal Distances | p. 181 |
| Case Study III: Variable-Size Ellipses, Fixed Apsidal Distances | p. 184 |
| Discussion | p. 187 |
| Conclusion | p. 188 |
| Summary | p. 188 |
| Reference | p. 189 |
| Formation Flying | p. 191 |
| Prologue | p. 191 |
| Collision Assessment | p. 192 |
| Preemptive Maneuvers | p. 194 |
| Safe Haven Parking | p. 197 |
| Discussion | p. 197 |
| Conclusion | p. 198 |
| Summary | p. 199 |
| References | p. 200 |
| Maximum Probability of Collision | p. 201 |
| Maximum Likelihood Approach | p. 201 |
| Maximum Probability Approach | p. 205 |
| Comparison of the Two Approaches | p. 211 |
| Numerical Results | p. 211 |
| Discussion | p. 212 |
| Conclusion | p. 215 |
| Summary | p. 215 |
| Reference | p. 216 |
| Close Encounters with Multiple Satellites | p. 217 |
| Transformation of pdf | p. 217 |
| Number Density of Orbiting Objects | p. 218 |
| Number of Collisions per Orbit (Part 1) | p. 219 |
| Geometry of Encounters | p. 221 |
| Number of Collisions per Orbit (Part 2) | p. 223 |
| Numerical Results | p. 232 |
| Discussion | p. 233 |
| Conclusion | p. 234 |
| Summary | p. 234 |
| References | p. 235 |
| Instantaneous Probability of Collision | p. 237 |
| Method of Approximating Distributions | p. 237 |
| Method of Equivalent Volume | p. 241 |
| Comparison of the Two Approaches | p. 244 |
| Numerical Results | p. 245 |
| Discussion | p. 250 |
| Conclusion | p. 252 |
| Summary | p. 252 |
| References | p. 253 |
| Spherical Error Probability Computation | p. 255 |
| Historical Background | p. 256 |
| Formulation in Terms of Noncentral Chi-Square Distribution | p. 257 |
| Formulation in Terms of Central Chi-Square Distribution | p. 261 |
| Formulation in Terms of Gaussian Distribution | p. 263 |
| Numerical Results | p. 265 |
| Application to Other Problems | p. 267 |
| Discussion | p. 269 |
| Conclusion | p. 270 |
| Summary | p. 270 |
| References | p. 271 |
| Computer Programs | p. 273 |
| Introduction | p. 273 |
| Spacecraft Encounters | p. 273 |
| The Encounter Region | p. 274 |
| The Isotropic Problem | p. 275 |
| Analytical Expressions for Short-Term Encounters | p. 276 |
| International Space Station Collision Probability | p. 279 |
| Maneuvers to Mitigate Potential Collision Threats | p. 279 |
| Analytical Expressions for Long-Term Encounters | p. 280 |
| Short-Term vs. Long-Term Spacecraft Encounters | p. 280 |
| Formation Flying | p. 281 |
| Maximum Probability of Collision | p. 281 |
| Close Encounters with Multiple Satellites | p. 282 |
| Instantaneous Probability of Collision | p. 282 |
| Spherical Error Probability Computation | p. 283 |
| Instructions for Using the Programs | p. 284 |
| A Novel Algorithm for Computing the Sun Vector | p. 285 |
| Enhanced Method of Computing Collision Probability | p. 303 |
| Derivation of Density Relations | p. 309 |
| Instantaneous Probability of Collision, Continued | p. 313 |
| Index | p. 319 |
| Supporting Materials | p. 325 |
| Table of Contents provided by Ingram. All Rights Reserved. |
Spacecraft Collision Probability
by Chan, F. KennethFormat: Hardcover
Pub. Date: 2008-03-30
Publisher(s): Amer Inst of Aeronautics &
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