SPACE DEBRIS Hazard Evaluation and Mitigation Edited by Nickolay N. Smirnov Moscow M.V. Lomonosov State University, Moscow, Russia London and New York
CONTENTS Preface Contributors ix xi Chapter 1: Orbital Debris Hazards Assessment and Mitigation Strategies 1 V.A. Chobotov 1.1. Space Debris Environment 1 1.1.1. Introduction 1 1.1.2. Space Debris Environment: Low Earth Orbit (LEO) 2 a) Debris Measurements 3 b) Future Debris Population Estimates 6 1.1.3. Space Debris Environment: Geosynchronous Orbit (GEO) 8 1.2. Collision Hazards 9 1.2.1. Collision Probability 9 a) Poisson Distribution 10 b) Distance of Closest Approach 10 c) Weibull Distribution 11 1.2.2. Breakup Modeling 14 a) Debris Cloud Evolution Modeling 16 1.3. Mitigation Strategies 17 1.4. Inter-Agency/International Activities 19 1.4.1. Inter-Agency Activities 19 1.4.2. International Activities 21 a) The International Academy of Astronautics (IAA) 21 b) The Inter-Agency Space Debris Coordination Committee (IADC) 22 c) United Nations (UN) 22 1.5. Summary and Conclusions 23 Chapter 2: European Space Agency Activities on Orbital Debris 25 W. Fluty 2.1. Introduction 25 2.2. Space Debris Research Activities 26 2.2.1. The Terrestrial Meteoroid and Debris Environment 26 2.2.2. Risk Analysis 29 2.2.3. Debris Protection and Mitigation 29
vi CONTENTS 2.3. Harmonization in Europe and International Cooperation 31 2.4. Conclusions 33 Chapter 3: Mathematical Model for Space Debris Evolution, Production and Self-Production 35 N.N. Smirnov 3.1. Introduction 35 3.2. Mathematical Model 37 3.3. Marginal Cases Analysis 44 3.4. Some Results of Numerical Investigations 50 3.5. Conclusions 53 Chapter 4: The Solution of Applied Problems Using the Space Debris Prediction and Analysis Model 55 A.I. Nazarenko 4.1. Basic Principles of the Model Construction. The Data on New Yearly Formed Objects 55 4.1.1. Introduction 55 4.1.2. Approach 57 4.1.3. Principles of the Space Debris Environment Forecast 60 4.1.4. The Data on New Yearly Formed Objects 61 4.1.5. Distribution of Parameters of New-Formed Objects 62 4.1.6. General Characteristics of SD Software 63 4.2. Current Space Debris Environment Containing Particles Larger than 0.1 cm 65 4.2.1. Introduction 65 4.2.2. Spatial Density Distribution Construction Technique 66 4.2.3. Velocity Distribution Construction Technique 70 4.2.4. Current Spatial Density Distribution 76 4.3. Collisions of Spacecrafts with Debris Particles Assessment 77 4.3.1. A Brief Review of the Used Methods 77 4.3.2. Development of the Technique for Collision Probability Evaluation 80 4.3.3. Characteristics of the Relative Flux of SOs 85 4.3.4. The Probability of Mutual Collisions for a Group of Objects 88 4.4. The Account of Shape and Orientation of Typical Spacecraft Modules 95 4.4.1. Aerodynamic Analogy 95 4.4.2. Determining the Coefficient C N for Typical SC Structure Components 98 4.4.3. Examples of Collision Probability Determination 100 4.5. Forecast of Space Debris Environment 106 4.5.1. General Characteristics of the Forecasting Algorithm 106 4.5.2. Initial Environment and Conditions of the Forecast 108 4.5.3. Example of a Debris Environment Forecast 110
CONTENTS vii Chapter 5: Geostationary Orbit Pollution and Its Long-Term Evolution 113 T. Yasaka 5.1. Objects Accumulation and Collisions Hazard in GEO 113 5.1.1. Objects Accumulation in GEO 113 5.1.2. Collision Hazard 117 5.2. Breakup Model 119 5.2.1. Momentum and Energy Relations 119 5.2.2. Velocity Distribution 120 5.2.3. Mass Distribution 121 5.2.4. Verification of Assumptions 122 5.2.5. Debris Cloud Evolution 123 5.3. Objects Number Evolution Modeling 124 5.3.1. Evolution Model 125 5.3.2. Parameters and Simulation Results 126 5.4. Necessary Preventive Measures 129 5.4.1. Graveyard Orbit 129 5.4.2. Explosions Control 129 5.4.3. Other Debris Sources 130 5.4.4. Necessary Measures 130 Chapter 6: Area/Mass and Mass Distributions of Orbital Debris 133 P.D. Anz-Meador and A.E. Potter 6.1. Background 133 6.2. A Case in Point: The Fragmentation of Cosmos 1484 134 6.3. Area-to-Mass Ratio from Orbital Decay 136 6.4. Area-to-Mass Ratio for Debris from Laboratory Tests 140 6.5. Mass Distributions for Orbital Debris Objects 140 6.6. Conclusions and Implications 147 6.7. Acknowledgement 148 Chapter 7: Space Debris Production in Different Types of Orbital Breakups 149 N.N. Smirnov, V.F. Nikitin and A.B. Kiselev 7.1. Introduction 149 7.2. Physical Models of Breakup Processes 151 7.2.1. The Model for the Energy Release 152 a) Combustion of Polydispersed Sprays in Weightlessness 152 b) Diffusive Combustion of Hypergolic Propellants in Accidental Mixing of Components on Perforation of the Common Bulkhead 153 c) Detonation of the Mixture in Propellant Tanks 161 7.2.2. The Model for the Dynamical Deforming of Walls 162 7.2.3. Fragmentation Models for Thin-Walled Containments 169
viii CONTENTS 7.2.4. Fragmentations in Collisions of Debris Particles 173 a) Mean Velocities and Energies of Fragments 173 b) Number of Fragments 174 c) The Minimal Mass of Fragments 175 d) Relative Velocities of Fragments 176 7.3. Fragmentation of Shells in Uniform Internal Loading 177 7.4. Breakups Caused by Non-uniform Internal Loading 179 7.5. Fragmentations Caused by Hypervelocity Collisions of Debris Particles with Pressurized Vessels 184 7.6. A Concept for Shield Design 191 7.7. Conclusions 192 Annex: Mathematical Models for Dynamics of Multiphase Media and Deformable Structures 193 N.N. Smirnov, A.B. Kiselev and V.F. Nikitin A.I. Turbulent Flows of Multiphase Polydispersed Chemically Reacting Mixtures 193 A. 1.1. Mathematical Model for the Gas Phase 194 A. 1.2. Dispersed Phase Modeling 197 A. 1.3. Fluxes from Model Particles and their Recalculation into Gas Phase Equations Source Terms 205 A. 1.4. Numerical Modeling Techniques 206 A. 1.5. Nomenclature 208 A.2. Mathematical Model for Dynamical Deforming and Breakup of Thin-Walled Elastoviscoplastic Shell 211 References 215 Index 227