Astronautics : the physics of space flight

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Preface to the Third Edition Preface to the Second Edition Preface to the First Edition Acknowledgements Contents Abbreviations Symbols Used and Terminology 1 Rocket Fundamentals 1.1 Rocket Principles 1.1.1 Repulsion Principle 1.1.2 Total Thrust 1.1.3 Equation of Rocket Motion 1.2 Jet Engine 1.2.1 Nozzle Divergence 1.2.2 Pressure Thrust 1.2.3 Momentum versus Pressure Thrust 1.3 Rocket Performance 1.3.1 Payload Considerations 1.3.2 Rocket Efficiency 1.3.3 Performance Parameters 1.4 Relativistic Rocket 1.4.1 Space Flight Dynamics 1.4.2 Relativistic Rocket Equation 1.4.3 Exhaust Considerations 1.4.4 External Efficiency 1.4.5 Space–Time Transformations 1.5 Problems 2 Rocket Flight 2.1 General Considerations 2.2 Rocket in Free Space 2.3 Rocket in a Gravitational Field 2.3.1 Impulsive Maneuvers 2.3.2 Brief Thrust 2.3.3 Gravitational Loss 2.4 Delta-v Budget and Fuel Demand 2.4.1 Delta-v Budget 2.4.2 Fuel Demand—Star Trek Plugged 2.5 Problems 3 Rocket Staging 3.1 Serial Staging 3.1.1 Definitions 3.1.2 Rocket Equation 3.2 Serial-Stage Optimization 3.2.1 Road to Stage Optimization 3.2.2 General Optimization 3.3 Analytical Solutions 3.3.1 Uniform Staging 3.3.2 Uniform Exhaust Velocities 3.3.3 Uneven Staging 3.4 Parallel Staging 3.5 Other Types of Staging 3.6 Problems 4 Thermal Propulsion 4.1 Engine Thermodynamics 4.1.1 Physics of Propellant Gases 4.1.2 Flow Velocity 4.1.3 Flow at the Throat 4.1.4 Flow in the Nozzle 4.2 Ideally Adapted Nozzle 4.2.1 Ideal-Adaptation Criterion 4.2.2 Ideal Nozzle Design 4.2.3 Shock Attenuation and Pogos 4.2.4 Ideal Engine Performance 4.3 Engine Thrust 4.3.1 Engine Performance Parameters 4.3.2 Thrust Performance 4.3.3 Nozzle Efficiency 4.4 Engine Design 4.4.1 Combustion Chamber 4.4.2 Nozzles 4.4.3 Design Guidelines 4.5 Problems 5 Electric Propulsion 5.1 Overview 5.2 Ion Thruster 5.2.1 Ion Acceleration and Flow 5.2.2 Ideal Engine Thrust 5.2.3 Thruster Performance 5.3 Electric Propulsion Optimization 5.4 Problem 6 Atmospheric and Ascent Flight 6.1 Earth’s Atmosphere 6.1.1 Density Master Equation 6.1.2 Atmospheric Structure 6.1.3 Piecewise-Exponential Model 6.2 Hypersonic Flow Theory 6.2.1 Free Molecular Flow 6.2.2 Newtonian Flow Theory 6.2.3 Drag and Lift Coefficients 6.2.4 Drag in Free Molecular Flow 6.2.5 Aerodynamic Forces 6.3 Equations of Motion 6.4 Ascent Flight 6.4.1 Ascent Phases 6.4.2 Optimization Problem 6.4.3 Gravity Turn 6.4.4 Pitch Maneuver 6.4.5 Constant-Pitch-Rate Maneuver 6.4.6 Terminal State Control 6.4.7 Optimal Ascent Trajectory 7 Orbits 7.1 Fundamental Physics 7.1.1 Gravitational Potential 7.1.2 Gravitational Force 7.1.3 Conservation Laws 7.1.4 Newton’s Laws of Motion 7.1.5 General Two-Body Problem 7.2 General Principles of Motion 7.2.1 Vector Derivatives 7.2.2 Motion in a Central Force Field 7.2.3 Vis-Viva Equation 7.2.4 Effective Radial Motion 7.3 Motion in a Gravitational Field 7.3.1 Orbit Equation 7.3.2 Position on the Orbit 7.3.3 Orbital Velocity 7.3.4 Orbital Energy 7.3.5 Orbital Elements 7.4 Keplerian Orbits 7.4.1 Circular Orbit 7.4.2 Elliptic Orbit 7.4.3 Hyperbolic Orbit 7.4.4 Parabolic Orbit 7.4.5 ε-Based Transformation 7.4.6 {\bi h} -Based Transformation 7.4.7 Conventional State Vector Propagation 7.4.8 Universal Variable Formulation 7.5 Radial Trajectories 7.5.1 Radial Elliptic Trajectory 7.5.2 Radial Hyperbolic Trajectory 7.5.3 Radial Parabolic Trajectory 7.5.4 Free Fall 7.5.5 Bounded Vertical Motion 7.6 Life in Other Universes? 7.6.1 Equation of Motion in n Dimensions 7.6.2 4-Dimensional Universe 7.6.3 Universes with ≥5 Dimensions 7.6.4 Universes with ≤2 Dimensions 7.7 Stellar Orbits 7.7.1 Motion in General Gravitational Potentials 7.7.2 Stellar Motion in General Galaxies 7.7.3 Stellar Orbits in Globular Cluster Galaxies 7.7.4 Stellar Motion in Disk-Shaped Galaxies 7.8 Problems 8 Orbital Maneuvering 8.1 One-Impulse Maneuvers 8.1.1 Elementary Maneuvers 8.1.2 Elementary Maneuvers in Circular Orbits 8.1.3 General Maneuvers 8.1.4 Tangent Plane Maneuvers 8.1.5 Genuine Plane Change Maneuvers 8.1.6 Tangent Maneuver 8.2 Lambert Transfer 8.2.1 Orbital Boundary Value Problem 8.2.2 Lambert Transfer Orbits 8.2.3 Lambert’s Problem 8.2.4 Minimum Effort Lambert Transfer 8.3 Hohmann Transfer 8.3.1 The Minimum Principle 8.3.2 Transfer Between Circular Orbits 8.3.3 Transfer Between Near-Circular Orbits 8.3.4 Sensitivity Analysis 8.4 Other Transfers 8.4.1 Parabolic Escape Transfer 8.4.2 Bi-elliptic Transfer 8.4.3 Super-Synchronous Transfer Orbits 8.4.4 n-Impulse Transfers 8.4.5 Continuous Thrust Transfer 8.5 Relative Orbits 8.5.1 General Equation of Motion 8.5.2 Circular Orbits 8.5.3 Flyaround Trajectories 8.5.4 Near-Circular Orbits 8.6 Orbital Rendezvous 8.6.1 Launch Phase 8.6.2 Phasing 8.6.3 Homing Phase 8.6.4 Closing Phase 8.6.5 Final Approach 8.6.6 Shuttle-ISS Rendezvous 8.6.7 Plume Impingement 8.7 Problems 9 Interplanetary Flight 9.1 Patched Conics 9.1.1 Sphere of Influence 9.1.2 Patched Conics 9.2 Departure Orbits 9.3 Transfer Orbits 9.3.1 Hohmann Transfers 9.3.2 Non-Hohmann Transfers 9.4 Arrival Orbit 9.5 Flyby Maneuvers 9.5.1 Overview 9.5.2 Flyby Framework 9.5.3 Planetocentric Flyby Analysis 9.5.4 Heliocentric Flyby Analysis 9.5.5 Transition of Orbital Elements 9.6 Weak Stability Boundary Transfers 9.7 Problems 10 Planetary Entry 10.1 Introduction 10.1.1 Aerothermodynamical Challenges 10.1.2 Entry Interface 10.1.3 Deorbit Phase 10.2 Equations of Motion 10.2.1 Normalized Equations of Motion 10.2.2 Reduced Equations of Motion 10.3 Elementary Results 10.3.1 Drag-Free Phase 10.3.2 Ballistic Reentry 10.3.3 Heat Flux 10.4 Reentry with Lift 10.4.1 Lift-Only Case 10.4.2 General Results 10.4.3 Near-Ballistic Reentry 10.5 Reflection and Skip Reentry 10.5.1 Reflection 10.5.2 Skip Reentry 10.5.3 Phugoid Mode 10.6 Lifting Reentry 10.6.1 Reentry Trajectory 10.6.2 Critical Deceleration 10.6.3 Heat Flux 10.7 Space Shuttle Reentry 10.7.1 Reentry Flight Design and Pre-entry Phase 10.7.2 Constant Heat Rate Phase (Thermal Control Phase) 10.7.3 Equilibrium Glide Phase 10.7.4 Constant-Drag Phase 10.7.5 Transition Phase 10.7.6 TAEM Phase 10.8 Problems 11 Three-Body Problem 11.1 The N-Body Problem 11.1.1 Integrals of Motion 11.1.2 Stability of an N-Body System 11.1.3 N-Body Choreographies 11.2 Synchronous 3-Body Orbits 11.2.1 Collinear Configuration 11.2.2 Equilateral Configuration 11.3 Restricted Three-Body Problem 11.3.1 Collinear Libration Points 11.3.2 Equilateral Libration Points 11.4 Circular Restricted Three-Body Problem 11.4.1 Equation of Motion 11.4.2 Jacobi’s Integral 11.4.3 Stability at Libration Points 11.4.4 General System Dynamics 11.5 Dynamics About Libration Points 11.5.1 Equation of Motion 11.5.2 Collinear Libration Points 11.5.3 Equilateral Libration Points 11.6 Problems 12 Orbit Perturbations 12.1 Problem Setting 12.1.1 Origins of Perturbations 12.1.2 Osculating Orbits 12.1.3 Gaussian Variational Equations 12.2 Gravitational Perturbations 12.2.1 Geoid 12.2.2 Gravitational Potential 12.2.3 Lagrange’s Planetary Equations 12.2.4 Numerical Perturbation Methods 12.3 Gravitational Perturbation Effects 12.3.1 Classification of Effects 12.3.2 Removing Short-Periodic Effects 12.3.3 Oblateness Perturbation 12.3.4 Higher-Order Perturbations 12.3.5 Sun-Synchronous Orbits 12.3.6 Frozen Orbits 12.3.7 Frozen Sun-Synchronous Orbits 12.4 Resonant Orbits 12.4.1 Resonance Conditions 12.4.2 Resonance Dynamics 12.4.3 Low Earth Orbits 12.4.4 GPS Orbits 12.4.5 Geostationary Orbit 12.5 Solar Radiation Pressure 12.5.1 Effects of Solar Radiation 12.5.2 Orbital Evolution 12.5.3 Correction Maneuvers 12.6 Celestial Perturbations 12.6.1 Lunisolar Perturbations 12.6.2 Relativistic Perturbations 12.7 Drag 12.7.1 Drag Perturbations 12.7.2 Orbit Circularization 12.7.3 Circular Orbits 12.7.4 Orbit Lifetime 12.8 Problems 13 Reference Frames 13.1 Space Frames 13.1.1 Inertial Reference Frames 13.1.2 Heliocentric Reference Frames 13.1.3 Terrestrial Reference Frames 13.1.4 Orbital Reference Frames 13.1.5 Vector Representations 13.2 Time Frames 14 Orbit Geometry and Determination 14.1 Orbit Geometry 14.1.1 Eclipse Duration 14.1.2 Access Area 14.2 Orbit Determination 14.2.1 Orbit Tracking 14.2.2 Generalized Orbit Determination Method 14.2.3 GEO Orbit from Angles-Only Data 14.2.4 Simple Orbit Estimation 14.2.5 Modified Battin’s Method 14.2.6 Advanced Orbit Determination 15 Spacecraft Attitude Dynamics 15.1 Fundamentals of Rotation 15.1.1 Elementary Physics 15.1.2 Equations of Rotational Motion 15.1.3 Coordinate Systems 15.1.4 Rotation-to-Translation Equivalence 15.2 Attitude Kinematics 15.2.1 Stability 15.2.2 Nutation 15.2.3 General Torque-Free Motion 15.3 Attitude Dynamics Under External Torque 15.3.1 External Torques 15.3.2 Road to Flat Spin 15.3.3 Flat Spin Dynamics 15.4 Gravity-Gradient Stabilization 15.4.1 Gravity-Gradient Torque 15.4.2 Gravity-Gradient Dynamics 16 Thermal Radiation Physics and Modeling Glossary for Thermal Modeling 16.1 Radiation Properties 16.1.1 Radiometric Concepts 16.1.2 Diffuse Radiators 16.1.3 Black-Body Radiator 16.1.4 Selective Surfaces 16.1.5 Kirchhoff’s Law 16.2 Radiation Exchange 16.2.1 Transmitted and Absorbed Flux 16.2.2 View Factor 16.2.3 Point Radiators 16.2.4 Radiation Exchange Between Two Bodies 16.2.5 Spacecraft Thermal Balance 16.2.6 α/ε Materials 16.3 Thermal Modeling 16.3.1 Thermal Requirements and Boundary Conditions 16.3.2 Heat Equation 16.3.3 Thermal Model Setup 16.3.4 Geometric Mathematical Model (GMM) 16.3.5 Thermal Mathematical Model (TMM) 16.3.6 Applied Thermal Design and Analysis 16.3.7 Case Studies 16.4 Problems Chap16 17 Correction to: Astronautics Correction to: U. Walter, Astronautics, https://doi.org/10.1007/978-3-319-74373-8 Appendix A: Planetary Parameters A.1 Mean Orbit Radius A.1.1 Titius–Bode Law A.1.2 Average over True Anomaly A.1.3 Time Average A.2 Mean Orbital Velocity Outline placeholder A.2.1 Average over True Anomaly A.2.2 Time Average Appendix B: Approximate Analytical Solution for Uneven Staging References Index