Ulrich Walter. Astronautics. The Physics of Space Flight. 2nd, Enlarged and Improved Edition

Transcription

1 Ulrich Walter Astronautics The Physics of Space Flight 2nd, Enlarged and Improved Edition

2 Preface to Second Edition Preface XVII Acknowledgments XIX List of Symbols XXI XV 1 Rocket Fundamentals Rocket Principles Momentum Thrust Effective Exhaust Velocity Pressure Thrust Momentum versus Pressure Thrust Rocket Equation of Motion Relativistic Rocket Space Flight Dynamics Relativistic Rocket Equation Exhaust Considerations External Efficiency Space-Time Transformations 21 2 Rocket Flight General Considerations Rocket in Free Space Rocket in a Gravitational Field Impulsive Maneuvers Brief Thrust' Gravitational Loss Propulsion and Fuel Demand Propulsion Demand Fuel Demand - Star Trek Plugged Rocket Performance Rocket Power 34

3 VIII Contents Rocket Efficiency Payload. Considerations 37 3 Rocket Staging Serial Staging Definitions Rocket Equation Serial-Stage Optimization Road to Stage Optimization General Optimization Analytical Solutions Uniform Staging, Uniform Exhaust Velocities Uneven Staging Parallel Staging Other Types of Staging 57 4 Thermal Propulsion Engine Thermodynamics Physics of Propellant Gases 60 A.I2 Flow Velocity Flow at the Throat Flow in the Nozzle Ideally Adapted Nozzle Ideal-Adaptation Criterion Ideal Nozzle Design Ideal Engine Performance Engine Thrust Characteristic Thrust Coefficients Thrust Performance Nozzle Efficiency Engine Design Combustion Chamber Nozzle Design Guidelines 86 5 Electric Propulsion Overview IonThruster Ion Acceleration and Flow Engine Thrust Thruster Efficiency Electric Propulsion Optimization 97

4 6 Ascent Flight Earth's Atmosphere Density Master Equation Homosphere (Barometric Formula) Heterosphere Piecewise-Exponential Model Equations of Motion Ascent Phases Ascent Optimization Optimization Problem Gravity Turn Pitch Maneuver Constant-Pitch-Rate Maneuver Optimum-Ascent Trajectory Orbits Equation of Motion Gravitational Potential Gravitational Field Conservation Laws Newton's Laws General Two-Body Problem Motion Principles Angular Momentum Conservation Motion in the Orbital Plane Kepler's Second Law Energy Conservation Effective Potential Motion in a Gravitational Field Orbit Equation Orbital Velocity Orbital Energy Orbital Elements (Keplerian Elements) Position on the Orbit Keplerian Orbits 'Circular Orbit Parabolic Orbit Elliptic Orbit 155 ' Hyperbolic Orbit Radial Orbits Radial Elliptic Orbit Radial Hyperbolic Orbit Radial Parabolic Orbit Free Fall Bounded Vertical Motion 170

5 7.6 life in Other Universes? Equation of Motion in n Dimensions dim Universe Universes with dim > Universes with dim < Orbital Maneuvering One-Impulse Maneuvers Basic Principles Maneuvers in Elliptical Orbits Maneuvers in Circular Orbits Lambert Transfer Orbital Boundary Value Problem Lambert Transfer Orbits Lambert's Problem Minimum Effort Lambert Transfer Hohmann Transfer The Minimum Principle Transfer between Circular Orbits Transfer between Near-Circular Orbits Sensitivity Analysis Other Transfers Bi-elliptic Transfer n-impulse Transfers Continuous Thrust Transfer Relative Orbits General Equation of Motion Hill's Equations Flyaround Trajectories Orbital Rendezvous Launch Phase Phasing Homing Phase Closing Phase Final Approach Shuttle-ISS Rendezvous Plume Impingement 257 Interplanetary Flight Patched Conies Sphere of Influence Patched Conies Departure Orbits Transit Orbits 270 * Hohmann Transfers Non-Hohmann Transfers 273

6 9.4 Arrival Orbit Flyby Maneuvers Overview Flyby Framework Planetocentric Flyby Analysis Heliocentric Flyby Analysis Transition of Orbital Elements Weak Stability Boundary Transfers Re-entry Introduction Thermal Challenges Entry Interface Deorbit Phase Equations of Motion Normalized Equations of Motion Reduced Equations of Motion Elementary Results Drag-Free Phase Ballistic Re-entry Heat Flux Re-entry with lift Lift-Only Case General Results Near-Ballistic Re-entry Reflection and Skip Re-entry Reflection Skip Re-entry PhygoidMode Lifting Re-entry Re-entry Trajectory Critical Deceleration Heat Flux Space Shuttle Re-entry Three-Body Problem Overview Synchronous Orbits Isomass Configurations Collinear Configuration Equilateral Configuration Restiicted Three-Body Problem Collinear Libration Points Equilateral Libration Points 374

7 XII Contents 11.4 Circular Restricted Three-Body Problem Equation of Motion Jacobi's Integral Stability at Libration Points Invariant Manifolds Dynamics about Libration Points Equation of Motion Collinear Libration Points Equilateral Libration Points Orbit Perturbations General Problem Problem Setting Gaussian Variational Equations Gravitational Perturbations Geoid Gravitational Potential Lagrange's Planetary Equations Numerical Perturbation Methods Perturbation Effects Oblateness Perturbations Higher-Order Perturbations Perturbation Orbit Design A Resonant Orbits Resonance Conditions Resonance Dynamics GPS Orbits Geostationary Orbit Solar Radiation Pressure Effects of Solar Radiation Orbital Evolution Correction Maneuvers Drag Drag Coefficient and Perturbations Orbit Circularization Circular Orbits Orbit Lifetime Celestial Perturbations Lunisolar Perturbations Relativistic Perturbations, Reference Frames Space Frames Time Frames 495

8 14 Orbit Determination Orbit Measurements Radar Tracking Other Tracking Systems Methods of Orbit Determination Orbit Estimation Simple Orbit Estimation Lambert's Method Conversion of Orbital Elements State Vector to Keplerian Elements Keplerian Elements to State Vector State Vector Propagation Propagating State Elements Vector Propagation Universal Propagator Rigid Body Dynamics Fundamentals of Rotation Elementary Physics Equations of Rotational Motion Coordinate Systems Rotation-to-Translation Equivalence Torque^Free Motion Stability Nutation Nutation under Energy Dissipation General Torque-Free Motion Gyro under External Torque 534 ' 15.4 Gravity-Gradient Stabilization A.I Gravity-Gradient Torque Gravity-Gradient Oscillations 538 Appendix A Planetary Parameters 543 A.I Mean Orbit Radius 543 A. 1.1 Titius-Bode Law 543 A. 1.2 Average over True Anomaly 544 A. 1.3 Time Average 544 A.2 Mean Orbital Velocity 545 A.2.1 Average over True Anomaly 545 A.2.2 Time Average 546 Appendix B Approximate Analytical Solution for Uneven Staging 547 References 551 Index 555