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As a crewmember of the D-2 shuttle mission and a full professor of astronautics at the Technical University in Munich, Ulrich Walter is an acknowledged expert in the field. He is also the author of a number of popular science books on space flight.
The second edition of this textbook is based on extensive teaching and his work with students, backed by numerous examples drawn from his own experience. With its end-of-chapter examples and problems, this work is suitable for graduate level or even undergraduate courses in space flight, as well as for professionals working in the space industry.
Preface XVII
Acknowledgments XIX
List of Symbols XXI
1 Rocket Fundamentals 1
1.1 Rocket Principles 2
1.1.1 Momentum Thrust 2
1.1.2 Effective Exhaust Velocity 4
1.1.3 Pressure Thrust 5
1.1.4 Momentum versus Pressure Thrust 9
1.2 Rocket Equation of Motion 12
1.3 Relativistic Rocket 13
1.3.1 Space Flight Dynamics 14
1.3.2 Relativistic Rocket Equation 16
1.3.3 Exhaust Considerations 18
1.3.4 External Efficiency 20
1.3.5 Space-Time Transformations 21
2 Rocket Flight 25
2.1 General Considerations 25
2.2 Rocket in Free Space 26
2.3 Rocket in a Gravitational Field 27
2.3.1 Impulsive Maneuvers 28
2.3.2 Brief Thrust 29
2.3.3 Gravitational Loss 29
2.4 Propulsion and Fuel Demand 30
2.4.1 Propulsion Demand 30
2.4.2 Fuel Demand - Star Trek Plugged 32
2.5 Rocket Performance 33
2.5.1 Rocket Power 34
2.5.2 Rocket Efficiency 34
2.5.3 Payload Considerations 37
3 Rocket Staging 41
3.1 Serial Staging 42
3.1.1 Definitions 42
3.1.2 Rocket Equation 45
3.2 Serial-Stage Optimization 45
3.2.1 Road to Stage Optimization 45
3.2.2 General Optimization 46
3.3 Analytical Solutions 50
3.3.1 Uniform Staging 51
3.3.2 Uniform Exhaust Velocities 53
3.3.3 Uneven Staging 54
3.4 Parallel Staging 55
3.5 Other Types of Staging 57
4 Thermal Propulsion 59
4.1 Engine Thermodynamics 60
4.1.1 Physics of Propellant Gases 60
4.1.2 Flow Velocity 64
4.1.3 Flow at the Throat 65
4.1.4 Flow in the Nozzle 66
4.2 Ideally Adapted Nozzle 71
4.2.1 Ideal-Adaptation Criterion 71
4.2.2 Ideal Nozzle Design 72
4.2.3 Ideal Engine Performance 74
4.3 Engine Thrust 75
4.3.1 Characteristic Thrust Coefficients 76
4.3.2 Thrust Performance 77
4.3.3 Nozzle Efficiency 80
4.4 Engine Design 81
4.4.1 Combustion Chamber 82
4.4.2 Nozzle 83
4.4.3 Design Guidelines 86
5 Electric Propulsion 89
5.1 Overview 89
5.2 Ion Thruster 90
5.2.1 Ion Acceleration and Flow 91
5.2.2 Engine Thrust 94
5.2.3 Thruster Efficiency 95
5.3 Electric Propulsion Optimization 97
6 Ascent Flight 101
6.1 Earth.s Atmosphere 101
6.1.1 Density Master Equation 101
6.1.2 Homosphere (Barometric Formula) 104
6.1.3 Heterosphere 105
6.1.4 Piecewise-Exponential Model 106
6.2 Equations of Motion 107
6.3 Ascent Phases 113
6.4 Ascent Optimization 115
6.4.1 Optimization Problem 115
6.4.2 Gravity Turn 118
6.4.3 Pitch Maneuver 120
6.4.4 Constant-Pitch-Rate Maneuver 120
6.4.5 Optimum-Ascent Trajectory 123
7 Orbits 125
7.1 Equation of Motion 125
7.1.1 Gravitational Potential 125
7.1.2 Gravitational Field 128
7.1.3 Conservation Laws 129
7.1.4 Newton.s Laws 130
7.1.5 General Two-Body Problem 133
7.2 Motion Principles 136
7.2.1 Angular Momentum Conservation 136
7.2.2 Motion in the Orbital Plane 137
7.2.3 Kepler.s Second Law 138
7.2.4 Energy Conservation 139
7.2.5 Effective Potential 140
7.3 Motion in a Gravitational Field 141
7.3.1 Orbit Equation 141
7.3.2 Orbital Velocity 144
7.3.3 Orbital Energy 146
7.3.4 Orbital Elements (Keplerian Elements) 147
7.3.5 Position on the Orbit 150
7.4 Keplerian Orbits 151
7.4.1 Circular Orbit 152
7.4.2 Parabolic Orbit 153
7.4.3 Elliptic Orbit 155
7.4.4 Hyperbolic Orbit 161
7.5 Radial Orbits 164
7.5.1 Radial Elliptic Orbit 166
7.5.2 Radial Hyperbolic Orbit 167
7.5.3 Radial Parabolic Orbit 168
7.5.4 Free Fall 169
7.5.5 Bounded Vertical Motion 170
7.6 Life in Other Universes? 172
7.6.1 Equation of Motion in n Dimensions 173
7.6.2 4-dim Universe 176
7.6.3 Universes with dim 5 177
7.6.4 Universes with dim 2 179
8 Orbital Maneuvering 187
8.1 One-Impulse Maneuvers 188
8.1.1 Basic Principles 188
8.1.2 Maneuvers in Elliptical Orbits 190
8.1.3 Maneuvers in Circular Orbits 195
8.2 Lambert Transfer 196
8.2.1 Orbital Boundary Value Problem 197
8.2.2 Lambert Transfer Orbits 200
8.2.3 Lambert.s Problem 204
8.2.4 Minimum Effort Lambert Transfer 206
8.3 Hohmann Transfer 207
8.3.1 The Minimum Principle 207
8.3.2 Transfer between Circular Orbits 210
8.3.3 Transfer between Near-Circular Orbits 214
8.3.4 Sensitivity Analysis 215
8.4 Other Transfers 218
8.4.1 Bi-elliptic Transfer 218
8.4.2 n-Impulse Transfers 220
8.4.3 Continuous Thrust Transfer 220
8.5 Relative Orbits 222
8.5.1 General Equation of Motion 222
8.5.2 Hill.s Equations 226
8.5.3 Flyaround Trajectories 229
8.6 Orbital Rendezvous 234
8.6.1 Launch Phase 236
8.6.2 Phasing 240
8.6.3 Homing Phase 241
8.6.4 Closing Phase 247
8.6.5 Final Approach 250
8.6.6 Shuttle-ISS Rendezvous 255
8.6.7 Plume Impingement 257
9 Interplanetary Flight 263
9.1 Patched Conics 263
9.1.1 Sphere of Influence 264
9.1.2 Patched Conics 266
9.2 Departure Orbits 267
9.3 Transit Orbits 270
9.3.1 Hohmann Transfers 270
9.3.2 Non-Hohmann Transfers 273
9.4 Arrival Orbit 279
9.5 Flyby Maneuvers 281
9.5.1 Overview 281
9.5.2 Flyby Framework 282
9.5.3 Planetocentric Flyby Analysis 285
9.5.4 Heliocentric Flyby Analysis 290
9.5.5 Transition of Orbital Elements 292
9.6 Weak Stability Boundary Transfers 296
10 Re-entry 301
10.1 Introduction 301
10.1.1 Thermal Challenges 302
10.1.2 Entry Interface 304
10.1.3 Deorbit Phase 305
10.2 Equations of Motion 309
10.2.1 Normalized Equations of Motion 311
10.2.2 Reduced Equations of Motion 315
10.3 Elementary Results 317
10.3.1 Drag-Free Phase 317
10.3.2 Ballistic Re-entry 319
10.3.3 Heat Flux 322
10.4 Re-entry with Lift 324
10.4.1 Lift-Only Case 324
10.4.2 General Results 326
10.4.3 Near-Ballistic Re-entry 329
10.5 Reflection and Skip Re-entry 334
10.5.1 Reflection 334
10.5.2 Skip Re-entry 338
10.5.3 Phygoid Mode 341
10.6 Lifting Re-entry 345
10.6.1 Re-entry Trajectory 347
10.6.2 Critical Deceleration 348
10.6.3 Heat Flux 349
10.6.4 Space Shuttle Re-entry 352
11 Three-Body Problem 359
11.1 Overview 359
11.2 Synchronous Orbits 361
11.2.1 Isomass Configurations 361
11.2.2 Collinear Configuration 361
11.2.3 Equilateral Configuration 367
11.3 Restricted Three-Body Problem 369
11.3.1 Collinear Libration Points 371
11.3.2 Equilateral Libration Points 374
11.4 Circular Restricted Three-Body Problem 374
11.4.1 Equation of Motion 376
11.4.2 Jacobi.s Integral 377
11.4.3 Stability at Libration Points 380
11.4.4 Invariant Manifolds 382
11.5 Dynamics about Libration Points 386
11.5.1 Equation of Motion 386
11.5.2 Collinear Libration Points 388
11.5.3 Equilateral Libration Points 400
12 Orbit Perturbations 409
12.1 General Problem 409
12.1.1 Problem Setting 409
12.1.2 Gaussian Variational Equations 411
12.2 Gravitational Perturbations 412
12.2.1 Geoid 412
12.2.2 Gravitational Potential 414
12.2.3 Lagrange.s Planetary Equations 422
12.2.4 Numerical Perturbation Methods 422
12.3 Perturbation Effects 425
12.3.1 Oblateness Perturbations 427
12.3.2 Higher-Order Perturbations 431
12.3.3 Perturbation Orbit Design 436
12.4 Resonant Orbits 438
12.4.1 Resonance Conditions 440
12.4.2 Resonance Dynamics 443
12.4.3 GPS Orbits 446
12.4.4 Geostationary Orbit 450
12.5 Solar Radiation Pressure 455
12.5.1 Effects of Solar Radiation 456
12.5.2 Orbital Evolution 459
12.5.3 Correction Maneuvers 462
12.6 Drag 464
12.6.1 Drag Coefficient and Perturbations 465
12.6.2 Orbit Circularization 468
12.6.3 Circular Orbits 472
12.6.4 Orbit Lifetime 475
12.7 Celestial Perturbations 478
12.7.1 Lunisolar Perturbations 478
12.7.2 Relativistic Perturbations 482
13 Reference Frames 489
13.1 Space Frames 489
13.2 Time Frames 495
14 Orbit Determination 499
14.1 Orbit Measurements 499
14.1.1 Radar Tracking 499
14.1.2 Other Tracking Systems 500
14.2 Methods of Orbit Determination 502
14.3 Orbit Estimation 503
14.3.1 Simple Orbit Estimation 503
14.3.2 Lambert.s Method 504
14.4 Conversion of Orbital Elements 506
14.4.1 State Vector to Keplerian Elements 506
14.4.2 Keplerian Elements to State Vector 508
14.5 State Vector Propagation 508
14.5.1 Propagating State Elements 509
14.5.2 Vector Propagation 511
14.5.3 Universal Propagator 512
15 Rigid Body Dynamics 513
15.1 Fundamentals of Rotation 513
15.1.1 Elementary Physics 513
15.1.2 Equations of Rotational Motion 519
15.1.3 Coordinate Systems 521
15.1.4 Rotation-to-Translation Equivalence 523
15.2 Torque-Free Motion 524
15.2.1 Stability 525
15.2.2 Nutation 527
15.2.3 Nutation under Energy Dissipation 530
15.2.4 General Torque-Free Motion 533
15.3 Gyro under External Torque 534
15.4 Gravity-Gradient Stabilization 536
15.4.1 Gravity-Gradient Torque 536
15.4.2 Gravity-Gradient Oscillations 538
Appendix A Planetary Parameters 543
A.1 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
ISBN: 9783527410651
ISBN-10: 3527410651
Series: Physics Textbook
Audience:
Professional
Format:
Hardcover
Language:
English
Published: 22nd May 2012
Publisher: Wiley-VCH Verlag GmbH
Dimensions (cm): 24.4 x 17.4
x 3.3
Weight (kg): 1.25
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