Space Flight Dynamics (2^nd Ed.)
Aerospace Series

Thorough coverage of space flight topics with self-contained chapters serving a variety of courses in orbital mechanics, spacecraft dynamics, and astronautics

This concise yet comprehensive book on space flight dynamics addresses all phases of a space mission: getting to space (launch trajectories), satellite motion in space (orbital motion, orbit transfers, attitude dynamics), and returning from space (entry flight mechanics). It focuses on orbital mechanics with emphasis on two-body motion, orbit determination, and orbital maneuvers with applications in Earth-centered missions and interplanetary missions.

Space Flight Dynamics presents wide-ranging information on a host of topics not always covered in competing books. It discusses relative motion, entry flight mechanics, low-thrust transfers, rocket propulsion fundamentals, attitude dynamics, and attitude control. The book is filled with illustrated concepts and real-world examples drawn from the space industry. Additionally, the book includes a ?computational toolbox? composed of MATLAB M-files for performing space mission analysis.

Key features:

• Provides practical, real-world examples illustrating key concepts throughout the book
• Accompanied by a website containing MATLAB M-files for conducting space mission analysis
• Presents numerous space flight topics absent in competing titles

Space Flight Dynamics is a welcome addition to the field, ideally suited for upper-level undergraduate and graduate students studying aerospace engineering.

Preface xi

1 Historical Overview 1

1.1 Introduction 1

1.2 Early Modern Period 1

1.3 Early Twentieth Century 3

1.4 Space Age 4

2 Two-Body Orbital Mechanics 7

2.1 Introduction 7

2.2 Two-Body Problem 7

2.3 Constants of Motion 11

2.3.1 Conservation of Angular Momentum 11

2.3.2 Conservation of Energy 13

2.4 Conic Sections 15

2.4.1 Trajectory Equation 15

2.4.2 Eccentricity Vector 20

2.4.3 Energy and Semimajor Axis 21

2.5 Elliptical Orbit 23

2.5.1 Ellipse Geometry 24

2.5.2 Flight-Path Angle and Velocity Components 24

2.5.3 Period of an Elliptical Orbit 31

2.5.4 Circular Orbit 32

2.5.5 Geocentric Orbits 33

2.6 Parabolic Trajectory 38

2.7 Hyperbolic Trajectory 42

2.8 Summary 46

Further Reading 46

Problems 47

3 Orbit Determination 55

3.1 Introduction 55

3.2 Coordinate Systems 55

3.3 Classical Orbital Elements 57

3.4 Transforming Cartesian Coordinates to Orbital Elements 60

3.5 Transforming Orbital Elements to Cartesian Coordinates 66

3.5.1 Coordinate Transformations 68

3.6 Ground Tracks 75

3.7 Orbit Determination from One Ground-Based Observation 79

3.7.1 Topocentric-Horizon Coordinate System 79

3.7.2 Inertial Position Vector 81

3.7.3 Inertial Velocity Vector 82

3.7.4 Ellipsoidal Earth Model 85

3.8 Orbit Determination from Three Position Vectors 88

3.9 Survey of Orbit-Determination Methods 95

3.9.1 Orbit Determination Using Angles-Only Measurements 95

3.9.2 Orbit Determination Using Three Position Vectors 97

3.9.3 Orbit Determination from Two Position Vectors and Time 97

3.9.4 Statistical Orbit Determination 98

3.10 Summary 99

References 100

Problems 100

4 Time of Flight 107

4.1 Introduction 107

4.2 Kepler’s Equation 107

4.2.1 Time of Flight Using Geometric Methods 107

4.2.2 Time of Flight Using Analytical Methods 108

4.2.3 Relating Eccentric and True Anomalies 112

4.3 Parabolic and Hyperbolic Time of Flight 117

4.3.1 Parabolic Trajectory Flight Time 117

4.3.2 Hyperbolic Trajectory Flight Time 119

4.4 Kepler’s Problem 123

4.5 Orbit Propagation Using Lagrangian Coefficients 127

4.6 Lambert’s Problem 135

4.7 Summary 145

References 145

Problems 146

5 Non-Keplerian Motion 151

5.1 Introduction 151

5.2 Special Perturbation Methods 152

5.2.1 Non-Spherical Central Body 153

5.3 General Perturbation Methods 159

5.3.1 Lagrange’s Variation of Parameters 160

5.3.2 Secular Perturbations due to Oblateness ( J2) 164

5.4 Gauss’ Variation of Parameters 174

5.5 Perturbation Accelerations for Earth Satellites 180

5.5.1 Non-Spherical Earth 180

5.5.2 Third-Body Gravity 182

5.5.3 Atmospheric Drag 185

5.5.4 Solar Radiation Pressure 189

5.6 Circular Restricted Three-Body Problem 192

5.6.1 Jacobi’s Integral 194

5.6.2 Lagrangian Points 195

5.7 Summary 203

References 203

Problems 204

6 Rocket Performance 213

6.1 Introduction 213

6.2 Rocket Propulsion Fundamentals 213

6.3 The Rocket Equation 214

6.4 Launch Trajectories 219

6.5 Staging 226

6.6 Launch Vehicle Performance 231

6.7 Impulsive Maneuvers 233

6.8 Summary 234

References 235

Problems 235

7 Impulsive Orbital Maneuvers 241

7.1 Introduction 241

7.2 Orbit Shaping 242

7.3 Hohmann Transfer 245

7.3.1 Coplanar Transfer with Tangential Impulses 248

7.4 General Coplanar Transfer 252

7.5 Inclination-Change Maneuver 256

7.6 Three-Dimensional Orbit Transfer 259

7.7 Summary 264

References 264

Problems 264

8 Relative Motion and Orbital Rendezvous 275

8.1 Introduction 275

8.2 Linear Clohessy–Wiltshire Equations 275

8.3 Homogeneous Solution of the Clohessy–Wiltshire Equations 280

8.4 Orbital Rendezvous Using the Clohessy–Wiltshire Equations 288

8.5 Summary 298

References 298

Problems 298

9 Low-Thrust Transfers 303

9.1 Introduction 303

9.2 Electric Propulsion Fundamentals 304

9.3 Coplanar Circle-to-Circle Transfer 306

9.3.1 Comparing Impulsive and Low-Thrust Transfers 313

9.4 Coplanar Transfer with Earth-Shadow Effects 315

9.5 Inclination-Change Maneuver 318

9.6 Transfer Between Inclined Circular Orbits 320

9.7 Combined Chemical-Electric Propulsion Transfer 322

9.8 Low-Thrust Transfer Issues 328

9.9 Summary 329

References 329

Problems 330

10 Interplanetary Trajectories 335

10.1 Introduction 335

10.2 Patched-Conic Method 338

10.2.1 Sphere of Influence 339

10.2.2 Coplanar Heliocentric Transfers between Circular Orbits 341

10.3 Phase Angle at Departure 351

10.4 Planetary Arrival 355

10.5 Heliocentric Transfers Using an Accurate Ephemeris 359

10.5.1 Pork-Chop Plots 367

10.5.2 Julian Date 368

10.6 Gravity Assists 370

10.7 Summary 378

References 379

Problems 379

11 Atmospheric Entry 385

11.1 Introduction 385

11.2 Entry Flight Mechanics 386

11.3 Ballistic Entry 390

11.4 Gliding Entry 396

11.5 Skip Entry 404

11.6 Entry Heating 412

11.7 Space Shuttle Entry 418

11.8 Summary 422

References 423

Problems 423

12 Attitude Dynamics 429

12.1 Introduction 429

12.2 Rigid Body Dynamics 430

12.2.1 Angular Momentum of a Rigid Body 432

12.2.2 Principal Axes 438

12.2.3 Rotational Kinetic Energy 439

12.2.4 Euler’s Moment Equations 441

12.3 Torque-Free Motion 442

12.3.1 Euler Angle Rates 447

12.4 Stability and Flexible Bodies 457

12.4.1 Spin Stability about the Principal Axes 457

12.4.2 Stability of Flexible Bodies 459

12.5 Spin Stabilization 464

12.5.1 Dual-Spin Stabilization 466

12.6 Disturbance Torques 467

12.6.1 Gravity-Gradient torque 467

12.6.2 Aerodynamic Torque 468

12.6.3 Solar Radiation Pressure Torque 469

12.6.4 Magnetic Torque 470

12.7 Gravity-Gradient Stabilization 470

12.8 Summary 476

References 477

Problems 477

13 Attitude Control 485

13.1 Introduction 485

13.2 Feedback Control Systems 485

13.2.1 Transfer Functions 486

13.2.2 Closed-Loop Control Systems 489

13.2.3 Second-Order System Response 490

13.3 Mechanisms for Attitude Control 497

13.3.1 Reaction Jets 497

13.3.2 Momentum-Exchange Devices 497

13.3.3 Magnetic Torquers 501

13.4 Attitude Maneuvers Using Reaction Wheels 501

13.5 Attitude Maneuvers Using Reaction Jets 513

13.5.1 Phase-Plane Analysis of Satellite Attitude Dynamics 513

13.5.2 Reaction Jet Control Law 518

13.6 Nutation Control Using Reaction Jets 527

13.7 Summary 534

References 535

Further Reading 535

Problems 535

Appendix A: Physical Constants 541

Appendix B: Review of Vectors 543

B.1 Introduction 543

B.2 Vectors 543

B.3 Vector Operations 544

B.3.1 Vector Addition 544

B.3.2 Cross Product 545

B.3.3 Dot Product 546

B.3.4 Scalar Triple Product 547

B.3.5 Vector Triple Product 547

Appendix C: Review of Particle Kinematics 549

C.1 Introduction 549

C.2 Cartesian Coordinates 549

C.3 Polar Coordinates 551

C.4 Normal-Tangential Coordinates 552

Index

Craig A. Kluever is C. W. LaPierre Professor of Mechanical and Aerospace Engineering, University of Missouri-Columbia, USA. He has industry experience as an aerospace engineer on the Space Shuttle program and has performed extensive research at the University of Missouri in collaboration with NASA involving trajectory optimization, space mission design, entry flight mechanics, and guidance and control of aerospace vehicles.