Klappentext

Introduction to Orbital Mechanics: A Practical Approach for Engineers presents all the essential elements of orbital mechanics, with a treatment that is direct and progressive. Suitable for use as in either a 14-week semester or a 10-week academic quarter, this textbook is an ideal introduction for students because it provides a thorough overview of the underlying fundamentals while still remaining concise and approachable in its coverage. The topics addressed include a historical overview of orbital mechanics and the essential physical foundations of orbital motion (the 2-body problem first, with multi-body problems introduced later in the text). Orbital motion is developed in both 2- and 3-dimensions, and the time problem is addressed from both mathematical and geometric perspectives. Orbital maneuvers and interplanetary trajectories and planetary encounters are presented. Methods for orbit determination are surveyed, with any needed detailed derivations provided in an appendix. The fundamentals of rockets and spacecraft propulsion are also introduced. Finally, there will be discussion of practical considerations including aerodynamic drag and launch dynamics. Example problems are included throughout each chapter in the book, detailed derivations are included in the appendices for reference, and end of chapter problems reinforce student understanding.

Inhalt

About the Author ix

Preface xi

1 Introduction 1

1.1 Astronomy and the Development of Orbital Mechanics 1

1.2 The Development of the Orbital Mechanics of Spacecraft 7

1.3 A First Estimate of Planetary Distances 10

1.4 Examples of Non-Western Astronomy 12

1.4.1 Babylonian 12

1.4.2 Chinese 13

1.4.3 Mayan 14

1.5 Problem 15

2 Orbits and Trajectories 17

2.1 Gravitational Forces, the 2-Body Model and Newton's "Laws" of Motion 17

2.2 Further Justification, and Limitations, of the 2-Body Model 19

2.3 The Governing Equation for 2-Body Orbital Motion 21

2.4 Conservation "Laws" of Angular Momentum and Energy 23

2.4.1 Table of Some Useful Vector Identities 23

2.4.2 Conservation of Specific Angular Momentum 24

2.4.3 Conservation of Specific Mechanical Energy 25

2.5 The Orbit Equation 27

2.6 The Geometry of 2-Body Orbits and Trajectories 28

2.6.1 Elliptical Orbits 29

2.6.2 Parabolic Trajectories 32

2.6.3 Relationships Between the Specific Mechanical Energy and Specific Angular Momentum

and the Geometry and Velocities of an Orbit 32

2.6.4 Hyperbolic Trajectories 35

2.6.5 "Degenerate" Cases 40

2.7 Problems 41

3 Elapsed Time and Position on Orbits and Trajectories 45

3.1 Circular Orbits 45

3.2 Elliptical Orbits 46

3.2.1 The Geometric Method 46

3.2.2 The Analytical Method 50

3.2.3 Orbits with Periapsis Passage 52

3.2.4 Inverse Problem 53

3.3 Parabolic Trajectories 55

3.4 Hyperbolic Trajectories 55

3.4.1 The Geometric Method 56

3.4.2 The Analytical Method 57

3.5 Problems 59

4 Orbits in Three Dimensions 65

4.1 Three-Dimensional Orbital Elements 65

4.2 Reference Frames 69

4.2.1 Heliocentric Reference Frame 69

4.2.2 Geocentric Reference Frame 71

4.2.3 Perifocal Reference Frame 72

4.2.4 Topocentric Reference Frame 73

4.3 Coordinate Frame Transformations 73

4.3.1 Transformations Between Perifocal and Geocentric Coordinates 76

4.4 Problems 80

5 Orbital Maneuvers 83

5.1 Impulsive Maneuvers 83

5.2 The Hohmann Transfer 84

5.3 Limiting Geometries for Transfer Between Two Orbits 86

5.4 Bi-Elliptic Hohmann Transfer 87

5.5 Phasing Maneuver 90

5.6 General Transfer 91

5.7 Chase Maneuver 94

5.8 Apse Line Rotation 95

5.9 Plane Changes 97

5.10 Combined Maneuvers 99

5.11 Problems 99

6 Interplanetary Trajectories and Maneuvers 103

6.1 Planetary Phasing 103

6.2 Patched-Conic Approximation 105

6.3 Sphere of Influence Concept 106

6.4 Earth-Departure Trajectories 108

6.5 Planetary Hohmann Transfers 109

6.6 General Planetary Approach 112

6.7 Planetary Encounters 115

6.8 Problems 120

7 Earth Satellites and Ground Tracks 123

7.1 Satellite Ground Tracks 123

7.2 Earth Rotation Effects 124

7.3 Geosynchronous/Geostationary Orbits 127

7.4 Orbital Perturbations - Gravitational Effects 130

7.5 Orbital Perturbations - Atmospheric Drag Effects 136

7.6 Problems 139

8 Methods for Orbit Determination 141

8.1 Simultaneous Velocity and Radius Vectors Known 141

8.2 Three Position Vectors Known 141

8.3 Lambert's Problem (Two Vector Positions Plus Times Known) 145

8.4 Topo-Based Systems 148

8.4.1 Range, Azimuth, and Elevation (and Their Rates) Known 148

8.4.2 Azimuths and Elevations Known at Multiple Times 150

8.5 Problems 152

9 Relative Motion and Restricted 3-Body Problem 155

9.1 Relative Motion 155

9.2 Restricted 3-Body Problem and Earth-Moon Trajectories 161

9.3 Restricted 3-Body Problem - Whole-Field Solution 164

9.4 Problems 169

10 Rocket Fundamentals and Space Propulsion 171

10.1 Principles of Rocket Thrust 171

10.2 Rocket Performance 174

10.3 Staging 177

10.4 Sounding Rockets 181

10.5 Electric Spacecraft Propulsion 183

10.6 Low Thrust Maneuvers for Orbit Raising 190

10.7 Problems 191

Appendix 1 Solar System Orbital Properties 195

Index 000