About the Author xi Preface xiii Acknowledgments xvii 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 Periods 10 1.4 Examples of Non-Western Astronomy 12 1.4.1 Babylonian 12 1.4.

2 Chinese 13 1.4.3 Mayan 15 1.5 Problem 16 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 Conservation of Specific Angular Momentum 24 2.4.2 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 Energy and Angular Momentum and the Eccentricity 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 Geometric Method - Elliptical Orbits 46 3.2.2 Analytical Method - Elliptical Orbits 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 Geometric Method - Hyperbolic Trajectories 56 3.4.

2 Analytical Method - Hyperbolic Trajectories 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, Geocentric, and Topocentric 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 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 128 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 (Gibbs''/Gauss'' Method) 141 8.3 Lambert''s Problem (Two Vector Positions Plus Times Known) 145 8.4 Topocentric-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 the 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 Properties 195 Index 197.