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Developed at the U.S. Air Force Academy, this teaching text is widely known and used throughout the astrodynamics and aerospace engineering communities. Completely revised and updated, this second edition takes into account new developments of the past four decades, especially regarding information technology. Central emphasis is placed on the use of the universal variable formulation, although classical methods are also discussed. The development of the basic two-body and n-body equations of motion serves as a foundation for all that follows. Subsequent topics include orbit determination and the classical orbital elements, coordinate transformations, and differential correction. The Kepler and Gauss problems are treated in detail, and two-body mechanics are applied to the ballistic missile problem. Perturbations, integration schemes and error, and analytic formulations of several common perturbations are introduced. Example problems and exercises appear throughout the text, along with photographs, diagrams, and drawings. Four helpful appendixes conclude the book.
About the Author
All of the authors are present or former members of the faculty of the Department of Astronautics at the U.S. Air Force Academy. Jerry E. White is still active, and William W. Saylor is the new team member.
Table of Contents
Preface About the Authors Chapter 1 Two-Body Orbital Mechanics 1.1 Historical Background and Basic Laws 1.2 Basic Laws 1 1.3 The N-Body Problem 1.4 The Two-Body Problem 1.5 Constants of Motion 1.6 The Trajectory Equation 1.7 Relating E and h to the Geometry of an Orbit 1.8 The Elliptical Orbit 1.9 The Circular Orbit 1.10 The Parabolic Orbit 1.11 The Hyperbolic Orbit 1.12 Canonical Units Chapter 2 Orbit Determination from Observations 2.1 Historical Background 2.2 Coordinate Systems 2.3 Classical Orbital Elements 2.4 Determining the Orbital Elements from r and v 2.5 Determining r and v from the Orbital Elements 2.6 Coordinate Transformations 2.7 Orbit Determination from a SingularRadar Observation 2.8 SEZ to IJK Transformation Using an Ellipsoid Earth Model 2.9 The Measurement of Time 2.10 Orbit Determination from Three Position Vectors 2.11 Orbit Determination from Optical Sightings 2.12 Improving a Preliminary Orbit by Differential Correct 2.13 Space Surveillance 2.14 Ground Track of a Satellite Chapter 3 Basic Orbital Maneuvers 3.1 Historical Background 3.2 Low-Altitude Earth Orbits 3.3 High-Altitude Earth Orbits 3.4 In-Plane Orbit Changes 3.5 Out-of-Plane Orbit Changes Chapter 4 Position and Velocity as a Function of Time 4.1 Historical Background 4.2 Time-of-Flight as a Function of Eccentric Anomaly 4.3 A Universal Formulation for Time-of-Flight 4.4 The Prediction Problem 4.5 Implementing the Universal Variable Formulation 4.6 Classical Formulations of the Kepler Problem Chapter 5 Orbit Determination from Two Positions and Time 5.1 Historical Background 5.2 The Gauss Problem—General Methods of Solution 5.3 Solutions of the Gauss Problem via Universal Variables 5.4 The p-Iteration Method 5.5 The Gauss Problem Using the f and g Series 5.6 The Original Gauss Method 5.7 Practical Applications of the Gauss Problem—Intercept and Rendezvous 5.8 Determination of Orbit from Sighting Directions at Station Chapter 6 Ballistic Missile Trajectories 6.1 Historical Background 6.2 The General Ballistic Missile Problem 6.3 Effect of Launching Errors on Range 6.4 The Effect of Earth Rotation Chapter 7 Lunar Trajectories 7.1 Historical Background 7.2 The Earth-Moon System 7.3 Simple Earth-Moon Trajectories 7.4 The Patched-Conic Approximation 7.5 Noncoplanar Lunar Trajectories Chapter 8 Interplanetary Trajectories 8.1 Historical Background 8.2 The Solar System 8.3 The Patched-Conic Approximation 8.4 Noncoplanar Interplanetary Trajectories 8.5 Planetary Flybys Chapter 9 Perturbations 9.1 Historical Background 9.2 Cowell’s Method 9.3 Encke’s Method 9.4 Variation of Parameters or Elements 9.5 Comments on Integration Schemes and Errors 9.6 Numerical Integration Methods 9.7 Analytic Formulations of Perturbative Accelerations Chapter 10 Special Topics 10.1 Historical Background 10.2 General Perturbation Models 10.3 NORAD Propagators and Two-Line Element Sets 10.4 Relative Motion of Satellites Appendix A Astrodynamic Constants Appendix B Vector Review B.1 Definitions B.2 Vector Operations B.3 Velocity Appendix C Gauss Problem Appendix D Proposed Three-Line Element Set Definition Index