Table of Contents

Preface Chapter 1 TWO-BODY ORBITAL MECHANICS 1.1 Historical Background and Basic Laws 1.2 The N-Body Problem 1.3 The Two-Body Problem 1.4 Constants of the Motion 1.5 The Trajectory Equation 1.6 Relating E and h to the Geometry of an Orbit 1.7 The Elliptical Orbit 1.8 The Circular Orbit 1.9 The Parabolic Orbit 1.10 The Hyperbolic Orbit 1.11 Canonical Units Exercises List of References 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 Single Radar 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 Correction 2.13 Space Survelliance 2.14 Type and Location of Sensors 2.15 Ground Track of a Satellite Exercises List of References Chapter 3 BASIC ORBITAL MANEUVERS 3.1 Low Altitiude Earth Orbits 3.2 High Altitude Earth Orbits 3.3 In-Plane Orbit Changes 3.4 Out-Of-Plane Orbit Changes Exercises List of References 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 Fomulation for Time-of-Flight 4.4 The Prediction Problem 4.5 Implementing the Universal Variable Formulation 4.6 Classical Formulations of the Kepler Problem Exercises List of References Chapter 5 ORBIT DETERMINATION FROM TWO POSITIONS AND TIME 5.1 Historical Background 5.2 The Gauss Problem - General Methods of Solution 5.3 Solution 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 Exercises List of References 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 Exercises List of References 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 Non-Coplanar Lunar Trajectories Exercises List of References Chapter 8 INTERPLANETARY TRAJECTORIES 8.1 Historical Background 8.2 The Solar System 8.3 The Patched-Conic Approximation 8.4 Non-Coplanar Interplanetary Trajectories Exercises List of References Chapter 9 PERTURBATIONS 9.1 Introduction and 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 Formulation of Perturbative Accelerations Exercises List of References Appendix A Astrodynamic Constants Appendix B Miscellaneous Constants and Conversions Appendix C Vector Review Appendix D Suggested Projects Index