Fundamentals of Astrodynamics

Teaching text developed by U.S. Air Force Academy and designed as a first course emphasizes the universal variable formulation. Develops the basic two-body andn-body equations of motion; orbit determination; classical orbital elements, coordinate transformations; differential correction; more. Includes specialized applications to lunar and interplanetary flight, example problems, exercises. 1971 edition.

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