Fundamentals of Astrodynamics and Applications

Transcription

1 Fundamentals of Astrodynamics and Applications Third Edition David A. Vallado with technical contributions by Wayne D. McClain Space Technology Library Published Jointly by Microcosm Press Hawthorne, CA Springer New York, NY

2 Vll Chapter 1 Chapter 2 Chapter 3 Equations of Motion Table of Contents 1.1 History.1.1 Ancient Era. 1.2 The Copernican Revolution.1.3 Kepler's Laws.1.4 Newton's Laws.1.5 Other Early Astrodynamic Contributions 1.2 Geometry of Conic Sections.2.1 Basic Parameters 1.3 Two-Body Equation.3.1 Assumptions for the Two-Body Equation.3.2 Specific Angular Momentum.3.3 Specific Mechanical Energy.3.4 Kepler's First Law (Trajectory Equation).3.5 Kepler's Second and Third Laws.3.6 Velocity Formulas 1.4 Three-body and «-body Equations Inertial, Relative, and Barycentric Formulas Ten Known Integrals General Three-Body Problem Kepler's Equation and Kepler's Problem 2.1 Historical Background 2.2 Kepler's Equation Alternate Formulation for Eccentric Anomaly Formulation for the Parabolic Anomaly Formulation for the Hyperbolic Anomaly Universal Formulation Solutions of Kepler's Equation Summary and Related Formulas 2.3 Kepler's Problem Solution Techniques 2.4 Satellite State Representations Classical Orbital Elements (Keplerian) Two-line Element Sets Other Element Sets Canonical Elements 2.5 Application: Orbital Elements from r and v 2.6 Application: r and v from Orbital Elements 2.7 Application: Groundtracks 2.8 Application: Find Time of Flight (FINDTOF) Coordinate and Time Systems 3.1 Historical Background 3.2 The Earth Location Parameters Shape of the Earth Gravitational Model

3 Vlll 3.3 Coordinate Systems Interplanetary Systems Earth-based Systems Satellite-based Systems Coordinate Transformations Coordinate Rotation Rotating Transformations Common Transformations Application: Converting UK (ECEF) to Latitude and Longitude Time Solar Time and Universal Time Sidereal Time Atomic Time Dynamical Time Coordinate Time Conversions Time Conversions DMS to Rad / Rad to DMS HMS to Rad / Rad to HMS HMStoTimeofDay/TimeofDaytoHMS YMD to Day of Year/Day of Year to YMD YMDHMStoDays/DaystoYMDHMS Julian Date to Gregorian Date Transforming Celestial and Terrestrial Coordinates IAU-2000 Resolutions Velocity Transformations IAU-76 / FK5 Reduction Other Reductions Computational Considerations Earth Models and Constants Canonical Units 242 Chapter 4 Observations Introduction Obtaining Data Quantity of Data : Types of Data Example Applications Introduction to Sensor Systems Observation Transformations Geocentric Right Ascension and Declination Topocentric Right Ascension and Declination Azimuth-Elevation Practical Az-El Conversions Transformations for Ecliptic Latitude and Longitude Practical Aspects of Surveillance 274 Chapter 5 Celestial Phenomena Solar Phenomena Application: Sun Position Vector Application: Sunrise, Sunset, and Twilight Times 283

4 IX 5.2 Lunar Phenomena Application: Moon Position Vector Application: Moon Rise and Set Times Phases of the Moon Celestial Applications Application: Planetary Ephemerides Eclipses Application: Sight and Light Ground Illumination Miscellaneous Phenomena 313 Chapter 6 Orbital Maneuvering Historical Background Introduction Coplanar Maneuvers Hohmann and Bi-elliptic Transfers Comparing Hohmann and Bi-elliptic Transfers Transfers Using the One-Tangent Burn General Transfers Noncoplanar Transfers Introduction Inclination-Only Changes Changes in the Right Ascension of the Ascending Node Changes to Inclination and the Ascending Node Combined Maneuvers Minimum-Inclination Maneuvers Fixed-Al? Maneuvering Circular Rendezvous Circular Coplanar Phasing Circular Noncoplanar Phasing Continuous-Thrust Transfers Introduction Orbit Raising Low-Thrust, Noncoplanar Transfers Relative Motion Position Solutions for Nearly Circular Orbits Trend Analysis Accuracy Analysis 4 Chapter 7 Initial Orbit Determination Historical Background Observations of Range, Azimuth, and Elevation Application: SITE-TRACK Angles-only Observations Laplace's Method Gauss's Technique Double r-iteration Mixed Observations Range and Range-Rate Processing Range-only Processing 448

5 7.5 Three Position Vectors and Time Gibbs Method Herrick-Gibbs Two Position Vectors and Time Lambert's Problem Lambert Minimum Energy Lambert Gauss's Solution Lambert's Problem Thome's Soluton Lambert Universal Variables Lambert Solution Battin Method Application: Targeting Problem 495 Chapter 8 Special Perturbation Techniques Historical Background Introduction to Perturbations Encke's Formulation Cowell's Formulation Numerical Integration Methods Implementing an Integrator and Determining Step Size Disturbing Forces Gravity Field of a Central Body Atmospheric Drag Third-Body Perturbations Solar-Radiation Pressure Other Perturbations Forming Numerical Solutions Application: Simplified Acceleration Model Application: Complex Acceleration Model Practical Considerations Verifying and Validating the Propagator Physical Data and Sources 597 Chapter 9 General Perturbation Techniques Historical Background Introduction The Method of Perturbations ' Variation of Parameters Lagrangian VOP (Conservative Effects) Gaussian VOP (Nonconservative and Conservative Effects) Hamilton's Formulation Disturbing-Potential Formulations Gravity Potential in Terms of the Satellite's Orbital Elements Third-Body Potential in Terms of the Satellite's Orbital Elements Tidal-Motion Potential in terms of the Satellite's Orbital Elements Linearized Perturbations and Effects Central-Body Analysis Drag Analysis Third-Body Analysis Solar-Radiation Analysis Forming Analytical Solutions Application: Perturbed Two-Body Propagation 686