Satellite Orbits : Models, Methods and Applications.

Intro -- Satellite Orbits -- Preface -- Contents -- 1. Around theWorld in a Hundred Minutes -- 1.1 A Portfolio of Satellite Orbits -- 1.1.1 Low-Earth Orbits -- 1.1.2 Orbits of Remote Sensing Satellites -- 1.1.3 Geostationary Orbits -- 1.1.4 Highly Elliptical Orbits -- 1.1.5 Constellations -- 1.2 Navigating in Space -- 1.2.1 Tracking Systems -- 1.2.2 A Matter of Effort -- 2. Introductory Astrodynamics -- 2.1 General Properties of the Two-Body Problem -- 2.1.1 Plane Motion and the Law of Areas -- 2.1.2 The Form of the Orbit -- 2.1.3 The Energy Integral -- 2.2 Prediction of Unperturbed Satellite Orbits -- 2.2.1 Kepler's Equation and the Time Dependence of Motion -- 2.2.2 Solving Kepler's Equation -- 2.2.3 The Orbit in Space -- 2.2.4 Orbital Elements from Position and Velocity -- 2.2.5 Non-Singular Elements -- 2.3 Ground-Based Satellite Observations -- 2.3.1 Satellite Ground Tracks -- 2.3.2 Satellite Motion in the Local Tangent Coordinate System -- 2.4 Preliminary Orbit Determination -- 2.4.1 Orbit Determination from Two Position Vectors -- 2.4.2 Orbit Determination from Three Sets of Angles -- Exercises -- Exercise 2.1 (Orbit raising using Hohmann transfer) -- Exercise 2.2 (Kepler's equation) -- Exercise 2.3 (Osculating Elements) -- Exercise 2.4 (Topocentric satellitemotion) -- Exercise 2.5 (Sun-synchronous Repeat Orbits) -- Exercise 2.6 (Initial Orbit Determination) -- 3. Force Model -- 3.1 Introduction -- 3.2 Geopotential -- 3.2.1 Expansion in Spherical Harmonics -- 3.2.2 Some Special Geopotential Coefficients -- 3.2.3 Gravity Models -- 3.2.4 Recursions -- 3.2.5 Acceleration -- 3.3 Sun and Moon -- 3.3.1 Perturbing Acceleration -- 3.3.2 Low-Precision Solar and Lunar Coordinates -- 3.3.3 Chebyshev Approximation -- 3.3.4 JPL Ephemerides -- 3.4 Solar Radiation Pressure -- 3.4.1 Eclipse Conditions -- 3.4.2 Shadow Function -- 3.5 Atmospheric Drag.

3.5.1 The Upper Atmosphere -- 3.5.2 The Harris-Priester Density Model -- 3.5.3 The Jacchia 1971 Density Model -- 3.5.4 A Comparison of Upper Atmosphere Density Models -- 3.5.5 Prediction of Solar and Geomagnetic Indices -- 3.6 Thrust Forces -- 3.7 Precision Modeling -- 3.7.1 Earth Radiation Pressure -- 3.7.2 Earth Tides -- 3.7.3 Relativistic Effects -- 3.7.4 Empirical Forces -- Exercises -- Exercise 3.1 (Gravity Field) -- Exercise 3.2 (Moon ephemerides) -- Exercise 3.3 (Accelerations) -- Exercise 3.4 (Orbit Perturbations) -- 4. Numerical Integration -- 4.1 Runge-Kutta Methods -- 4.1.1 Introduction -- 4.1.2 General Runge-Kutta Formulas -- 4.1.3 Stepsize Control -- 4.1.4 Runge-Kutta-Nystr�om Methods -- 4.1.5 Continuous Methods -- 4.1.6 Comparison of Runge-Kutta Methods -- 4.2 Multistep Methods -- 4.2.1 Introduction -- 4.2.2 Adams-Bashforth Methods -- 4.2.3 Adams-Moulton and Predictor-Corrector Methods -- 4.2.4 Interpolation -- 4.2.5 Variable Order and Stepsize Methods -- 4.2.6 Stoermer and Cowell Methods -- 4.2.7 Gauss-Jackson or Second Sum Methods -- 4.2.8 Comparison of Multistep Methods -- 4.3 Extrapolation Methods -- 4.3.1 The Mid-Point Rule -- 4.3.2 Extrapolation -- 4.3.3 Comparison of Extrapolation Methods -- 4.4 Comparison -- Exercises -- Exercise 4.1 (4th-Order Runge-Kutta Method) -- Exercise 4.2 (4th-Order Gauss-Jackson Method) -- Exercise 4.3 (Stepsize Control for Eccentric Orbits) -- 5. Time and Reference Systems -- 5.1 Time -- 5.1.1 Ephemeris Time -- 5.1.2 Atomic Time -- 5.1.3 Relativistic Time Scales -- 5.1.4 Sidereal Time and Universal Time -- 5.2 Celestial and Terrestrial Reference Systems -- 5.3 Precession and Nutation -- 5.3.1 Lunisolar Torques and the Motion of the Earth's Rotation Axis -- 5.3.2 Coordinate Changes due to Precession -- 5.3.3 Nutation -- 5.4 Earth Rotation and Polar Motion.

5.4.1 Rotation About the Celestial Ephemeris Pole -- 5.4.2 Free Eulerian Precession -- 5.4.3 Observation and Extrapolation of Polar Motion -- 5.4.4 Transformation to the International Reference Pole -- 5.5 Geodetic Datums -- Exercises -- Exercise 5.1 (ICRSto ITRSTransformation) -- Exercise 5.2 (Velocity in the Earth-fixed Frame) -- Exercise 5.3 (Geodetic coordinates) -- 6. Satellite Tracking and ObservationModels -- 6.1 Tracking Systems -- 6.1.1 Radar Tracking -- 6.1.2 Laser Tracking -- 6.1.3 The Global Positioning System -- 6.2 Tracking Data Models -- 6.2.1 Transmitter and Receiver Motion -- 6.2.2 Angle Measurements -- 6.2.3 Range Measurements -- 6.2.4 Doppler Measurements -- 6.2.5 GPS Measurements -- 6.3 Media Corrections -- 6.3.1 Interaction of Radiation and Atmosphere -- 6.3.2 Tropospheric Refraction -- 6.3.3 Ionospheric Refraction -- Exercises -- Exercise 6.1 (Light-Time Iteration) -- Exercise 6.2 (Range Rate Modeling) -- Exercise 6.3 (User Clock Error from GPS Pseudorange) -- Exercise 6.4 (Tropospheric Refraction) -- 7. Linearization -- 7.1 Two-Body State Transition Matrix -- 7.1.1 Orbital-Elements Transition Matrix -- 7.1.2 Keplerian-to-Cartesian Partial Derivatives -- 7.1.3 Cartesian-to-Keplerian Partial Derivatives -- 7.1.4 The State Transition Matrix and Its Inverse -- 7.2 Variational Equations -- 7.2.1 The Differential Equation of the State Transition Matrix -- 7.2.2 The Differential Equation of the Sensitivity Matrix -- 0. 7.2.3 Form and Solution of the Variational Equations -- 7.2.4 The Inverse of the State Transition Matrix -- 7.3 Partial Derivatives of the Acceleration -- 7.3.1 Geopotential -- 7.3.2 Point-Mass Perturbations -- 7.3.3 Solar Radiation Pressure -- 7.3.4 Drag -- 7.3.5 Thrust -- 7.4 Partials of the Measurements with Respect to the StateVector -- 7.5 Partials with Respect to Measurement Model Parameters.

7.6 Difference Quotient Approximations -- Exercises -- Exercise 7.1 (State TransitionMatrix) -- 8. Orbit Determination and Parameter Estimation -- 8.1 Weighted Least-Squares Estimation -- 8.1.1 Linearization and Normal Equations -- 8.1.2 Weighting -- 8.1.3 Statistical Interpretation -- 8.1.4 Consider Parameters -- 8.1.5 Estimation with A Priori Information -- 8.2 Numerical Solution of Least-Squares Problems -- 8.2.1 QR Factorization -- 8.2.2 Householder Transformations -- 8.2.3 Givens Rotations -- 8.2.4 Singular Value Decomposition -- 8.3 Kalman Filtering -- 8.3.1 Recursive Formulation of Least-Squares Estimation -- 8.3.2 Sequential Estimation -- 8.3.3 Extended Kalman Filter -- 8.3.4 Factorization Methods -- 8.3.5 Process Noise -- 8.4 Comparison of Batch and Sequential Estimation -- Exercises -- Exercise 8.1 (Givens Rotations) -- Exercise 8.2 (Least-Squares Orbit Determination) -- Exercise 8.3 (Orbit Determination by Extended Kalman Filter) -- 9. Applications -- 9.1 Orbit Determination Error Analysis -- 9.1.1 A Linearized Orbit Model -- 9.1.2 Consider Covariance Analysis -- 9.1.3 The GEODA Program -- 9.1.4 Case Studies -- 9.2 Real-Time Orbit Determination -- 9.2.1 Model and Filter Design -- 9.2.2 The RTOD Program -- 9.2.3 Case Studies -- 9.3 Relay Satellite Orbit Determination -- 9.3.1 Mathematical Models -- 9.3.2 The TDRSOD Program -- 9.3.3 Case Study -- Appendix A -- A.1 Calendrical Calculations -- A.1.1 Modified Julian Date from the Calendar Date -- A.1.2 Calendar Date from the Modified Julian Date -- A.2 GPS Orbit Models -- A.2.1 Almanac Model -- A.2.2 Broadcast Ephemeris Model -- Appendix B -- B.1 Internet Resources -- B.2 Source Codes on Springer's Extra Materials Server -- B.2.1 Contents -- B.2.2 System Requirements -- B.2.3 Executing the Programs -- B.2.4 Compilation and Linking -- B.2.5 Index of Library Functions -- List of Symbols.

References -- Index.

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