Satellite Orbits: Models, Methods, and ApplicationsSatellite Orbits -Models, Methods, and Applications has been written as a compre hensive textbook that guides the reader through the theory and practice of satellite orbit prediction and determination. Starting from the basic principles of orbital mechanics, it covers elaborate force models as weH as precise methods of satellite tracking and their mathematical treatment. A multitude of numerical algorithms used in present-day satellite trajectory computation is described in detail, with proper focus on numerical integration and parameter estimation. The wide range of levels provided renders the book suitable for an advanced undergraduate or gradu ate course on spaceflight mechanics, up to a professional reference in navigation, geodesy and space science. Furthermore, we hope that it is considered useful by the increasing number of satellite engineers and operators trying to obtain a deeper understanding of flight dynamics. The idea for this book emerged when we realized that documentation on the methods, models and tools of orbit determination was either spread over numerous technical and scientific publications, or hidden in software descriptions that are not, in general, accessible to a wider community. Having worked for many years in the field of spaceflight dynamics and satellite operations, we tried to keep in c10se touch with questions and problems that arise during daily work, and to stress the practical aspects of orbit determination. Nevertheless, our interest in the underlying physics motivated us to present topics from first principles, and make the book much more than just a cookbook on spacecraft trajectory computation. |
Contents
Around the World in a Hundred Minutes | 1 |
111 LowEarth Orbits | 2 |
112 Orbits of Remote Sensing Satellites | 3 |
113 Geostationary Orbits | 4 |
114 Highly Elliptical Orbits | 6 |
115 Constellations | 7 |
12 Navigating in Space | 8 |
122 A Matter of Effort | 10 |
542 Free Eulerian Precession | 182 |
543 Observation and Extrapolation of Polar Motion | 183 |
544 Transformation to the International Reference Pole | 185 |
Exercises | 190 |
Satellite Tracking and Observation Models | 193 |
612 Laser Tracking | 202 |
613 The Global Positioning System | 203 |
62 Tracking Data Models | 208 |
Introductory Astrodynamics | 15 |
21 General Properties of the TwoBody Problem | 16 |
212 The Form of the Orbit | 17 |
213 The Energy Integral | 19 |
22 Prediction of Unperturbed Satellite Orbits | 22 |
222 Solving Keplers Equation | 23 |
223 The Orbit in Space | 24 |
224 Orbital Elements from Position and Velocity | 28 |
225 NonSingular Elements | 29 |
23 GroundBased Satellite Observations | 32 |
232 Satellite Motion in the Local Tangent Coordinate System | 36 |
24 Preliminary Orbit Determination | 39 |
241 Orbit Determination from Two Position Vectors | 40 |
242 Orbit Determination from Three Sets of Angles | 43 |
Exercises | 47 |
Force Model | 53 |
32 Geopotential | 56 |
322 Some Special Geopotential Coefficients | 59 |
323 Gravity Models | 61 |
324 Recursions | 66 |
325 Acceleration | 68 |
33 Sun and Moon | 69 |
332 LowPrecision Solar and Lunar Coordinates | 70 |
333 Chebyshev Approximation | 73 |
334 JPL Ephemerides | 75 |
34 Solar Radiation Pressure | 77 |
341 Eclipse Conditions | 80 |
342 Shadow Function | 81 |
35 Atmospheric Drag | 83 |
351 The Upper Atmosphere | 86 |
352 The HarrisPriester Density Model | 89 |
353 The Jacchia 1971 Density Model | 91 |
354 A Comparison of Upper Atmosphere Density Models | 98 |
355 Prediction of Solar and Geomagnetic Indices | 102 |
36 Thrust Forces | 104 |
37 Precision Modeling | 107 |
372 Earth Tides | 108 |
373 Relativistic Effects | 110 |
374 Empirical Forces | 112 |
Exercises | 113 |
Numerical Integration | 117 |
41 RungeKutta Methods | 118 |
412 General RungeKutta Formulas | 120 |
413 Stepsize Control | 121 |
414 RungeKuttaNystrom Methods | 123 |
415 Continuous Methods | 127 |
416 Comparison of RungeKutta Methods | 129 |
42 Multistep Methods | 132 |
422 AdamsBashforth Methods | 134 |
423 AdamsMoulton and PredictorCorrector Methods | 136 |
424 Interpolation | 140 |
425 Variable Order and Stepsize Methods | 141 |
426 Stoermer and Cowell Methods | 143 |
427 Gauss Jackson or Second Sum Methods | 145 |
428 Comparison of Multistep Methods | 146 |
43 Extrapolation Methods | 147 |
432 Extrapolation | 148 |
433 Comparison of Extrapolation Methods | 150 |
44 Comparison | 151 |
Exercises | 154 |
Time and Reference Systems | 157 |
511 Ephemeris Time | 160 |
512 Atomic Time | 161 |
513 Relativistic Time Scales | 162 |
514 Sidereal Time and Universal Time | 165 |
52 Celestial and Terrestrial Reference Systems | 169 |
53 Precession and Nutation | 172 |
532 Coordinate Changes due to Precession | 174 |
533 Nutation | 178 |
54 Earth Rotation and Polar Motion | 181 |
622 Angle Measurements | 209 |
623 Range Measurements | 213 |
624 Doppler Measurements | 215 |
625 GPS Measurements | 217 |
63 Media Corrections | 219 |
632 Tropospheric Refraction | 221 |
633 Ionospheric Refraction | 225 |
Exercises | 229 |
Linearization | 233 |
71 TwoBody State Transition Matrix | 235 |
712 KepleriantoCartesian Partial Derivatives | 236 |
713 CartesiantoKeplerian Partial Derivatives | 238 |
714 The State Transition Matrix and Its Inverse | 239 |
72 Variational Equations | 240 |
722 The Differential Equation of the Sensitivity Matrix | 241 |
724 The Inverse of the State Transition Matrix | 243 |
73 Partial Derivatives of the Acceleration | 244 |
732 PointMass Perturbations | 247 |
733 Solar Radiation Pressure | 248 |
735 Thrust | 249 |
74 Partials of the Measurements with Respect to the State Vector | 250 |
75 Partials with Respect to Measurement Model Parameters | 252 |
76 Difference Quotient Approximations | 253 |
Exercises | 255 |
Orbit Determination and Parameter Estimation | 257 |
81 Weighted LeastSquares Estimation | 258 |
811 Linearization and Normal Equations | 260 |
812 Weighting | 262 |
813 Statistical Interpretation | 263 |
814 Consider Parameters | 265 |
815 Estimation with A Priori Information | 266 |
82 Numerical Solution of LeastSquares Problems | 268 |
822 Householder Transformations | 270 |
823 Givens Rotations | 272 |
824 Singular Value Decomposition | 274 |
83 Kalman Filtering | 276 |
831 Recursive Formulation of LeastSquares Estimation | 277 |
832 Sequential Estimation | 280 |
833 Extended Kalman Filter | 282 |
834 Factorization Methods | 283 |
835 Process Noise | 284 |
84 Comparison of Batch and Sequential Estimation | 286 |
Exercises | 289 |
Applications | 293 |
911 A Linearized Orbit Model | 294 |
912 Consider Covariance Analysis | 297 |
913 The GEODA Program | 299 |
914 Case Studies | 300 |
92 RealTime Orbit Determination | 303 |
922 The RTOD Program | 306 |
923 Case Studies | 307 |
93 Relay Satellite Orbit Determination | 312 |
932 The TDRSOD Program | 313 |
933 Case Study | 315 |
Appendix A | 319 |
A11 Modified Julian Date from the Calendar Date | 321 |
A 12 Calendar Date from the Modified Julian Date | 322 |
A2 GPS Orbit Models | 324 |
A21 Almanac Model | 325 |
A22 Broadcast Ephemeris Model | 326 |
Appendix B | 329 |
B2 The Enclosed CDROM | 330 |
B22 System Requirements | 331 |
B24 Compilation and Linking | 332 |
B25 Index of Library Functions | 335 |
List of Symbols | 339 |
347 | |
361 | |
Other editions - View all
Satellite Orbits: Models, Methods and Applications Oliver Montenbruck,Eberhard Gill Limited preview - 2012 |
Satellite Orbits: Models, Methods and Applications Oliver Montenbruck,Eberhard Gill No preview available - 2013 |
Satellite Orbits: Models, Methods and Applications Oliver Montenbruck,Eberhard Gill No preview available - 2011 |
Common terms and phrases
acceleration accuracy algorithm altitude angle antenna applied approximation atmospheric clock coefficients computation coordinate system covariance denotes density described difference differential equations Doppler Earth Earth's rotation eccentric anomaly eccentricity ecliptic Ephemeris equatorial equinox errors estimation evaluations exospheric force model frequency function geocentric geodetic geostationary satellites given GPS satellite gravity field ground station inertial ionospheric iteration Jacchia Kalman filter Kepler's equation Keplerian least-squares light-time correction longitude low-Earth mean anomaly multistep methods noise nutation observations obtained orbit determination orbital elements orbital plane parameters partial derivatives perigee perturbations polar motion polynomial position and velocity position vector priori pseudoranges range measurements range rate reference ellipsoid reference system refraction respect right ascension Runge-Kutta methods satellite orbit satellite's semi-major axis signal solar radiation pressure solution spacecraft TDRS temperature tracking trajectory transformation transition matrix values variational equations
Popular passages
Page 356 - Nerem. RS. Lerch. FJ. Marshall. JA. Pavlis. EC. Putney. BH. Tapley. BD. Eanes, RJ, Ries. JC, Schutz, BE, Shum, CK. Watkins. MM. Klosko. SM, Chan. JC, Luthcke. SB. Patel, GB. Pavlis. NK. Williamson. RG. Rapp. RH. Biancale. R., and Nouel, F. (1994). Gravity model development for TOPEX/POSEIDON: Joint Gravity Models 1 and 2.
Page 357 - Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, Austin, Texas...
Page 349 - On the Computation of the Spherical Harmonic Terms needed during the Numerical Integration of the Orbital Motion of an Artificial Satellite; Celestial Mechanics 2, 207-216 (1970).
Page 350 - Fehlberg, E.: Classical fifth-, sixth-, seventh-, and eighth-order RungeKutta formulas with step-size control, NASA Technical Report, NASA TR R-287, Oct.
Page 358 - A Simple, Efficient Starting Value for the Iterative Solution of Kepler's Equation,
Page 355 - Putney, BH, Christodoulidis, DC, Smith, DE, Felsentreger, TL, Sanchez, BV, Klosko, SM, Pavlis, EC, Martin, TV, Robbins, JW, Williamson, RG, Colombo, OL, Rowlands, DD, Eddy, WF, Chandler, NL, Rachlin, KE, Patel, GB, Bhati, S. and Chinn, DS, 1988, A New Gravitational Model for the Earth From Satellite Tracking Data: GEM-T1, Journal of Geophysical Research, 93(B6), 6169-6215.
Page 359 - Orientation of the JPL Ephemerides, DE200/LE200, to the Dynamical Equinox of J2000.