Fundamentals of Astrodynamics and Applications (The Space Technology Library)

by David A Vallado

• ISBN13: 9781881883128
• ISBN10: 1881883124
• Format: Paperback
• Copyright: 2001-05-21
• Publisher: MICROCOSM LIMITED

Table of Contents

Equations of Motion	1	(48)
History	1	(11)
Ancient Era	1	(6)
The Copernican Revolution	7	(2)
Kepler's Laws	9	(1)
Newton's Laws	10	(2)
Other Early Astrodynamic Contributions	12	(1)
Geometry of Conic Sections	12	(8)
Basic Parameters	12	(8)
Two-body Equation	20	(13)
Assumptions for the Two-Body Equation	23	(1)
Specific Angular Momentum	23	(2)
Specific Mechanical Energy	25	(2)
Kepler's First Law (Trajectory Equation)	27	(2)
Kepler's Second and Third Laws	29	(3)
Velocity Formulas	32	(1)
Three-body and n-body Equations	33	(16)
Inertial, Relative, and Barycentric Formulas	33	(4)
Ten Known Integrals	37	(3)
General Three-body Problem	40	(9)
Kepler's Equation and Kepler's Problem	49	(86)
Historical Background	49	(2)
Kepler's Equation	51	(36)
Alternate Formulation for Ecentric Anomaly	57	(1)
Formulation for the Parabolic Anomaly	58	(2)
Formulation for the Hyperbolic Anomaly	60	(6)
Universal Formulation	66	(5)
Solutions of Kepler's Equation	71	(14)
Summary and Related Formulas	85	(2)
Kepler's Problem	87	(16)
Solution Techniques	88	(15)
Satellite State Representations	103	(15)
Classical Orbital Elements (Keplerian)	104	(9)
2-line Element Sets	113	(3)
Equinoctial Elements	116	(1)
Canonical Elements	117	(1)
Application: Orbital Elements from r and v	118	(4)
Application: r and v from Orbital Elements	122	(4)
Application: Groundtracks	126	(4)
Application: Find Time of Flight (FindTOF)	130	(5)
Coordinate and Time Systems	135	(98)
Historical Background	135	(2)
The Earth	137	(14)
Location Parameters	139	(1)
Shape of the Earth	140	(7)
Gravitational Model	147	(4)
Coordinate Systems	151	(14)
Interplanetary Systems	156	(1)
Earth-based Systems	157	(4)
Satellite-based Systems	161	(4)
Coordinate Transformations	165	(14)
Coordinate Rotation	166	(5)
Rotating Transformations	171	(1)
Common Transformations	172	(2)
Application: Converting IJK To Latitude and Longitude	174	(5)
Time	179	(19)
Solar Time and Universal Time	182	(7)
Sidereal Time	189	(4)
Atomic Time	193	(1)
Dynamical Time	194	(4)
Time Conversions	198	(7)
DMS to Rad/Rad to DMS	199	(1)
HMS to Rad/Rad to HMS	200	(1)
HMS to Time of Day/Time of Day to HMS	201	(1)
YMD to Day of Year/Day of Year to YMD	201	(1)
YMDHMS to Days/Days to YMDHMS	202	(1)
Julian Date to Gregorian Date	203	(2)
Transforming Celestial and Terrestrial Coordinates	205	(23)
Non-rotating Origin	207	(4)
FK5 Reduction	211	(3)
Precession (FK5)	214	(2)
Nutation (FK5)	216	(3)
Sidereal Time (FK5)	219	(1)
Polar Motion (FK5)	219	(1)
Summary (FK5)	220	(7)
FK4 Reduction	227	(1)
Earth Models and Constants	228	(5)
Canonical Units	228	(5)
Observations	233	(30)
Introduction	233	(1)
Obtaining Data	234	(5)
Quantity of Data	237	(1)
Types of Data	238	(1)
Example Applications	239	(1)
Introduction to Sensor Systems	239	(5)
Observation Transformations	244	(19)
Geocentric Right Ascension and Declination	246	(2)
Topocentric Right Ascension and Declination	248	(2)
Azimuth-Elevation	250	(5)
Practical Az-El Conversions	255	(2)
Transformations for Ecliptic Latitude and Longitude	257	(6)
Celestial Phenomena	263	(40)
Solar Phenomena	263	(8)
Application: Sun Position Vector	263	(4)
Application: Sunrise, Sunset, and Twilight Times	267	(4)
Lunar Phenomena	271	(10)
Application: Moon Position Vector	272	(4)
Application: Moon Rise and Set Times	276	(4)
Phases of the Moon	280	(1)
Celestial Applications	281	(22)
Application: Planetary Ephemerides	281	(4)
Eclipses	285	(6)
Application: Sight and Light	291	(4)
Ground Illumination	295	(2)
Miscellaneous Phenomena	297	(6)
Orbital Maneuvering	303	(98)
Historical Background	303	(1)
Introduction	304	(1)
Coplanar Maneuvers	305	(18)
Hohmann and Bi-elliptic Transfers	308	(6)
Comparing Hohmann and Bi-elliptic Transfers	314	(3)
Transfers Using the One-Tangent Burn	317	(6)
General Transfers	323	(1)
Noncoplanar Transfers	323	(13)
Introduction	323	(5)
Inclination-Only Changes	328	(3)
Changes in the Longitude of Ascending Node	331	(3)
Changes to Inclination and Longitude of Ascending Node	334	(2)
Combined Maneuvers	336	(7)
Minimum-Inclination Maneuvers	336	(3)
Fixed-Dv Maneuvering	339	(4)
Circular Rendezvous	343	(13)
Circular Coplanar Phasing	343	(7)
Circular Noncoplanar Phasing	350	(6)
Continuous-Thrust Transfers	356	(16)
Introduction	357	(3)
Orbit Raising	360	(6)
Low-Thrust, Noncoplanar Transfers	366	(6)
Relative Motion	372	(29)
Position Solutions for Nearly Circular Orbits	377	(4)
Trend Analysis	381	(14)
Extending the Results	395	(6)
Initial Orbit Determination	401	(88)
Historical Background	401	(3)
Observations of Range, Azimuth, and Elevation	404	(7)
Application: Site-Track	404	(7)
Angles-only Observations	411	(16)
Laplace's Method	413	(4)
Gauss's Technique	417	(5)
Double r-iteration	422	(5)
Mixed Observations	427	(5)
Range and Range-Rate Processing	428	(2)
Range-only Processing	430	(2)
Three Position Vectors and Time	432	(13)
Gibbs Method	432	(7)
Herrick-Gibbs	439	(6)
Two Position Vectors and Time---Lambert's Problem	445	(23)
Lambert---Minimum Energy	447	(7)
Lambert---Gauss's Solution	454	(5)
Lambert---Universal Variables	459	(5)
Lambert Solution---Battin Method	464	(4)
Application: Targeting Problem	468	(21)
Special Perturbation Techniques	489	(76)
Historical Background	489	(1)
Introduction to Perturbations	490	(5)
Encke's Formulation	495	(2)
Cowell's Formulation	497	(1)
Numerical Integration Methods	498	(10)
Implementing an Integrator and Determining Step Size	506	(2)
Disturbing Forces	508	(40)
Gravity Field of a Central Body	509	(12)
Atmospheric Drag	521	(18)
Third-Body Perturbations	539	(4)
Solar-Radiation Pressure	543	(3)
Other Perturbations	546	(2)
Forming Numerical Solutions	548	(8)
Application: Simplified Acceleration Model	550	(3)
Application: Complex Acceleration Model	553	(3)
Practical Considerations	556	(9)
Validating the Propagator	556	(1)
Physical Data and Sources	557	(8)
General Perturbation Techniques	565	(108)
Historical Background	565	(4)
Introduction	569	(6)
The Method of Perturbations	573	(2)
Variation of Parameters	575	(18)
Lagrangian VOP (Conservative Effects)	577	(7)
Gaussian VOP (Nonconservative and Conservative Effects)	584	(9)
Hamilton's Formulation	593	(3)
Disturbing-Potential Formulations	596	(6)
Gravity Potential in Terms of the Satellite's Orbital Elements	597	(1)
Third-Body Potential in Terms of the Satellite's Orbital Elements	598	(3)
Tidal-Motion Potential in terms of the Satellite's Orbital Elements	601	(1)
Linearized Perturbations and Effects	602	(42)
Central-Body Analysis	602	(24)
Drag Analysis	626	(8)
Third-Body Analysis	634	(6)
Solar-Radiation Analysis	640	(4)
Forming Analytical Solutions	644	(8)
Application: Perturbed Two-body Propagation	645	(2)
Kozai's Method	647	(2)
Brouwer's Method	649	(2)
Operational Applications	651	(1)
Semianalytical Solutions	652	(6)
The Draper Semianalytical Satellite Theory (DSST)	653	(5)
Practical Considerations	658	(9)
Expected Accuracy of Propagation Techniques	658	(5)
Initial Conditions, Sources, and Conversions	663	(4)
Summary of Perturbation Effects	667	(6)
Orbit Determination and Estimation	673	(92)
Historical Background	673	(3)
Linear Least Squares	676	(17)
Error Analysis	681	(10)
Linear Weighted Least Squares	691	(2)
Nonlinear Least Squares	693	(8)
Application: Orbit Determination With Differential Correction	701	(12)
Calculating the Partial-Derivative Matrix (A)	703	(4)
Implementing Least-Squares Techniques	707	(6)
Sequential-Batch Least Squares	713	(5)
Kalman Filtering	718	(21)
Kalman Filter (Linear System)	726	(5)
Linearized Kalman Filter (LKF)	731	(2)
Extended Kalman Filter (EKF)	733	(3)
Successful Filtering Applications	736	(1)
Summary of Kalman Filters	737	(2)
Forming Differential Correction Solutions	739	(14)
Calculating the Matrices	739	(11)
Implementing Differential-Correction Solutions	750	(3)
Practical Considerations	753	(12)
Data	754	(3)
Update Intervals and Fit Spans	757	(2)
Analyzing the Results of Differential Corrections	759	(3)
Application: Detecting Maneuvers	762	(1)
Application: Predicting Reentry	762	(3)
Mission Analysis	765	(86)
Introduction	765	(3)
Satellite Populations	767	(1)
Mission Orbits	768	(6)
Stationkeeping	771	(2)
Mission Planning	773	(1)
Geometries for Surveillance and Reconnaissance	774	(7)
Designing and Maintaining Mission Orbits	781	(31)
Sun-Synchronous Orbits	782	(6)
Repeat-Groundtrack Orbits	788	(9)
Minimum Altitude Variation Orbits	797	(6)
Frozen-Orbit Eccentricity and Argument of Perigee	803	(2)
Application: Designing a Specialized Orbit	805	(7)
Navigation---the Global Positioning System	812	(13)
Historical Background	813	(2)
System Introduction	815	(2)
Signals from GPS Satellites	817	(8)
Predicting Satellite Look Angles	825	(10)
Predict Formulation	825	(5)
Rise/Set	830	(5)
Determining Close Approaches	835	(16)
Finding the Close-Approach Functions	837	(8)
Statistical Analysis	845	(6)
Appendix A Dictionary of Symbols	851	(14)
Appendix B Modeling the Atmosphere	865	(16)
B.1 Jacchia-Roberts Atmosphere	865	(9)
B.1.1 Evaluating Temperature	865	(2)
B.1.2 Robert's Corrections to Temperature	867	(1)
B.1.3 Evaluating Density	868	(1)
B.1.4 Robert's Corrections to Density	869	(5)
B.2 Russian GOST Atmosphere	874	(7)
Appendix C Mathematical Fundamentals	881	(22)
C.1 Introduction	881	(1)
C.2 Vector Fundamentals	881	(2)
C.3 Matrix Fundamentals	883	(1)
C.4 Trigonometric Fundamentals	884	(6)
C.4.1 Planar Trigonometry	886	(1)
C.4.2 Spherical Trigonometry	887	(3)
C.5 Numerical Techniques	890	(13)
C.5.1 Polynomial Solutions	890	(3)
C.5.2 Interpolation	893	(1)
C.5.3 Blending and Splining Techniques	894	(9)
Appendix D Constants and Expansions	903
D.1 Gravitational Coefficients	903
D.2 Planetary Constants	905
D.3 Reduction Coefficients	908
D.4 Planetary Ephemerides	911
D.5 Data Sources	915
D.6 Computer Programming	917