Orbital Mechanics, Third Edition (AIAA Education Series)

Designed to be used as a graduate student textbook and a reference for the professional, this third edition is structured to make it easier for users to look up the things they need to know. It includes contemporary developments in space exploration (eg, Galileo, Cassini, Mars Odyssey missions). Also, the chapter on space debris has been rewritten to reflect developments in that area. The chapters cover basic aspects off orbital mechanics, from celestial relationships to the problems of space debris. The book is written in language that should be familiar to space professionals and graduate students, with all of the equations, diagrams, and graphs provided. The accompanying CD-ROM includes "HW Solutions" which presents a range of viewpoints and guidelines for solving selected problems inthe text; "Orbital Calculator", which provides an interactive environment for the generation of Keplerian orbits, orbital transfer manoeuvres, and animation of ellipses, hyperbolas, and interplanetary orbits; and "Orbital Mechanics Solutions". Front Matter......Page 1 Foreword......Page 3 About the Authors......Page 6 Preface......Page 5 Table of Contents......Page 0 Table of Contents......Page 7 1.1 A Historical Perspective......Page 12 1.2 Velocity and Acceleration......Page 16 Problems......Page 20 Selected Solutions......Page 21 2.1 Coordinate Systems......Page 22 2.2 Time Systems......Page 28 References......Page 31 3.2 General and Restricted Two-Body Problem......Page 32 3.3 Conservation of Mechanical Energy......Page 34 3.4 Conservation of Angular Momentum......Page 35 3.5 Orbital Parameters of a Satellite......Page 36 3.6 Orbital Elements......Page 39 Problems......Page 42 Selected Solutions......Page 44 4.1 General Relationships......Page 45 4.2 Solving Kepler's Equation......Page 50 4.3 A Universal Approach......Page 65 4.4 Expressions with f and g......Page 69 4.5 Summary of the Universal Approach......Page 70 4.6 The Classical Element Set......Page 71 4.8 Modified Classical to Cartesian Transformation......Page 72 4.9 Rectangular to Modified Classical Elements Transformation......Page 76 4.10 The Spherical (ADBARV) Coordinate System......Page 77 4.11 Rectangular to Spherical Transformation......Page 78 4.12 Spherical to Rectangular Transformation......Page 79 4.13 The Earth-Relative Spherical (LDBARV) Coordinate System......Page 80 4.14 Geodetic and Geocentric Altitudes......Page 81 4.15 Converting from Perigee/Apogee Radii to Perigee/Apogee Altitudes......Page 86 4.16 Converting from Perigee/Apogee Altitudes to Perigee/Apogee Radii......Page 87 References......Page 92 Problems......Page 93 Selected Solutions......Page 95 5.1 Orbital Energy......Page 96 5.2 Single-Impulse Maneuvers......Page 98 5.3 Single- and Two-Impulse Transfer Comparison for Coplanar Transfers Between Elliptic Orbits That Differ Only in Their Apsidal Orientation......Page 101 5.4 Hohmann Transfer......Page 103 5.5 The Bi-elliptic Transfer......Page 105 5.6 Restricted Three-Impulse Plane Change Maneuver for Circular Orbits......Page 108 5.7 General Three-Impulse Plane Change Maneuver for Circular Orbit......Page 112 5.8 Hohmann Transfer with Split-Plane Change......Page 113 5.10 Transfer Between Coplanar Elliptic Orbits......Page 116 Problems......Page 118 Selected Solutions......Page 124 6.2 Fixed-Impulse Transfers......Page 126 6.3 Finite-Duration Bums: Gravity Losses......Page 135 6.4 Very Low Thrust Transfers......Page 139 Problems......Page 141 Selected Solutions......Page 143 7.1 Space Rendezvous......Page 144 7.2 Terminal Rendezvous......Page 164 7.3 Applications of Rendezvous Equations......Page 171 7.4 An Exact Analytical Solution for Two-Dimensional Relative Motion......Page 181 7.5 Optimal Multiple-Impulse Rendezvous......Page 186 References......Page 190 Problems......Page 191 Selected Solutions......Page 192 8.1 A General Overview of Orbit Perturbations......Page 194 8.2 Earth Gravity Harmonics......Page 195 8.3 Lunisolar Gravitational Attractions......Page 196 8.4 Radiation Pressure Effects......Page 197 8.5 Atmospheric Drag......Page 198 8.6 Tidal Friction Effects and Mutual Gravitational Attraction......Page 199 References......Page 201 9.1 Equations of Motion......Page 202 9.2 Methods of Solution......Page 204 9.3 Potential Theory......Page 211 9.4 More Definitions of Gravity Harmonics......Page 213 9.5 Perturbations Due to Oblateness (J_2)......Page 216 9.6 Integration of the Equations of Variation......Page 218 References......Page 222 10.1 Earth's Oblateness (J_2) Effects......Page 223 10.2 Critical Inclination......Page 225 10.3 Sun-Synchronous Orbits......Page 226 10.4 J_3 Effects and Frozen Orbits......Page 228 10.5 Earth's Triaxiality Effects and East-West Stationkeeping......Page 229 10.6 Third-Body Perturbations and North/South Stationkeeping......Page 230 10.7 Solar-Radiation-Pressure Effects......Page 231 10.8 Atmospheric Drag Effects......Page 235 10.9 Tidal Friction Effects......Page 238 10.10 Long-Term Inclination Variations......Page 241 References......Page 245 Problems......Page 246 Selected Solutions......Page 248 11.1 Launch Window Considerations......Page 249 11.2 Time of Event Occurrence......Page 261 11.3 Ground-Trace Considerations......Page 262 11.4 Highly Eccentric, Critically Inclined Q = 2 Orbits (Molniya)......Page 264 11.5 Frozen Orbits......Page 267 References......Page 271 12.1 Introduction......Page 273 12.2 Historical Background......Page 274 12.3 Important Concepts......Page 282 12.4 Lunar Trajectories......Page 287 12.5 Analytical Approximations......Page 288 12.7 Interplanetary Trajectories......Page 295 12.8 Galileo Mission......Page 302 12.9 Cassini-Huygens Mission to Saturn and Titan......Page 304 12.10 Mars Odyssey Mission......Page 306 Problems......Page 307 Selected Solutions......Page 308 13.1 Introduction......Page 309 13.2 Space Debris Environment: Low Earth Orbit......Page 310 13.3 Debris Measurements......Page 311 13.4 Space Debris Environment: Geosynchronous Equatorial Orbit......Page 315 13.5 Spatial Density......Page 318 13.6 Collision Hazard Assessment Methods......Page 323 13.7 Collision Hazards Associated with Orbit Operations......Page 328 13.8 Debris Cloud Modeling......Page 330 13.9 Lifetime of Nontrackable Debris......Page 335 13.10 Methods of Debris Control......Page 336 13.11 Shielding......Page 337 13.12 Collision Avoidance......Page 338 References......Page 340 14.2 The Edelbaum Low-Thrust Orbit-Transfer Problem......Page 343 14.3 The Full Six-State Formulation Using Nonsingular Equinoctial Orbit Elements......Page 362 14.4 Orbit Transfer with Continuous Constant Acceleration......Page 380 14.5 Orbit Transfer with Variable Specific Impulse......Page 397 Appendix: The Partials of the M Matrix......Page 407 References......Page 417 15.1 Coverage from a Single Satellite......Page 419 15.2 Design of Optimal Satellite Constellations for Continuous Zonal and Global Coverage......Page 437 15.3 Considerations in Selecting Satellite Constellations......Page 447 15.4 Nontypical Coverage Patterns......Page 450 References......Page 454 Problems......Page 456 Selected Solutions......Page 458 I......Page 461 S......Page 462 Z......Page 463 Annotation Designed To Be Used As A Graduate Student Textbook And A Ready Reference For The Busy Professional, This Third Edition Of Orbital Mechanics Is Structured So That You Can Easily Look Up The Things You Need To Know. This Edition Includes More Recent Developments In Space Exploration (e.g. Galileo, Cassini, Mars Odyssey Missions). Also, The Chapter On Space Debris Was Rewritten To Reflect New Developments In That Area. The Well-organized Chapters Cover Every Basic Aspect Of Orbital Mechanics, From Celestial Relationships To The Problems Of Space Debris. The Book Is Clearly Written In Language Familiar To Aerospace Professionals And Graduate Students, With All Of The Equations, Diagrams, And Graphs You Would Like To Have Close At Hand. An Updated Software Package On Cd-rom Includes: Hw Solutions, Which Presents A Range Of Viewpoints And Guidelines For Solving Selected Problems In The Text; Orbital Calculator, Which Provides An Interactive Environment For The Generation Of Keplerian Orbits, Orbital Transfer Maneuvers, And Animation Of Ellipses, Hyperbolas, 'and Interplanetary Orbits; And Orbital Mechanics Solutions. Edited By Vladimir A. Chobotov. Includes Bibliographical References And Index. Designed to be used as a graduate student textbook and a reference for the professional, this third edition is structured to make it easier to use. It includes contemporary developments in space exploration and covers developments in the area concerning space debris.