Orbital Mechanics, Third Edition Book

	Foreword	v
	Preface	vii
	About the Authors	ix
Chapter 1.	Basic Concepts	1
1.1	A Historical Perspective	1
1.2	Velocity and Acceleration	5
	Problems	9
	Selected Solutions	10
Chapter 2.	Celestial Relationships	11
2.1	Coordinate Systems	11
2.2	Time Systems	17
	References	20
Chapter 3.	Keplerian Orbits	21
3.1	Newton's Universal Law of Gravitation	21
3.2	General and Restricted Two-Body Problem	21
3.3	Conservation of Mechanical Energy	23
3.4	Conservation of Angular Momentum	24
3.5	Orbital Parameters of a Satellite	25
3.6	Orbital Elements	28
	References	31
	Problems	31
	Selected Solutions	33
Chapter 4.	Position and Velocity as a Function of Time	35
4.1	General Relationships	35
4.2	Solving Kepler's Equation	40
4.3	A Universal Approach	55
4.4	Expressions with f and g	59
4.5	Summary of the Universal Approach	60
4.6	The Classical Element Set	61
4.7	The Rectangular Coordinate System	62
4.8	Modified Classical to Cartesian Transformation	62
4.9	Rectangular to Modified Classical Elements Transformation	66
4.10	The Spherical (ADBARV) Coordinate System	67
4.11	Rectangular to Spherical Transformation	68
4.12	Spherical to Rectangular Transformation	69
4.13	The Earth-Relative Spherical (LDBARV) Coordinate System	70
4.14	Geodetic and Geocentric Altitudes	71
4.15	Converting from Perigee/Apogee Radii to Perigee/Apogee Altitudes	76
4.16	Converting from Perigee/Apogee Altitudes to Perigee/Apogee Radii	77
	References	82
	Problems	83
	Selected Solutions	85
Chapter 5.	Orbital Maneuvers	87
5.1	Orbital Energy	87
5.2	Single-Impulse Maneuvers	89
5.3	Single- and Two-Impulse Transfer Comparison for Coplanar Transfers Between Elliptic Orbits That Differ Only in Their Apsidal Orientation	92
5.4	Hohmann Transfer	94
5.5	The Bi-elliptic Transfer	96
5.6	Restricted Three-Impulse Plane Change Maneuver for Circular Orbits	99
5.7	General Three-Impulse Plane Change Maneuver for Circular Orbit	103
5.8	Hohmann Transfer with Split-Plane Change	104
5.9	Bi-elliptic Transfer with Split-Plane Change	107
5.10	Transfer Between Coplanar Elliptic Orbits	107
	References	109
	Problems	109
	Selected Solutions	115
Chapter 6.	Complications to Impulsive Maneuvers	117
6.1	N-Impulse Maneuvers	117
6.2	Fixed-Impulse Transfers	117
6.3	Finite-Duration Burns: Gravity Losses	126
6.4	Very Low Thrust Transfers	130
	Reference	132
	Problems	132
	Selected Solutions	134
Chapter 7.	Relative Motion in Orbit	135
7.1	Space Rendezvous	135
7.2	Terminal Rendezvous	155
7.3	Applications of Rendezvous Equations	162
7.4	An Exact Analytical Solution for Two-Dimensional Relative Motion	172
7.5	Optimal Multiple-Impulse Rendezvous	177
	References	181
	Problems	182
	Selected Solutions	183
Chapter 8.	Introduction to Orbit Perturbations	185
8.1	A General Overview of Orbit Perturbations	185
8.2	Earth Gravity Harmonics	186
8.3	Lunisolar Gravitational Attractions	187
8.4	Radiation Pressure Effects	188
8.5	Atmospheric Drag	189
8.6	Tidal Friction Effects and Mutual Gravitational Attraction	190
	References	192
Chapter 9.	Orbit Perturbations: Mathematical Foundations	193
9.1	Equations of Motion	193
9.2	Methods of Solution	195
9.3	Potential Theory	202
9.4	More Definitions of Gravity Harmonics	204
9.5	Perturbations Due to Oblateness (J[subscript 2])	207
9.6	Integration of the Equations of Variation	209
	References	213
Chapter 10.	Applications of Orbit Perturbations	215
10.1	Earth's Oblateness (J[subscript 2]) Effects	215
10.2	Critical Inclination	217
10.3	Sun-Synchronous Orbits	218
10.4	J[subscript 3] Effects and Frozen Orbits	220
10.5	Earth's Triaxiality Effects and East-West Stationkeeping	221
10.6	Third-Body Perturbations and North/South Stationkeeping	222
10.7	Solar-Radiation-Pressure Effects	223
10.8	Atmospheric Drag Effects	227
10.9	Tidal Friction Effects	230
10.10	Long-Term Inclination Variations	233
	References	237
	Problems	238
	Selected Solutions	240
Chapter 11.	Orbital Systems	241
11.1	Launch Window Considerations	241
11.2	Time of Event Occurrence	253
11.3	Ground-Trace Considerations	254
11.4	Highly Eccentric, Critically Inclined Q = 2 Orbits (Molniya)	256
11.5	Frozen Orbits	259
	References	263
Chapter 12.	Lunar and Interplanetary Trajectories	265
12.1	Introduction	265
12.2	Historical Background	266
12.3	Important Concepts	274
12.4	Lunar Trajectories	279
12.5	Analytical Approximations	280
12.6	Three-Dimensional Trajectories	287
12.7	Interplanetary Trajectories	287
12.8	Galileo Mission	294
12.9	Cassini-Huygens Mission to Saturn and Titan	296
12.10	Mars Odyssey Mission	298
	References	299
	Problems	299
	Selected Solutions	300
Chapter 13.	Space Debris	301
13.1	Introduction	301
13.2	Space Debris Environment: Low Earth Orbit	302
13.3	Debris Measurements	303
13.4	Space Debris Environment: Geosynchronous Equatorial Orbit	307
13.5	Spatial Density	310
13.6	Collision Hazard Assessment Methods	315
13.7	Collision Hazards Associated with Orbit Operations	320
13.8	Debris Cloud Modeling	322
13.9	Lifetime of Nontrackable Debris	327
13.10	Methods of Debris Control	328
13.11	Shielding	329
13.12	Collision Avoidance	330
	References	332
Chapter 14.	Optimal Low-Thrust Orbit Transfer	335
14.1	Introduction	335
14.2	The Edelbaum Low-Thrust Orbit-Transfer Problem	335
14.3	The Full Six-State Formulation Using Nonsingular Equinoctial Orbit Elements	354
14.4	Orbit Transfer with Continuous Constant Acceleration	372
14.5	Orbit Transfer with Variable Specific Impulse	389
Appendix	The Partials of the M Matrix	399
	References	409
Chapter 15.	Orbital Coverage	411
15.1	Coverage from a Single Satellite	411
15.2	Design of Optimal Satellite Constellations for Continuous Zonal and Global Coverage	429
15.3	Considerations in Selecting Satellite Constellations	439
15.4	Nontypical Coverage Patterns	442
	References	446
	Problems	448
	Selected Solutions	450
	Index	453
	Series Pages	457