Chapter 1 N-Body Problem 1 --
1.2 Equations of Motion for the n-Body Problem 4 --
1.3 Justification of the Two-Body Model 8 --
1.4 Two-Body Problem 11 --
1.6 Parabolic, Hyperbolic, and Rectilinear Orbits 16 --
1.7 Energy of the Orbit 17 --
Chapter 2 Position in Orbit as a Function of Time 25 --
2.2 Position and Time in an Elliptic Orbit 25 --
2.3 Solution for the Eccentric Anomaly 29 --
2.4 F and g Functions and Series 31 --
2.5 Position versus Time in Hyperbolic and Parabolic Orbits: Universal Variables 36 --
Chapter 3 Orbit in Space 46 --
3.2 Orbital Elements 46 --
3.3 Determining the Orbital Elements from r and v 50 --
3.4 Velocity Hodographs 55 --
Chapter 4 Three-Body Problem 60 --
4.2 Stationary Solutions of the Three-Body Problem 60 --
4.3 Circular Restricted Problem 65 --
4.4 Surfaces of Zero Velocity 66 --
4.5 Stability of the Equilibrium Points 66 --
4.6 Periodic Orbits in the Restricted Case 70 --
4.7 Invariant Manifolds 72 --
4.8 Special Solutions of the Problem 75 --
Chapter 5 Lambert's Problem 79 --
5.2 Transfer Orbits Between Specified Points 79 --
5.3 Lambert's Theorem 84 --
5.4 Properties of the Solutions to Lambert's Equation 86 --
5.5 Terminal Velocity Vectors 91 --
5.6 Applications of Lambert's Equation 94 --
5.7 Multiple-Revolution Lambert Solutions 95 --
Chapter 6 Rocket Dynamics 101 --
6.2 Rocket Equation 101 --
6.3 Solution of the Rocket Equation in Field-Free Space 103 --
6.4 Solution of the Rocket Equation with External Forces 107 --
6.5 Rocket Payloads and Staging 108 --
6.6 Optimal Staging 113 --
Chapter 7 Impulsive Orbit Transfer 119 --
7.2 Impulsive Thrust Approximation 119 --
7.3 Two-Impulse Transfer between Circular Orbits 121 --
7.4 Hohmann Transfer 123 --
7.5 Coplanar Extensions of the Hohmann Transfer 127 --
7.6 Noncoplanar Extensions of the Hohmann Transfer 130 --
7.7 Conditions for Interception and Rendezvous 133 --
Chapter 8 Continuous-Thrust Orbit Transfer 138 --
8.2 Equation of Motion 139 --
8.3 Propellant Consumption 139 --
8.4 Quasi-Circular Orbit Transfer 142 --
8.5 Effects of Nonconstant Mass 144 --
8.6 Optimal Quasi-Circular Orbit Transfer 145 --
8.7 Constant-Radial-Thrust Acceleration 146 --
8.8 Shifted Circular Orbits 151 --
Chapter 9 Interplanetary Mission Analysis 154 --
9.2 Sphere of Influence 155 --
9.3 Patched-Conic Method 158 --
9.4 Velocity Change from Circular to Hyperbolic Orbit 162 --
9.5 Planetary Flyby (Gravity-Assist) Trajectories 163 --
9.6 Flyby Following a Hohmann Transfer 166 --
9.7 Gravity-Assist Applications 171 --
Chapter 10 Linear Orbit Theory 179 --
10.2 Linearization of the Equations of Motion 179 --
10.3 Hill-Clohessy-Wiltshire (CW) Equations 182 --
10.4 Solution of the CW Equations 184 --
10.5 Linear Impulsive Rendezvous 189 --
10.6 State Transition Matrix for a General Conic Orbit 192 --
Chapter 11 Perturbation 197 --
11.2 Perturbation Equations 198 --
11.3 Effect of Atmospheric Drag 205 --
11.4 Effect of Earth Oblateness 206 --
11.5 Effects of Solar-Lunar Attraction 209 --
11.6 Effect on the Orbit of the Moon 214 --
Chapter 12 Canonical Systems and the Lagrange Variational Equations 219 --
12.2 Hamilton's Equations 220 --
12.3 Canonical Transformations 220 --
12.4 Necessary and Sufficient Conditions for a Canonical Transformation 222 --
12.5 Generating Functions 224 --
12.6 Jacobi's Theorem 226 --
12.7 Canonical Equations for the Two-Body Problem 228 --
12.8 Delaunay Variables 231 --
12.9 Average Effects of Earth Oblateness Using Delaunay Variables 232 --
12.10 Lagrange Equations 234 --
Chapter 13 Perturbations Due to Nonspherical Terms in the Earth's Potential 238 --
13.2 Effect of the Zonal Harmonic Terms 239 --
13.3 Short-Period Variations 241 --
13.4 Long-Period Variations 242 --
13.5 Variations at O(Jb2p2s) 243 --
13.6 Potential in Terms of Conventional Elements 245 --
13.7 Variations Due to the Tesseral Harmonics 247 --
13.8 Resonance of a Near-Geostationary Orbit 249 --
Chapter 14 Orbit Determination 253 --
14.2 Angles-Only Orbit Determination 255 --
14.3 Laplacian Initial Orbit Determination 256 --
14.4 Gaussian Initial Orbit Determination 259 --
14.5 Orbit Determination from Two Position Vectors 263 --
14.6 Differential Correction 263.