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| Preface | |
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| Acknowledgments | |
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| The n-Body Problem | |
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| Introduction | |
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| Equations of Motion for the n-Body Problem | |
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| Justification of the Two-Body Model | |
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| The Two-Body Problem | |
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| The Elliptic Orbit | |
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| Parabolic, Hyperbolic, and Rectilinear Orbits | |
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| Energy of the Orbit | |
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| References | |
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| Problems | |
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| Position in Orbit as a Function of Time | |
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| Introduction | |
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| Position and Time in an Elliptic Orbit | |
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| Solution for the Eccentric Anomaly | |
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| The f and g Functions and Series | |
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| Position versus Time in Hyperbolic and Parabolic Orbits: Universal Variables | |
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| References | |
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| Problems | |
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| The Orbit in Space | |
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| Introduction | |
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| The Orbital Elements | |
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| Determining the Orbital Elements from r and v | |
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| Velocity Hodographs | |
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| References | |
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| Problems | |
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| The Three-Body Problem | |
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| Introduction | |
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| Stationary Solutions of the Three-Body Problem | |
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| The Circular Restricted Problem | |
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| Surfaces of Zero Velocity | |
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| Stability of the Equilibrium Points | |
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| Periodic Orbits in the Restricted Case | |
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| Invariant Manifolds | |
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| Special Solutions of the Problem | |
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| References | |
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| Problems | |
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| Lambert's Problem | |
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| Introduction | |
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| Transfer Orbits Between Specified Points | |
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| Lambert's Theorem | |
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| Properties of the Solutions to Lambert's Equation | |
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| The Terminal Velocity Vectors | |
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| Applications of Lambert's Equation | |
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| Multiple-Revolution Lambert Solutions | |
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| References | |
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| Problems | |
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| Rocket Dynamics | |
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| Introduction | |
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| The Rocket Equation | |
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| Solution of the Rocket Equation in Field-Free Space | |
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| Solution of the Rocket Equation with External Forces | |
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| Rocket Payloads and Staging | |
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| Optimal Staging | |
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| References | |
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| Problems | |
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| Impulsive Orbit Transfer | |
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| Introduction | |
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| The Impulsive Thrust Approximation | |
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| Two-Impulse Transfer between Circular Orbits | |
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| The Hohmann Transfer | |
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| Coplanar Extensions of the Hohmann Transfer | |
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| Noncoplanar Extensions of the Hohmann Transfer | |
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| Conditions for Interception and Rendezvous | |
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| References | |
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| Problems | |
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| Continuous-Thrust Orbit Transfer | |
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| Introduction | |
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| Equation of Motion | |
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| Propellant Consumption | |
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| Quasi-Circular Orbit Transfer | |
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| The Effects of Nonconstant Mass | |
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| Optimal Quasi-Circular Orbit Transfer | |
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| Constant-Radial-Thrust Acceleration | |
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| Shifted Circular Orbits | |
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| References | |
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| Problems | |
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| Interplanetary Mission Analysis | |
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| Introduction | |
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| Sphere of Influence | |
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| Patched-Conic Method | |
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| Velocity Change from Circular to Hyperbolic Orbit | |
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| Planetary Flyby (Gravity-Assist) Trajectories | |
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| Flyby Following a Hohmann Transfer | |
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| Gravity-Assist Applications | |
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| References | |
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| Problems | |
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| Linear Orbit Theory | |
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| Introduction | |
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| Linearization of the Equations of Motion | |
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| The Hill-Clohessy-Wiltshire (CW) Equations | |
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| The Solution of the CW Equations | |
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| Linear Impulsive Rendezvous | |
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| State Transition Matrix for a General Conic Orbit | |
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| References | |
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| Problems | |
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| Perturbation | |
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| Introduction | |
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| The Perturbation Equations | |
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| Effect of Atmospheric Drag | |
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| Effect of Earth Oblateness | |
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| Effects of Solar-Lunar Attraction | |
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| Effect on the Orbit of the Moon | |
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| References | |
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| Problems | |
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| Canonical Systems and the Lagrange Variational Equations | |
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| Introduction | |
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| Hamilton's Equations | |
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| Canonical Transformations | |
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| Necessary and Sufficient Conditions for a Canonical Transformation | |
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| Generating Functions | |
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| Jacobi's Theorem | |
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| Canonical Equations for the Two-Body Problem | |
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| The Delaunay Variables | |
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| Average Effects of Earth Oblateness Using Delaunay Variables | |
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| Lagrange Equations | |
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| References | |
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| Problems | |
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| Perturbations Due to Nonspherical Terms in the Earth's Potential | |
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| Introduction | |
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| Effect of the Zonal Harmonic Terms | |
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| Short-Period Variations | |
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| Long-Period Variations | |
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| Variations at O(J<sub>2</sub><sup>2</sup>) | |
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| The Potential in Terms of Conventional Elements | |
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| Variations Due to the Tesseral Harmonics | |
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| Resonance of a Near-Geostationary Orbit | |
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| References | |
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| Problems | |
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| Orbit Determination | |
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| Introduction | |
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| Angles-Only Orbit Determination | |
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| Laplacian Initial Orbit Determination | |
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| Gaussian Initial Orbit Determination | |
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| Orbit Determination from Two Position Vectors | |
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| Differential Correction | |
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| References | |
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| Problems | |
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| Astronomical Constants | |
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| Physical Characteristics of the Planets | |
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| Elements of the Planetary Orbits | |
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| Index | |