Orbital Mechanics

Each Chapter ends with References and Problems. Chapter 1: The n-Body Problem 1.1 Introduction 1.2 Equations of Motion for the n-Body Problem 1.3 Justification of the Two-Body Model 1.4 The Two-Body Problem 1.5 The Elliptic Orbit 1.6 Parabolic, Hyperbolic, and Rectilinear Orbits 1.7 Energy of the Orbit Chapter 2: Position in Orbit as a Function of Time 2.1 Introduction 2.2 Position and Time in an Elliptic Orbit 2.3 Solution for the Eccentric Anomaly 2.4 The f and g Functions and Series 2.5 Position versus Time in Hyperbolic and Parabolic Orbits: Universal Variables Chapter 3: The Orbit in Space 3.1 Introduction 3.2 The Orbital Elements 3.3 Determining the Orbital Elements from r and v 3.4 Velocity Hodographs Chapter 4: The Three-Body Problem 4.1 Introduction 4.2 Stationary Solutions of the Three-Body Problem 4.3 The Circular Restricted Problem 4.4 Surfaces of Zero Velocity 4.5 Stability of the Equilibrium Points 4.6 Periodic Orbits in the Restricted Case 4.7 Invariant Manifolds 4.8 Special Solutions Chapter 5: Lambert's Problem 5.1 Introduction 5.2 Transfer Orbits Between Specified Points 5.3 Lambert's Theorem 5.4 Properties of the Solutions to Lambert's Equation 5.5 The Terminal Velocity Vectors 5.6 Applications of Lambert's Equation 5.7 Multiple-Revolution Lambert Solutions Chapter 6: Rocket Dynamics 6.1 Introduction 6.2 The Rocket Equation 6.3 Solution of the Rocket Equation in Field-Free Space 6.4 Solution of the Rocket Equation with External Forces 6.5 Rocket Payloads and Staging 6.6 Optimal Staging Chapter 7: Impulsive Orbit Transfer 7.1 Introduction 7.2 The Impulsive Thrust Approximation 7.3 Two-Impulse Transfer Between Circular Orbits 7.4 The Hohmann Transfer 7.5 Coplanar Extensions of the Hohmann Transfer 7.6 Noncoplanar Extensions of the Hohmann Transfer 7.7 Conditions for Interception and Rendezvous Chapter 8: Continuous-Thrust Transfer 8.1 Introduction 8.2 Equation of Motion 8.3 Propellant Consumption 8.4 Quasi-Circular Orbit Transfer 8.5 The Effects of Nonconstant Mass 8.6 Optimal Quasi-Circular Orbit Transfer 8.7 Constant-Radial-Thrust Acceleration 8.8 Shifted Circular Orbits Chapter 9: Interplanetary Mission Analysis 9.1 Introduction 9.2 Sphere of Influence 9.3 Patched Conic Method 9.4 Velocity Change from Circular to Hyperbolic Orbit 9.5 Planetary Flyby (Gravity-Assist) Trajectories 9.6 Gravity-Assist Applications Chapter 10: Linear Orbit Theory 10.1 Introduction 10.2 Linearization of the Equations of Motion 10.3 The Hill-Clohessy-Wiltshire (CW) Equations 10.4 The Solution of the CW Equations 10.5 Linear Impulsive Rendezvous 10.6 State Transition Matrix for a General Conic Orbit Chapter 11: Perturbation 11.1 Introduction 11.2 The Perturbation Equations 11.3 Effect of Atmospheric Drag 11.4 Effect of Earth Oblateness 11.5 Effects of Solar-Lunar Attraction 11.6 Effect on the Orbit of the Moon Chapter 12: Canonical Systems and the Lagrange Equations 12.1 Introduction 12.2 Hamilton's Equations 12.3 Canonical Transformations 12.4 Necessary and Sufficient Conditions for a Canonical Transformation 12.5 Generating Functions 12.6 Jacobi's Theorem 12.7 Canonical Equations for the Two-Body Problem 12.8 The Delaunay Variables 12.9 Average Effects of Earth Oblateness Using Delaunay Variables 12.10 Lagrange Equations Chapter 13: Perturbations Due to Nonspherical Terms in the Earth's Potential 13.1 Introduction 13.2 Effect of the Zonal Harmonic Terms 13.3 Short-Period Variations 13.4 Long-Period Variations 13.5 Variations at O(J2/2) 13.6 The Potential in Terms of Conventional Elements 13.7 Variations Due to the Tesseral Harmonics 13.8 Resonance of a Near-Geostationary Orbit Chapter 14: Orbit Determination 14.1 Introduction 14.2 Angles-Only Orbit Determination 14.3 Laplacian Initial Orbit Determination 14.4 Gaussian Initial Orbit Determination 14.5 Orbit Determination from Two Position Vectors 14.6 Differential Correction Appendix 1: Astronomical Constants Appendix 2: Physical Characteristics of the Planets Appendix 3: Elements of the Planetary Orbits Index

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