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One of the major challenges of modern space mission design is the orbital mechanics -- determining how to get a spacecraft to its destination using a limited amount of propellant. Recent missions such as Voyager and Galileo required gravity assist maneuvers at several planets to accomplishtheir objectives. Today's students of aerospace engineering face the challenge of calculating these types of complex spacecraft trajectories. This classroom-tested textbook takes its title from an elective course which has been taught to senior undergraduates and first-year graduate students forthe past 22 years. The subject of orbital mechanics is developed starting from the first principles, using Newton's laws of motion and the law of gravitation to prove Kepler's empirical laws of planetary motion. Unlike many texts the authors also use first principles to derive other importantresults including Kepler's equation, Lambert's time-of-flight equation, the rocket equation, the Hill-Clohessy-Wiltshire equations of relative motion, Gauss' equations for the variation of the elements, and the Gauss and Laplace methods of orbit determination. The subject of orbit transfer receivesspecial attention. Optimal orbit transfers such as the Hohmann transfer, minimum-fuel transfers using more than two impulses, and non-coplanar orbital transfer are discussed. Patched-conic interplanetary trajectories including gravity-assist maneuvers are the subject of an entire chapter and areparticularly relevant to modern space missions.
John E. Prussing is Professor Emeritus of Aerospace Engineering at the University of Illinois at Urbana-Champaign.
Bruce A. Conway is Professor of Aerospace Engineering at the University of Illinois at Urbana-Champaign.
Table of Contents
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 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