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Orbital Mechanics

ISBN-10: 0199837708
ISBN-13: 9780199837700
Edition: 2nd
List price: $119.95
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Description: 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  More...

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Book details

List price: $119.95
Edition: 2nd
Publisher: Oxford University Press, Incorporated
Publication date: 12/12/2012
Binding: Hardcover
Pages: 304
Size: 6.25" wide x 9.25" long x 0.75" tall
Weight: 1.628

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 accomplish their 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 for the 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 important results 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 receives special 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 are particularly relevant to modern space missions.

Bruce Conway is a Professor of Aerospace Engineering at the University of Illinois, Urbana-Champaign. He received his Ph.D. in aeronautics and astronautics at Stanford University in 1981. Professor Conway's research interests include orbital mechanics, optimal control, differential games, and improved methods for the numerical solution of problems in optimization.

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

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