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Orbital Mechanics

Second Edition

John E. Prussing and Bruce A. Conway

Publication Date - December 2012

ISBN: 9780199837700

304 pages
6-1/8 x 9-1/4 inches

In Stock

Retail Price to Students: $99.95

The classic text on orbital mechanics is now the most current text on orbital mechanics


For nearly two decades, Orbital Mechanics by John E. Prussing and Bruce A. Conway has been the most authoritative textbook on space trajectories and orbital transfers.

Completely revised and updated, this edition provides:

* Current data and statistics, along with coverage of new research and the most recent developments in the field

* Three new chapters: "The Three-Body Problem" (Ch. 4), "Continuous-Thrust Transfer" (Ch. 8), and "Canonical Systems and the Lagrange Equations" (Ch. 12)

* New material on multiple-revolution Lambert solutions, gravity-assist applications, and the state transition matrix for a general conic orbit

* New examples and problems throughout

* A new Companion Website with PowerPoint slides (www.oup.com/us/prussing)

About the Author(s)

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.

Previous Publication Date(s)

September 1993


"An excellent book for teaching both at the undergraduate and graduate levels. It is well organized, starting with the basics and proceeding in a logical manner to more advanced topics. The authors provide some interesting and entertaining anecdotes concerning the history of the subject, as well as many current applications."--Bruce Burlton, Carleton University

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 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


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