544 Pages
    by CRC Press

    544 Pages
    by CRC Press

    Long established as one of the premier references in the fields of astronomy, planetary science, and physics, the fourth edition of Orbital Motion continues to offer comprehensive coverage of the analytical methods of classical celestial mechanics while introducing the recent numerical experiments on the orbital evolution of gravitating masses and the astrodynamics of artificial satellites and interplanetary probes.

    Following detailed reviews of earlier editions by distinguished lecturers in the USA and Europe, the author has carefully revised and updated this edition. Each chapter provides a thorough introduction to prepare you for more complex concepts, reflecting a consistent perspective and cohesive organization that is used throughout the book. A noted expert in the field, the author not only discusses fundamental concepts, but also offers analyses of more complex topics, such as modern galactic studies and dynamical parallaxes.

    New to the Fourth Edition:

    •          Numerous updates and reorganization of all chapters to encompass new methods

    •          New results from recent work in areas such as satellite dynamics

    •          New chapter on the Caledonian symmetrical n-body problem

    Extending its coverage to meet a growing need for this subject in satellite and aerospace engineering, Orbital Motion, Fourth Edition remains a top reference for postgraduate and advanced undergraduate students, professionals such as engineers, and serious amateur astronomers.

    PREFACE TO FOURTH EDITION
    THE RESTLESS UNIVERSE
    Introduction
    The Solar System
    Stellar Motions
    Clusters of Galaxies
    Conclusion
    Bibliography
    COORDINATE AND TIME-KEEPING SYSTEMS
    Introduction
    Position on the Earth’s Surface
    The Horizontal System
    The Equatorial System
    The Ecliptic System
    Elements of the Orbit in Space
    Rectangular Coordinate Systems
    Orbital Plane Coordinate Systems
    Transformation of Systems
    Galactic Coordinate System
    Time Measurement
    Bibliography
    THE REDUCTION OF OBSERVATIONAL DATA
    Introduction
    Observational Techniques
    Refraction
    Precession and Nutation
    Aberration
    Proper Motion
    Stellar Parallax
    Geocentric Parallax
    Review of Procedures
    Bibliography
    THE TWO-BODY PROBLEM
    Introduction
    Newton’s Laws of Motion
    Newton’s Law of Gravitation
    The Solution to the Two-Body Problem
    The Elliptic Orbit
    The Parabolic Orbit
    The Hyperbolic Orbit
    The Rectilinear Orbit
    Barycentric Orbits
    Classification of Orbits with Respect to the Energy Constant
    The Orbit in Space
    The f and g Series
    The Use of Recurrence Relations
    Universal Variables
    Bibliography
    THE MANY-BODY PROBLEM
    Introduction
    The Equations of Motion in the Many-Body Problem
    The Ten Known Integrals and Their Meanings
    The Force Function
    The Virial Theorem
    Sundman’s Inequality
    The Mirror Theorem
    Reassessment of the Many-Body Problem
    Lagrange’s Solutions of the Three-Body Problem
    General Remarks on the Lagrange Solutions
    The Circular Restricted Three Body Problem
    The General Three-Body Problem
    Jacobian Coordinates for the Many-Body Problem
    The Hierarchical Three-Body Stability Criterion
    Bibliography
    THE CALEDONIAN SYMMETRIC N-BODY PROBLEM
    Introduction
    The Equations of Motions
    Sundman’s Inequality
    Boundaries of Real and Imaginary Motion
    The Caledonian Symmetric Model for n = 1
    The Caledonian Symmetric Model for n = 2
    The Caledonian Symmetric Model for n = 3
    The Caledonian Symmetric N-Body Model for odd N
    Bibliography
    GENERAL PERTURBATIONS
    The Nature of the Problem
    The Equations of Relative Motion
    The Disturbing Function
    The Sphere of Influence
    The Potential of a Body of Arbitrary Shape
    Potential at a Point within a Sphere
    The Method of the Variation of Parameters
    Lagrange’s Equations of Motion
    Hamilton’s Canonic Equations
    Derivation of Lagrange’s Planetary Equations from Hamilton’s Canonic Equations
    Bibliography
    SPECIAL PERTURBATIONS
    Introduction
    Factors in Special Perturbation Problems
    Cowell’s Method
    Encke’s Method
    The Use of Perturbational Equations
    Regularization Methods
    Numerical Integrations Methods
    Bibliography
    THE STABILITY AND EVOLUTION OF THE SOLAR SYSTEM
    Introduction
    Chaos and Resonance
    Planetary Ephemerides
    The Asteroids
    Rings, Shepherds, Tadpoles, Horseshoes, and Co-Orbitals
    Near-Commensurable Satellite Orbits
    Large-Scale Numerical Integrations
    Empirical Stability Criteria
    Conclusions
    Bibliography
    LUNAR THEORY
    Introduction
    The Earth–Moon System
    The Saros
    Measurement of the Moon’s Distance, Mass, and Size
    The Moon’s Rotation
    Selenographic Coordinates
    The Moon’s Figure
    The Main Lunar Problem
    The Sun’s Orbit in the Main Lunar Problem
    The Orbit of the Moon
    Lunar Theories
    The Secular Acceleration of the Moon
    Bibliography
    ARTIFICIAL SATELLITES
    Introduction
    The Earth as a Planet
    Forces Acting on an Artificial Earth Satellite
    The Orbit of a Satellite about an Oblate Planet
    The Use of Hamilton–Jacobi Theory in the Artificial Satellite Problem
    The Effect of Atmospheric Drag on an Artificial Satellite
    Tesseral and Sectorial Harmonics in the Earth’s Gravitational Field
    Bibliography
    ROCKET DYNAMICS AND TRANSFER ORBITS
    Introduction
    Motion of a Rocket
    Transfer between Orbits in a Single Central Force Field
    Transfer Orbits in Two or More Force Fields
    Bibliography
    INTERPLANETARY AND LUNAR TRAJECTORIES
    Introduction
    Trajectories in Earth–Moon Space
    Feasibility and Precision Study Methods
    The Use of Jacobi’s Integral
    The Use of the Lagrangian Solutions
    The Use of Two-Body Solutions
    Artificial Lunar Satellites
    Interplanetary Trajectories
    The Solar System as a Central Force Field
    Minimum-Energy Interplanetary Transfer Orbits
    The Use of Parking Orbits in Interplanetary Missions
    The Effect of Errors in Interplanetary Orbits
    Bibliography
    ORBIT DETERMINATION AND INTERPLANETARY NAVIGATION
    Introduction
    The Theory of Orbit Determination
    Laplace’s Method
    Gauss’s Method
    Olbers’ Method for Parabolic Orbits
    Orbit Determination with Additional Observational Data
    The Improvement of Orbits
    Interplanetary Navigation
    Bibliography
    BINARY AND OTHER FEW-BODY SYSTEMS
    Introduction
    Visual Binaries
    The Mass–Luminosity Relation
    Dynamical Parallaxes
    Eclipsing Binaries
    Spectroscopic Binaries
    Combination of Deduced Data
    Binary Orbital Elements
    The Period of a Binary
    Apsidal Motion
    Forces Acting on a Binary System
    Triple Systems
    The Inadequacy of Newton’s Law of Gravitation
    The Figures of Stars in Binary Systems
    The Roche Limits
    Circumstellar Matter
    The Origin of Binary Systems
    Bibliography
    MANY-BODY STELLAR SYSTEMS
    Introduction
    The Sphere of Influence
    The Binary Encounter
    The Cumulative Effect of Small Encounters
    Some Fundamental Concepts
    The Fundamental Theorems of Stellar Dynamics
    Some Special Cases for a Stellar System in a Steady State
    Galactic Rotation
    Spherical Stellar Systems
    Modern Galactic Studies
    Bibliography
    ANSWERS TO PROBLEMS
    APPENDIX I: Astronomical and Related Constants
    APPENDIX II: The Earth’s Gravitational Field
    APPENDIX III: Mean Elements of the Planetary Orbits; Approximate Elements of the Ten Largest Asteroids
    APPENDIX IV: Physical Elements of the Planets; Planetary Ring Systems; Satellite Elements and Dimensions
    INDEX

    Biography

    A.E. Roy, Professor Emeritus of Astronomy, Honorary Senior Research Fellow, University of Glasgow.

    “Roy updates this fourth edition of an established text to include new research results … While the text is intended for advanced undergraduate and graduate students in disciplines ranging from astronomy and planetary science to aerospace and satellite engineering, its discussion of orbital computation will be of interest to serious amateur astronomers.”
    —SciTech Book News, December 2006

    “Each chapter is accompanied by exercises (with answers and some hints) that are designed to give the student confidence. This book retains its usefulness as a comprehensive text on introductory celestial mechanics… .”
    — James Collett,Physical Science Educational Reviews,Vol. 7 Issue 1, June 2006

    Praise for the Third Edition
     “…a classic text … on the orbits of everything from galactic clusters down to grapefruit-sized Earth satellites.”
    Planet Space Science