Orbital Motion (Paperback, 4 ed)

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