Orbital Motion

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