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D21DF248B9BC2FF1BD81C979635ED444C0E49252
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April 20, 2026, 7:18 p.m.
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| Fukushima T. Position and Motion of Celestial Bodies 2024.pdf | 6.2 MB |
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SOURCE: Fukushima T. Position and Motion of Celestial Bodies 2024
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COVER
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MEDIAINFO
Textbook in PDF format The present book is different from the existing textbooks in some aspects. First, we explain astrometry and celestial mechanics in a single book. Many books focus on one of them. However, the two issues are deeply interrelated. Next, we cover both Newtonian mechanics and the general theory of relativity. Most textbooks deal with Newtonian mechanics only. Third, we discuss the rotational motion of celestial bodies. Modern literature on astronomy does not explain rotational dynamics. Also, the book is up-to-date because it mentions the latest IAU resolutions on fundamental astronomy. Then, I developed an English edition here using DeepL Translator and Grammarly with the help of Prof. Toshikazu Shigeyama and the editorial staff at Springer-Nature company. Of course, we had to omit some materials since they are meaningful only for Japanese readers. Examples are descriptions of the technical terms in Japanese and the references written in Japanese. Also, I enlarged the contents by adding references, interesting columns, some exercises, and their model answers to facili- tate readers’ understanding. I will be grateful if this enhanced English version will stimulate students and non-experts. Preface to the English Edition Preface to the Second Japanese Edition Preface to the First Japanese Edition About This Book List of Contributors Note on References Abreviations Contributors Position of Celestial Bodies Measurement of Position Principle of Measurement Measurable Quantity Observable Quantity Examples of Mass Measurement Difficulties Improvement of Measurement Accuracy and the New Role of Astrometry Repeated Measurements and Averaging Operations General Theory of Error and Uncertainty Least-Squares Method Measurement of Time Principled Difficulties in Time Measurement Definition of a Second and Accuracy and Stability Principle of Quartz and Atomic Clocks The New Standard: Optical Clock GNSS Clock Pulsar Time Observation Distance Measurement Unit of Length Rangefinder Measurement Using GNSS Range and Range Rate Integrated Doppler Measurement Laser Ranging Astrometry Angle Measurement Narrow-Field Astrometry Wide-Field Astrometry Radio Interferometry and Position Measurement Fundamental Equations of Interferometry Cross-correlation Phase Delay and Group Delay Radio Source Catalog Delta Differential One-Way Range Measurement Devices and Facilities Atomic Clock Laser Ranging Equipment Astrograph Meridian Circle Astrometry Satellite Very Long Baseline Interferometer (VLBI) Phase-Referencing VLBI Representation of Position Time Expressions Apparent Solar Time and Mean Solar Time Universal Time International Atomic Time and Coordinated Universal Time Julian Date Dynamical Time and Coordinate Time Representation of Spatial Positions Horizontal and Equatorial Coordinate Systems Ecliptic Coordinate System and Vernal Equinox Relationship Between Horizontal and Equatorial Coordinate Systems Observer Location: International Terrestrial Reference System International Celestial Reference System Earth's Orientation Precession and Nutation Precession Theory Nutation Theory Representation of Coordinates Sidereal Time and the Earth Rotation Angle Polar Motion Propagation of Electromagnetic Waves Light-Time Equation Aberration Round-Trip Time Measurement Interferometric Observation Pulsar GNSS Propagation Delay Relativistic Effects Theories of Relativity and Time Delay Gravitational Bending of Light Propagation Delay Due to Gravitation Aberration Motion of Celestial Bodies Fundamentals of Celestial Mechanics Laws of Motion Space and Time Position, Velocity, and Acceleration Newton's Three Laws of Motion Conserved Quantities of Motion Conserved Quantity Law of Momentum Conservation Law of Angular Momentum Conservation Law of Energy Conservation Symmetry and Conservation Laws Special Conserved Quantities Universal Attraction Law of Universal Attraction Extension to Many-Body Systems Gravitational Potential Gravitation of Spherically Symmetric Finite Body Gravitational Field Equation Extensions to General Finite Bodies Poisson Equation Green's Function Gravitational Field of a Finite Body From Newton to Einstein Transition to New Mechanics Lorentz Transformation Proper Time and Coordinate Time Summary of the Special Theory of Relativity Concept of the General Theory of Relativity Geodesic Equations Post-Newtonian Approximation Motion of Photon EIH Equation of Motion Orbital Motion Solution of the Two-Body Problem Setting up Equations of Motion Reduction to the One-Body Problem Angular Momentum Integral Eccentricity Integral Energy Integral Introduction of Polar Coordinates Solution Classification Orbital Elements Determination of an Orbit in Three-Dimensional Space True Anomaly as a Function of Time Time of Pericenter Passage: The Case of an Elliptic Orbit Time of Pericenter Passage: the case of a parabolic orbit Time of Pericenter Passage: The Case of a Hyperbolic Orbit Kepler Equations Principle of the Newton Method Solution of Kepler Equations Conversion from Orbital Elements to Position and Velocity Vectors Perturbed Two-Body Problem Various Perturbations Equation of Variation of Orbital Elements Examples of Orbit Variation Three-Body Problem Example of the Three-Body Problem Regularization of the Two-Body Problem Special Solutions of the Three-Body Problem Rotational Motion Dynamics of Mass Point System Equation of Motion of a Mass Point System and Motion of Barycenter Angular Momentum Vector of Mass Point System Angular Momentum Vector Around the Barycenter Kinetic Energy Around the Barycenter Motion of a Rigid Body Around a Fixed Point Fixed Points in Motion of the Rigid Body Angular Velocity Vector of the Rigid Body Moment of Inertia and Product of Inertia Rigid Body Rotating Around Fixed Axis Ellipsoid of Inertia Principal Moments of Inertia Motion of Rigid Body under no external forces Euler's Equations of Motion An Application of Euler's Equations of Motion—the Earth's polar motion Poinsot's Construction Euler Angles Representation of Angular Velocity Vector by Euler angles Torque-Free Rotation of a rigid body in the inertial coordinate system Motion of Rigid Body Under External Force Gravitational Potential Created by Rigid Bodies Lagrangian Equation of Motion and Poisson Approximation Rewriting of Gravitational Potential Precession Nutation Appendices Model Answers to Exercises Answers for Chap Separation Angle Expression in Spherical Coordinates NTP The Transformation from the Standard Coordinates to the Equatorial Coordinates Limit of Two-Way Laser Ranging Optical Interferometer Astrometry Using Media Other than Electromagnetic Waves Answers for Chap The Day of the Week Latitude Equation Equatorial-Ecliptic Coordinate Transformation Importance of Ecliptic Coordinate System Gravitational Bending of Light Answers for Chap Non-central Force Principle of Rocket Propulsion Laplace's Black Hole Associated Legendre Function Gravitational Time Dilation Answers for Chap The Transformation from the Jacobi Coordinates to the Inertial Coordinates Conversion to Orbital Elements Numerical Solution of Kepler Equation Peculiarity of the Moon's Orbit Periodic Solutions of upper NN-Body Problem Answers for Chap Comparison Chart of Orbital and Rotational Motion Principal Moments of Inertia Variable Transformation to Jacobi Elliptic Functions Angle Solution Constants Mathematical Formulae Trigonometric Functions Hyperbolic Functions Differentiation Finite Products and Finite Series Series Expansions Vector Analysis Plane Trigonometry Spherical Trigonometry Fundamental Rotation Matrices Special Functions Symbols Index
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