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