Essential Relativistic Celestial Mechanics [Hardcover]

Essential Relativistic Celestial Mechanics presents a systematic exposition of the essential questions of relativistic celestial mechanics and their relation to relativistic astrometry. The book focuses on the comparison of calculated and measurable quantities that is of paramount importance in using general relativity as a necessary framework in the discussion of high-precision observations and for the construction of accurate dynamical ephemerides. It discusses the results of the general relativistic theory of motion of celestial bodies and describes the relativistic theory of astronomical reference frames, time scales, and the reduction of observations.MATHEMATICAL TOOLS
Elements of Newtonian celestial mechanics
Elements of Riemannian geometry and tensor analysis
Elements of special theory of relativity

GRT FIELD EQUATIONS
Basic principles of GRT
Weak gravitational field
Problem of measurable quantities in GRT

ONE-BODY PROBLEM
Schwarzschild problem
Light propagation in the Schwarzschild problem
Field of rotating spheroid

APPROXIMATE SOLUTIONS OF THE FIELD EQUATIONS AND APPROXIMATE EQUATIONS OF MOTION
N-body problem
Geocentric reference frame
Equations in variations for the spherically symmetrical metric spaces
Gravitational radiation and motion in binary system

EQUATIONS OF MOTION OF SOLAR SYSTEM BODIES
Equations of motion of Earth's artificial satellites
Motion of the major planets
Motion of the Moon

RELATIVISTIC REDUCTION OF ASTROMETRIC MEASUREMENTS
General principles of reduction
Relativistic theory of astronomical reference systems
Relativistic reduction of astrometric observations
Relativistic reduction of radio observations

RELATIVISTIC EFFECTS IN GEODYNAMICS
Timescales on Earth
Clocks and satellites in the circumterrestrial space

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