Introduction. Spherical Trigonometry. Fundamental Formulae of Spherical Trigonometry.
Polar Spherical Triangle. Rectangular and Square Spherical Triangle.
Celestial Sphere. Elements of Celestial Sphere. Coordinate Systems (The Horizon System, the Local Equatorial System, the Celestial Equatorial System, the Ecliptic System, the Galactic System, the Geographic System). Connections Between Coordinate Systems. Special Positions of Celestial Bodies on the Celestial Sphere (Rising , Setting, Passage across the Meridian, Passage across the Prime Vertical, Maximal Elongation). Increasing of Horizon Coordinates.
Frames of Reference. Inertial System. Precession, Nutation and Proper Motion. The Origin of the Referential Frame. The Special Theory of Relativity. The General Theory of Relativity.
Apparent Motions. Apparent Annual Solar Motion. Apparent Lunar Motion. Apparent Motion of Planets, Comets and Meteors. Ptolemy's Geocentric Model.
Real Motions. Copernican Heliocentric Model. Real Motion of the Earth - Kepler's Laws. Real Lunar Orbiting the Earth. Real Planetary Motion and Explanation of Apparent Planetary Motions.
The Problem of Two Bodies. Basic Equations. The Gravity Law. Kepler's Equation for a Limiting Orbit. Kepler's Laws. The Solution of Kepler's Equation. Kepler's Solution in General Relativity. Relativistic Perihilion Shift.
Orbits. Orbit in Space. Calculation of Ephemerides. Planetary Masses. Preliminary Orbit Determination. Titius - Bode Law. Eclipses.
Time. Sidereal Time. Mean Time (Zone Time, Daylight Savings Time). Polar Motion. Irregularity in Earth's Rotation. Ephemeris Time. Atomic Time. New Dynamical Systems of Time TDT and TDB. Proper and Coordinate Time. Universal Time Systems UT (UT0, UT1, UT2, UTC, TAI). Year (Species and Definitions). Julian and Besselian Year. Calendars.
Geocentric Coordinates. Refraction. Approximate Formulae for Refraction. Refractive Constants and Tables. The Refractive Influence on Coordinates. Diurnal Parallax. The Diurnal Parallax Influence on Coordinates. Diurnal Aberration. The Diurnal Aberration Influence on Coordinates.
Heliocentric and Barycentric Coordinates. Annual Parallax. The Annual Parallax Influence on Co-ordinates. Annual Aberration. The Annual Aberration Influence on Coordinates. Planetary Aberration.
Precession and Nutation. Lunisolar Precession. Planetary Precession. General Precession. The Precession Influence on Coordinates. Nutation. The Nutation Influence on Coordinates.
Proper Motion. Components of Stellar Motion. Proper Motion. Radial Velocity. The Proper Motion Influence on Coordinates.
Mean and Apparent Coordinates. Definitions. Annual and Centurial Changes. The Real Position of Stars. The Apparent Position of Stars. Reduction. Astronomical Almanacs.
Astronomical Instruments. Meridian Circle. Description and Working Principle. Meridian Circle Errors (Collimation, Tilt and Azimuth). Solar Clock. Absolute and Relative Determination of Equatorial Coordinates. Star Catalogues. Systematic Catalogue Errors. Clock States and Geographic Longitude. Determination of Geographic Latitude.