1. Introduction to Celestial Mechanics – historical review, modern developments and applications in space and planetary science. Overview of the solar system, extraplanetary systems and the population of Earth’s artificial satellites.
2. Positional astronomy – reference and coordinate systems, time measurement systems. Astrometric parameters and methods of their measurement. Astronomical catalogs and ephemerides. Transits and occultations.
3. Laboratory exercise 1: calculation of the position of a moving object and error estimation, using online tools (Astrometry.NET, Horizons/JPL). Determination of coordinates with exact plate solution.
4. Two-body problem – Kepler motion, orbital elements and Kepler’s equation. Methods of determining orbits from observations.
5. Rotation – equations of motion. Tides and rotation. Tidal phenomena in the solar system and in extraplanetary systems.
6. Laboratory exercise 2: Determination of orbital elements from observations. Orbit optimization (least squares method) using specialized software.
7. Artificial satellites – rocket equation, propulsion systems, orbit corrections and orbit transfer. Perigee/apogee shift, Hohmann transfer and GEO orbit placement. Space debris.
8. Orbital perturbations – Gauss and Lagrange equations. Aerodynamic friction. Solar radiation pressure. Approximate solutions.
9. Laboratory exercise 3: numerical solution of the Kepler equation and determination of satellite groundtrack. Calculation of orbital transfer. Solving the equations of motion under the influence of atmospheric friction.
10. Gravitational perturbations – canonical variables and Delaunay equations. Earth potential – oblate spheroid approximation. Special satellite orbits (GEO, Molniya/Tundra, Sun-synchronous).
11. The 3-body problem. Lagrange points and Tisserand parameter. Disturbing function and approximate solutions of the equations of motion.
12. Laboratory exercise 4: Numerical integration of satellite and planetary orbits using N-body simulator.
13. Dynamical evolution of the solar system – planetary orbits, asteroid and comet orbits. Stability of exoplanetary systems.