The topics covered by the course include: 1) The fundamental concepts of Newtonian mechanics and the gravitational potential theory, gravitational potential outside uniform spheroid and due to uniform disk (ring), motion in rotating reference frames, elements of the rigid body dynamics, basic concepts in the Lagrangian mechanics. 2) The N-body problem in the classical framework, the first integrals of the equations of motion, the virial theorem, the dark matter concept, planetary N-body problemn and the equations of motion in relative coordinates, Jacobi and Poincare variables. 3) The Taylor integration scheme for the ordinary differential equations (ODE) as the canonical method of solving the equations of motion in classical and celestial mechanics, perturbed two body problem (e.g., due to relativistic and non-point mass interactions). 4) The theory of motion in central force fields, qualitative analysis of systems with one-degree of freedom, the two body problem, elements of conic curves theory, Keplerian laws, classification and parametrisation of Keplerian orbits (geometric and dynamical elements), simple models of motion in galactic gravitational environments (such as the Henon-Heiles model, the logarithmic, and the Yukawa potentials). 5) Orbits of the planets in the Solar System, the figure of the Earth, tidal interactions among the Earth, Moon, and Sun, the secular evolution and the long-term stability of the Solar system. 6) The two-body orbits kinematic fitting (the Neutsch method) and the merit function for observations made with various techniques (astrometry, eclipse timing, radial velocities), determining the mass function and orbits of binary stars and extrasolar planetary systems. 7) The circular and elliptic restricted three body problems as the fundamental models for astrodynamics (motion of man-made objects in space) and a non-trivial generalisation of the Kepler problem, libration points, elements of the stability and deterministic chaos theory.
