Two-body problem. Central orbits. General integrals of motion. Conservation laws. Relationship
between integral constants and orbital parameters. Kepler’s laws. Gauss’s constant, astronomical
unit, masses of planets. Energy integral and limits of velocities. Elliptical, parabolic and hyperbolic motion. Solution of Kepler’s equation. Orbit in space. Types of orbits in the Solar system. Ephemeris calculation. Time series. Fundamentals of orbit determination.
N-body problem. General integrals. Relative coordinates, concept of preturbations, disturbing function. Virial Theorem. General integrals of the n-body motion. Disturbing function. Perturbed orbits. Small impulses and the change of orbital elements. Lagrange's planetary equations, 1-st order solution. Introduction to resonances.
Restricted three-body problem. Jacobi integral. Lagrangian equilibrium points, stable and unstable solution. Tisserand invariant. Gravitational spheres.
Numerical solution of n-body problem, Cowell and Encke type.
Gravitational potential of a finite body. Perturbations in satellite motion.
Outcome:
The students will proof the understanding of two and n body problem.