Celesial Mechanics 1-4

Type of instruction




Part of degree program


Recommended in

Semesters 1-4

Typically offered in

Autumn/Spring semester

Course description

Semester 1: General perturbaion theory

Canonical perturbaion theory: Hamilton-Jacobi method, acion-angle variables. The fundamental theorem of perturbaion theory, Delaunay's lunar theory and eliminaion method. Poincaré-Zeipel method. Theory of resonant perturbaions. Lie transform perturbaion theory. Superconvergent perturbaion theory. Ordered and chaoic moions: KAM theory.

Ordered and chaoic orbits in the restricted three-body problem. Lyapunov indicators. Poincaré mappings. Hénon-Heiles problem. Symplecic mappings, symplecic integrators.

Semester 2: Dynamics of planetary systems

Resonances of irst and second order. Resonant encounters, capture into and passing through a resonance. Muliple resonances.Resonances in the Solar System.

Dynamics of the Solar System: Moion of giant planets. Stability of the Solar System. Rotaion of the planets and moons. Dynamics of resonant asteroids.

Exoplanetary systems: Dynamical classiicaion of muliple planetary systems. Resonant, interacing and hierarchical systems. Planet-disk interacions. Stability of exoplanetary systems.

Semester 3: The three-body problem

The general three-body problem: Equaions of moion and irst integrals. The Lagrange-Jacobi equaion. Classiicaion of inal coniguraions. The Euler-Lagrange soluions.

The restricted three-body problem: Equaions of moion, the Jacobi-integral. Equilibrium soluions and their stability. Zero velocity curves. Regularizaion transformaions. Periodic and numerical soluions. The ellipic restricted three-body problem. The Hill-problem.

Semester 4: Theory of ariicial satellites

The gravitaional potenial. Terrestrial gravitaional perturbaions.

Lunisolar perturbaions. Non-gravitaional perturbaions.

  • Smart: Celesial mechanics. Literary Licensing, 2013
  • Kartunen et al.: Fundamental Astronomy. 5Th ed., Springer, 2003, ISBN 978-3-540-34143-7
  • Freedman and Kaufmann: Universe. 8th ed., W. H. Freeman Publ., 2007, ISBN: 978-0716785842