3-FAA-005 Analytical and Numerical Methods in Celestial Mechanics

Provides: doc. RNDr. Jozef Klačka, PhD.

Form and extent of the course: Lecture - 2 hours per week

Semester: 1^st

Number of credits: 10

Evaluation during the course: individual task

Concluding evaluation: exam

Objectives of the course: To be able to use analytical and numerical methods of celestial mechanics.

Brief outline of the course:

Motivation - Newton's equation of motion and orbital elements in celestial mechanics. Gravitational attraction between bodies of finite dimensions. Perturbation equations of celestial mechanics - derivation from Newton's equation of motion. Simple application to motion of the Moon. Nongravitational effects. The effect of electromagnetic radiation on motion of particles: types of osculating orbital elements, detail analytical calculation of orbital evolution up to the second order of perturbation theory, secular evolution of orbital elements, orbital resonances with planets. Influence of the solar (stellar) wind. Oort's cloud of comets and gravitational perturbations of the Galaxy - secular evolution of cometary orbits. Comparison between analytical and numerical solutions.

Literature:

Brouwer D., Clemence G. M.: 1961, Methods of Celestial Mechanics, Academic Press, New York.

Murray C. D., Dermott S. F.: 1999, Solar System Dynamics, Cambridge Univ. Press

Hockney R. W., Eastwood J. W.: 1992, Computer Simulation Using Particles, J. W. Arrowsmith Ltd, Bristol

Press W. H., Flannery B. P., Teukolsky S. A., Vetterling W. T.: Numerical Recipes,

Cambridge Univ. Press

Language of instruction: Slovak