Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Master


MMM1008 Planetary system dynamics
Hours: C+S+L
Didactic Mathematics - in Hungarian
Interdiciplinary Computational - in Hungarian
Teaching Staff in Charge
Assoc.Prof. SZENKOVITS Ferenc, Ph.D.,
The aim of this course is to offer models and methods adequate to study the dynamics of planetary systems, with special attention to stability and chaos.
At the and of this course the students will be able:
- to use adequate models and methods of the celestial mechanics for different concrete planetary systems;
- to determine orbital elements from observational data;
- to determinate ephemerids for planets;
- to detect chaos in the specific dynamical systems.
1. Orbit determination
1.1. Distance determination from three observations
1.2. The Gaussian equations
1.3. Orbital elements
1.4. Position determination from four observations
1.5. Orbital corrections
1.6. The Herget method
2. Planetary dynamics
2.1. Planets
2.2. Natural satellites
2.3. Asteroids
3. The motions of the Moon
3.1. The Delaunay theory
3.2. The Hill—Brown theory
3.3 Hill@s periodical solutions
3.4. The Hill differential equation
3.5. Motion of the perigee of the Moon
3.6. The apsidal line of the Moon orbit
3.7. The general solution of the Hill-Brown Theory
4. Extrasolar planetary systems
4.1. Detection
4.2. Formation
4.3. Resonant perturbations
4.4. Regular and chaotic motions
4.5. Numerical tools for chaos detection
4.6. Planets in Binary systems
1. Beutler, Gerhard: Methods of celestial mechanics, I—II, Springer, 2005.
2. Boccaletti, D. – Pucacco, G.: Theory of orbits, Vol. 1—2, Springer, Berlin Heidelberg, 1996, 1998.
3. Contopoulos, George: Order and Chaos in Dynamical Astronomy, Springer, 2002.
4. Diacu, F. – Holmes, P.: Întâlniri cereşti – originea haosului şi a stabilităţii, Soc. Ştiinţă şi Tehnică SA, Bucureşti,1996.
5. Drâmbă, Constantin: Elemente de mecanică cerească, Bibl. SSMF, Bu
6. Érdi Bálint: Égi mechanika, Tankönyvkiadó, Budapest, 1992.
7. Érdi Bálint: Égi mechanika, II. Rész, A Hold mozgása, Tankönyvkiadó, Budapest, 1974.
8. Érdi Bálint: A Naprendszer dinamikája, ELTE Eötvös Kiadó, Budapest, 2001.
9. Murray C.D., Dermott S.F: Solar System Dynamics, Cambridge University Press, 2005.
10. Roy, A. E.: Orbital motion, Third Edition, Adam Hilger, Bristol and Philadelphia, 1988.
Evaluation in seminaries (33%);
Individual project (33%);
Final test (33%).
Links: Syllabus for all subjects
Romanian version for this subject
Rtf format for this subject