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

SUBJECT

Code
Subject
MMM1008 Planetary system dynamics
Section
Semester
Hours: C+S+L
Category
Type
Mathematics Computational - in Hungarian
3
2+2+0
speciality
optional
Didactic Mathematics - in Hungarian
3
2+2+0
speciality
optional
Interdiciplinary Computational - in Hungarian
3
2+2+0
speciality
optional
Teaching Staff in Charge
Assoc.Prof. SZENKOVITS Ferenc, Ph.D.,  fszenkomath.ubbcluj.ro
Aims
The aim of this cours in to offer modells and methods adecvate to study the dynamics of planetary systems, with spetial attention to stability and chaoticity.
The absolvents of this cours will be able:
- to use adecvate models and methods of the celestila mechanics for different concret planetary systemc;
- to determine orbital elements from observational data;
- to determinate ephemerides for planets;
- to detect chaoticity in the specific dynamical systems.
Content
1. Orbit determination
1.1. Distance determination from three observations
1.2. The Gaussian equations
1.3. Orbitale 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 motins of the Moon
3.1. The Delaunay theory
3.2. The Hill—Brown theory
3.3 Hill@s periodical sollutions
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 sollution of the Hill-Brown Theory
4. Extrasolar planetary systems
4.1. Detection
4.2. Formation
4.3. Rezonant perturbations
4.4. Regular and chaotic motions
4.5. Numerical tools for chaos detection
4.6. Planets in Binary systems
References
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
1. Érdi Bálint: Égi mechanika, Tankönyvkiadó, Budapest, 1992.
2. Érdi Bálint: Égi mechanika, II. Rész, A Hold mozgása, Tankönyvkiadó, Budapest, 1974.
3. Érdi Bálint: A Naprendszer dinamikája, ELTE Eötvös Kiadó, Budapest, 2001.
4. Roy, A. E.: Orbital motion, Third Edition, Adam Hilger, Bristol and Philadelphia, 1988.
cureşti, 1958.
Assessment
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