Universitatea Babeş-Bolyai Cluj-Napoca
Facultatea de Matematică şi Informatică
Ciclul de studii: Masterat
Domeniul: Matematica
Programul de studii: Matematică Aplicată
Limba de predare: Engleză

SYLLABUS

I. General data
Code	Subject	
MMM1003	Celestical Mechanics	

Semester	Hours: C+S+L	Category	Status	
3	2+2+0	speciality	optional	

II. Full status faculty members
Name and	Scientific	Didactic	Chair	Type of activity	
surname	title	title		C	S	L	
SZENKOVITS Ferenc	Ph.D.	Assoc.Prof.	Mechanics and Astronomy	*	*		

Associated faculty members
Name and	Scientific	Institution	Type of	Type of activity	
surname	title		position	C	S	L	

III. Course objectives
This course is an introduction to the Celestial mechanics which focuses on the dynamics of celestial bodies. The basic results concerning the classical models of the two-body and the many-body (including the three-body problems) are presented. Methods dedicated to general and particular perturbations are studied and applied to the basic models of the celestial mechanics. Home works include exercises of both practical and theoretical nature, and also writing computer programs.
By the graduation of this class, the students will get the following competences:
•	Will be able to construct the mathematical model for different systems of celestial bodies.
•	Will be able to deduce basic properties of the models.
•	Will be able to apply the general and special perturbation methods.
•	Will be able to perform numerical integration of the systems of ordinary differential equations involved.	

IV. Course contents
The two-body problem. 
The many-body problem (including the restricted and the general three-body problem). 
General and special perturbations.	

V. Bibliography
1.	1. Érdi, Bálint: Égi mechanika, Tankönyvkiadó, Budapest, 1992. (library)
2.	Roy, A. E.: Orbital motion, Third Edition, Adam Hilger, Bristol and Philadelphia, 1988. (library)
3.	Szenkovits, Ferenc: Celestial mechanics (http://www.ubbcluj.ro/~fszenko)	

VI. Thematic of didactic activities per weeks
WEEK 1 (2 hours course + 2 hours seminar) ([1], pp: 34-50 ; [2], pp: 70-88)
1 The two-body problem
   1.1 Newton’s laws of motion and of gravitation
   1.2 The solution of the two-body problem
WEEK 2 ([1], pp: 50-55 ; [2], pp: 76-89)
   1.3 The elliptic orbit
WEEK 3 ([1], pp: 55-61 ; [2], pp: 89-96)
   1.4 The parabolic orbit
   1.5 The hyperbolic orbit
WEEK 4 ([1], pp: 61-80 ; [2], pp: 97-110)
   1.6 The rectilinear orbit
   1.7 Barycentric orbits
   1.8 Classification of orbits with respect to the energy constant
   1.9 The orbits in space
   1.10 The f and g series
   1.11 The use of recurrence relations
WEEK 5 ([1], pp: 9-18 ; [2], pp: 111-120)
2. The many-body problem
   2.1 The equation of motion in the many-body problem
   2.2 The ten known integrals and their meanings
   2.3 The force function
   2.4 The virial theorem
WEEK 6 ([1], pp: 164-176 ; [2], pp: 121-150)
   2.5 Lagrange’s solutions of the three-body problem
   2.6 The circular restricted three-body problem
WEEK 7 ([1], pp: 176-246 ; [2], pp: 150-161)
   2.7 The general three-body problem
   2.8 Jacobian coordinates for the many-body problem
WEEK 8 ( [2], pp: 164-179)
3. General perturbations
   3.1 The nature of the problem
   3.2 The equations of the relative motion
   3.3 The disturbing function
   3.4 The sphere of influence
   3.5 The potential of a body of arbitrary shape
   3.6 Potential at a point within a sphere
WEEK 9 ([1], pp: 247-252 ; [2], pp: 179-194)
   3.7 The method of the variation of the parameters
WEEK 10 ([1], pp: 262-270 ; [2], pp: 194-198)
   3.8 Lagrange’s equations of motion
WEEK 11 ([1], pp: 304-311 ; [2], pp: 198-205)
   3.9 Hamilton’s canonic equations
   3.10 Derivation of Lagrange’s planetary equations from Hamilton’s canonic equations
WEEK 12 ( [2], pp: 206-212)
4. Special perturbations
   4.1 Factors in special perturbation problems
   4.2 Cowell’s method
   4.3 Encke’s method
WEEK 13 (; [2], pp: 212-227)
   4.4 The use of perturbational equations
   4.5 Regularization methods 
WEEK 14 ([1], pp: 28-33 ; [2], pp: 227-238)
   4.6 Numerical integration methods	

VII. Didactic methods used
Lecture, colloquy, modelling, problem solving, individual and team projects.	

VIII. Assessment
The activity ends with a written final. The exam subjects have theoretical questions from all the studied topics, and one problem, among the problems studied at the course and the seminar. There is an evaluation of the overall seminar activity, and the documentations prepared for the programming projects will be evaluated. The final grade is the mean of the grades mentioned above. The final grade = Home works 50%. Written Exam 50%.	

IX. Additional 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.	Drâmbă, Constantin: Elemente de mecanică cerească, Bibl. SSMF, Bucureşti, 1958.
4.	Érdi Bálint: Égi mechanika, Tankönyvkiadó, Budapest, 1992. 
5.	Moulton, Forest Ray:  An introduction to celestial mechanics, The Macmillan Company, London, 1923.
6.	Roy, A. E.: Orbital motion, Third Edition, Adam Hilger, Bristol and Philadelphia, 1988. 
7.	Stiefel, E. L. – Scheifele, G.: Linear and regular celestial mechanics, Springer-Verlag, Berlin Heidelberd New York, 1971.
8.	Szebehely, Victor: Theory of orbits, Academic Press, New York – San Francisco – London, 1967.
9.	Szebehely, Victor: Adventures in celestial mechanics, University of Texas Press, Austin, 1989.
10.	Wintner Aurel: The analytical foundations of celestial mechanics, Princeton, New Yersey, 1947.	

	Date,	20.04.2007				Course responsible,
							Assoc.Prof. SZENKOVITS Ferenc, Ph.D.