
Course unit
THEORY OF ORBITS
SCN1032624, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2018/19
Lecturers
No lecturer assigned to this course unit
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
FIS/05 
Astronomy and Astrophysics 
6.0 
Course unit organization
Period 
First semester 
Year 
2nd Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
6.0 
48 
102.0 
No turn 
Examination board
Examination board not defined
Prerequisites:

Analytical Mechanics. Celestial mechanics or Orbital Mechanics or Astrodynamics. 
Target skills and knowledge:

The aim of this course is to provide:
1) advanced knowledge of the dynamics of gravitationally interacting bodies in the framework of Newtonian Mechanics, including perturbations of nongravitational origin;
2) an opportunity to carry out analytical developments, also with the use of algebraic manipulator systems (e.g., Mathematica), which are characteristic of the theories of motion of celestial objects, both natural and artificial;
3) handson experience by developing numerical computational tools (in Matlab, Fortran90, C++, Python) for application to the prediction and the determination of the motion of celestial objects. 
Examination methods:

Oral final exam (discussion of final project and of two topics covered in the lectures in which the student is expected to propose and justify specific methodologies and techniques to be adopted for the solution of standard problems encountered in predicting the dynamical behavior of complex celestial system or when handling observational data of such systems). 
Assessment criteria:

Evaluation criteria:
1) Homework assignments (40% of the final mark).
2) Final project and presentation (40% of the final mark).
3) Final oral exam at the moment of the final project presentation (20% of the final mark). 
Course unit contents:

1) Perturbation theory (in the coordinates and in the orbital elements).
2) Series developments on the twobody problem.
3) Development of the disturbing function.
4) Lunar theory.
5) Planetary theory.
6) Theory of resonant motion (mean motion resonances, Kozai's theory, etc.).
7) Theory of the potential.
8) The motion of a space probe about a nearly spherical body (Kaula’s theory).
9) The motion of a space probe near an irregularly shaped body (asteroid, comet).
10) Spinorbit coupling and tidal evolution.
11) Estimation of the gravitational potential.
12) The theory of patched conics and the design of gravityassist interplanetary trajectories.
13) Trajectory design and optimization.
14) Lowthrust trajectory design and optimization.
15) Introduction to optimal control  Optimal satellite formationkeeping. 
Planned learning activities and teaching methods:

The course includes:
1) regular lectures with the use of the blackboard;
2) introduction to highprecision computer simulation of the dynamics of a system of celestial bodies;
3) discussion on the identification of topics for the final project.
All the activities are in Italian. 
Additional notes about suggested reading:

Textbooks. Lecture notes of the teachers "S. Casotto, Introduction to the theory of orbits".
"Boccaletti, Dino; Pucacco, Giuseppe, Theory of orbits 1: Integrable systems and nonperturbative methods. Berlin: SpringerVerlag, 1996.
Boccaletti, Dino; Pucacco, Giuseppe, Theory of orbits 2: Perturbative and geometrical methods. Berlin: SpringerVerlag, 1999.
Kaula, William M., Theory of satellite geodesy. Mineola (NY): Dover, 2000." 
Textbooks (and optional supplementary readings) 

Boccaletti, Dino; Pucacco, Giuseppe, Theory of orbits 1: Integrable systems and nonperturbative methods. Berlin: SpringerVerlag, 1996.

Boccaletti, Dino; Pucacco, Giuseppe, Theory of orbits 2: Perturbative and geometrical methods. Berlin: SpringerVerlag, 1999.

Kaula, William M., Theory of satellite geodesy. Mineola (NY): Dover, 2000.

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