
Course unit
CELESTIAL MECHANICS
SCN1032619, A.A. 2017/18
Information concerning the students who enrolled in A.Y. 2017/18
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
FIS/05 
Astronomy and Astrophysics 
6.0 
Mode of delivery (when and how)
Period 
Second semester 
Year 
1st Year 
Teaching method 
frontal 
Organisation of didactics
Type of hours 
Credits 
Hours of teaching 
Hours of Individual study 
Shifts 
Lecture 
6.0 
48 
102.0 
No turn 
Start of activities 
26/02/2018 
End of activities 
01/06/2018 
Prerequisites:

Students are expected to be familiar with Rational Mechanics and Mathematical Analysis, including the elementary theory of Ordinary Differential Equations.
A fair amount of curiosity about dynamical phenomena observed in the Solar and other planetary systems is useful, together with an interest in their precise modeling and computation and the design of exploration missions. 
Target skills and knowledge:

• Develop an understanding of dynamical phenomena in gravitating systems
• Application of Newtonian Mechanics to the solution of the fundamental problems of the Celestial Mechanics of natural bodies and artificial satellites
• Solution of Inverse Problems with applications to Orbit Determination
• Introduction to the design of orbits for planetary and interplanetary exploration
• Develop numerical computations in Matlab (or compiled languages), including the numerical integration of the equations of motion
• Learn how to use the General Mission Analysis Tool (GMAT) 
Examination methods:

Homework, Final project report, Oral presentation of final report and discussion of the results and other topics covered during the lectures. 
Assessment criteria:

Homework 40%, Final project 30%, Oral exam 30% 
Course unit contents:

1. The equations of motion of gravitating systems
2. The TwoBody Problem and an initial value problem (IVP)
3. The TwoBody Problem and a boundary value problem (BVP)
4. Orbital maneuvers
5. Space and time reference systems
6. The computation of a Keplerian ephemeris
7. Preliminary orbit determination
8. Keplerian relative motion and its generalization
9. Regularization and Universal Formulation of the TwoBody Problem
10. The TBP as a boundary value problem (BVP) – Lambert targeting
11. The Problem of Three Bodies and its homographic solutions
12. The Circular Restricted ThreeBody Problem – Jacobi’s integral, surfaces of zero velocity, Lagrangian points, Stability, Periodic orbits
13. The theory of Patched Conics and the design of gravityassist interplanetary trajectories
14. Elements of perturbations and a the motion of an artificial Earth satellite 
Planned learning activities and teaching methods:

Lectures, homework assignments, Matlab (Fortran, C++, ...) code development, computer lab activities, special topic analysis during final project. 
Additional notes about suggested reading:

Casotto, Lecture notes on Celestial Mechanics 
Textbooks (and optional supplementary readings) 

Danby, John M. Anthony, Fundamentals of celestial mechanics. Richmond (Va.): WillmannBell, 1988.

Roy, Archie Edmiston, Orbital motion. New York: London, Taylor & Francis, 2005.

Vallado, David A.; McClain, Wayne D., Fundamentals of astrodynamics and applications. Hawthorne: CA, Microcosm press, New York, SpringerVerlag, 2007.

Murray, Carl D.; Dermott, Stamòey F., Solar System Dynamics. Cambridge: Cambridge University Press, 2000.

Cordani, B., I cieli in una stanza. Una storia della Meccanica Celeste dagli epicicli di Tolomeo ai tori di Kologorov.. Padova: Libreriauniversitaria.it, 2016.

Curtis, Howard D., Orbital mechanics for engineering students. Amsterdam: Elsevier Butterworth Heinemann, 2013.


