First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
Course unit
SCN1032619, A.A. 2017/18

Information concerning the students who enrolled in A.Y. 2017/18

Information on the course unit
Degree course Second cycle degree in
SC1173, Degree course structure A.Y. 2010/11, A.Y. 2017/18
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Degree course track ASTRONOMIA [001PD]
Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination CELESTIAL MECHANICS
Website of the academic structure
Department of reference Department of Physics and Astronomy
Mandatory attendance
Language of instruction English
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge STEFANO CASOTTO FIS/05

Course unit code Course unit name Teacher in charge Degree course code

ECTS: details
Type Scientific-Disciplinary 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
Hours of
Individual study
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 Two-Body Problem and an initial value problem (IVP)
3. The Two-Body 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 Two-Body 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 Three-Body Problem – Jacobi’s integral, surfaces of zero velocity, Lagrangian points, Stability, Periodic orbits
13. The theory of Patched Conics and the design of gravity-assist 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.): Willmann-Bell, 1988. Cerca nel catalogo
  • Roy, Archie Edmiston, Orbital motion. New York: London, Taylor & Francis, 2005. Cerca nel catalogo
  • Vallado, David A.; McClain, Wayne D., Fundamentals of astrodynamics and applications. Hawthorne: CA, Microcosm press, New York, Springer-Verlag, 2007. Cerca nel catalogo
  • 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:, 2016. Cerca nel catalogo
  • Curtis, Howard D., Orbital mechanics for engineering students. Amsterdam: Elsevier Butterworth Heinemann, 2013. Cerca nel catalogo