Organizzazione della Didattica


Celestial Mechanics




Frontali Esercizi Laboratorio Studio Individuale
ORE: 48 0 0 85


I anno2 semestre







Calendario Attività Didattiche




Responsabile Insegnamento

Dott. CASOTTO STEFANOFIS/05Dipartimento di Fisica e Astronomia "Galileo Galilei"

Altri Docenti

Non previsti

Attività di Supporto alla Didattica

Non previste


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.

• 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)

Lectures, homework assignments, Matlab (Fortran, C++, ...) code development, computer lab activities, special topic analysis during final project.

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

Homework, Final project report, Oral presentation of final report and discussion.

Homework 30%, Final project 40%, Oral exam 30%

Danby, John M. Anthony, Fundamentals of celestial mechanics. Richmond (Va.): Willmann-Bell, 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, Springer-Verlag, 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:, 2016 Curtis, Howard D., Orbital mechanics for engineering students. Amsterdam: Elsevier Butterworth Heinemann, 2013

Casotto, Lezioni di Meccanica Celeste