03391 - Celestial Mechanics

Learning outcomes

At the end of the course, students will gain an understanding of the key methods of celestial mechanics and some of its most important astrophysical applications. They will become familiar with the main results of the gravitational N-body problem with a particular emphasis on the 2- and 3-body problem. Finally, students will acquire a basic knowledge of perturbation theory and numerical orbit integration.

Course contents

Historical background on Celestial Mechanics - Fundamentals of Newtonian, Lagrangian and Hamiltonian mechanics - The N-body problem - Integrals of motion and conservation laws - The gravitational two-body problem - Reduced mass - Elliptic, parabolic and hyperbolic orbits - Kepler's laws - Systems of coordinates - Orbital elements - Kepler's equation - Action-angle coordinates - Orbital maneuvers - The gravitational three-body problem - The restricted, circular three-body problem - Jacobi's integral - Tisserand's criterion - Zero-velocity surfaces  - Lagrangian points - Stability of Lagrangian points - Orbits around Lagrangian points - Introduction to perturbation theory - The disturbing function - Precession of Mercury's perihelion (classical and relativistic treatment) - Numerical integration of orbits.

Readings/Bibliography

Main textbooks:

• S. Tremaine "Dynamics of planetary systems", Princeton University Press (selected parts of chapters 1, 2, 3, 4 and 5).
• A.E. Roy "Orbital Motion", Taylor & Francis (selected parts of chapters 2, 5 e 7).
• C.D. Murray & S.F. Dermott "Solar system dynamics", Cambridge University Press, (selected parts of chapters 2 1, 2, 3, 6, 9).
• L.D. Landau & E.M. Lifshitz "Mechanics", Butterworth–Heinemann (selected parts of chapters 2 1, 2, 3, 7)
• H. Goldstein, C. Poole, J. Safko “Classical mechanics” (3rd edition), Addison-Wesley (selected parts of chapters 2 1, 2, 3, 8, 9, 10).
  

Specific sections of textbooks and articles will be suggested during classes.

Notes prepared by the lecturer.

Teaching methods

Lectures with discussion of illustrative problems linked to the topics covered in class.

Assessment methods

The assessment method will be based on an oral exam in which the student will be asked to answer three questions about three different topics among those presented during the lectures. The first question will be about a topic freely chosen by the student. Students could also be asked to solve problems similar to the those illustrated in class. The oral exam is aimed at verifying the knowledge of the methods of celestial mechanics and the understanding of its astrophysical applications.

Teaching tools

Blackboard and projector.

Office hours

See the website of Federico Marinacci