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 3-body problem. Finally, students will acquire a basic knowledge of perturbation theory and numerical orbit integration.

Course contents

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 - Lagrangian points - The restricted, circular three-body problem - Jacobi's integral - Zero-velocity surfaces  - Stability of Lagrangian points - Periodic orbits - Regular and chaotic orbits - The general three-body problem -  Hierarchical dynamical systems - Introduction to perturbation theory - Lagrange's planetary equations - Lidov-Kozai oscillations - Precession of Mercury's perihelion - Numerical integration of orbits - Structure of the Solar System - Resonances - Dynamical evolution of the Solar System - Extrasolar planetary systems

Readings/Bibliography

Main textbooks:

• 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 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