Celestial Mechanics

A.Y. 2020/2021
Overall hours
Learning objectives
1. Introduction to the classical and modern methods of Celestial mechanics.

2. The problem of three bodies.
Expected learning outcomes
The classical mathematical methods of Celestial Mechanics.
Course syllabus and organization

Single session

Lesson period
Second semester
Didactic methods
The lessons will be held on a virtual platform (for example Zoom or Microsoft Teams) and can be followed both synchronously based on the time of the second semester and asynchronously because they will be recorded and left available to students (for example by publishing them on Ariel or directly on the teacher's page).

Program and reference material will not change.

Methods of verifying learning and assessment criteria will not be subject to changes.
Course syllabus
Introduction to classical and modern methods of celestial mechanics.
1) Planetary motion. Kepler's ellipses. Newton's gravitation. The orbital elements. Determination of orbits. Recalls of Hamiltonian formalism and canonical variables.
2) Perturbative methods: from Laplace and Lagrange theory to KAM tori.
3) The three-body problem.
4) The problem of the stability of the solar system and Nekhoroshev's theory.
5) The dynamics of extrasolar systems.
Prerequisites for admission
Knowledge of analysis, geometry, linear algebra and mathematical physics provided in the three-year degree course in Mathematics.
In particular Newtonian Mechanics, Lagrangian Mechanics.
Teaching methods
Lectures, strongly recommended frequency.
Teaching Resources
Lecture notes and a list of recommended books available in the library will be available on the teacher's web page.
Assessment methods and Criteria
The exam consists of a written test or a project, followed by an oral test.
MAT/07 - MATHEMATICAL PHYSICS - University credits: 6
Lessons: 42 hours
Professor: Sansottera Marco