- Docente: Carlo Nipoti
- Credits: 6
- SSD: FIS/05
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: First cycle degree programme (L) in Astronomy (cod. 8004)
Learning outcomes
The aim of the course is providing the student with the fundamental
tools of celestial mechanics and introducing some important
astrophysical applications. At the end of the course the
student will be familiar with the main results on the gravitational
N-body problem and, in particular, on the three-body problem. The
student will also have a basic knowledge of the methods of general
perturbations and numerical integration of orbits.
Course contents
Fundamentals of Newtonian, Lagrangian and Hamiltonian mechanics -
The N-body problem - Integrals of motion and conservation laws - The gravitational two-body problem -
The reduced mass - Elliptic, parabolic and hyperbolic orbits -
Kepler's laws - Systems of coordinates - Orbital elements -
Kepler's equation - Action-angle variables - The gravitational three-body problem -
Lagrangian equilibrium points - The circular restricted three-body
problem - Jacobi's integral - Surfaces of zero velocity - Stability
of the Lagrangian points - Periodic orbits - Regular and chaotic orbits - The general three-body
problem - Hierarchical dynamical systems - Introduction to
perturbation theory - The disturbing
function - Lagrange's planetary equations - Lidov-Kozai oscillations - Precession of the perihelion of Mercury - Numerical integration of orbits -
Multiple systems of stars - Dynamics of binary supermassive black
holes in the centres of galaxies - Structure of the Solar System
- Resonances - Dynamical evolution of the Solar System -
Extrasolar planetary systems
Readings/Bibliography
The main reference textbooks are:
- A.E. Roy "Orbital Motion" Taylor & Francis (selected sections from chapters 2, 5, 7)
- C.D. Murray & S.F. Dermott "Solar system dynamics", Cambridge
University Press (selected sections from chapters 1, 2, 3, 6, 9)
- L.D. Landau & E.M. Lifshitz "Mechanics", Butterworth–Heinemann (selected sections from chapters 1, 2, 3, 7)
Other books and articles will be suggested during the
lectures.
Lecture notes will be made available to the students.
Teaching methods
Lectures
Assessment methods
The assessment method will be based on an oral examination in which
the student will be asked to answer three questions about three
different topics among those presented during the lectures. The
oral examination is aimed at verifying the knowlegde of both the
methods of celestial mechanics and the astrophysical applications.
Teaching tools
Blackboard and projector
Office hours
See the website of Carlo Nipoti