Stellar Orbits: Understanding Galactic Dynamics

This lecture focuses on the dynamics of stellar orbits within the Milky Way, particularly in the Sun's neighborhood. The instructor begins by discussing the Oort constants and their significance in understanding the global motions of stars. The lecture emphasizes the use of epicyclic frequencies to analyze stellar movements and how these relate to the overall dynamics of the galaxy. The instructor introduces the concept of integral of motions and Poincaré maps, which are essential for visualizing the behavior of stars in different gravitational potentials. The discussion progresses to the mathematical framework necessary for deriving these quantities, including the use of Taylor expansions and Jacobian matrices. The instructor explains how local observations can inform us about the broader galactic dynamics, despite the challenges posed by dust and limited visibility. The lecture concludes with insights into how recent data from the Gaia satellite has enhanced our understanding of these stellar motions and the implications for galactic structure.