Abstract

“Distorted” gas discs in which the orbital motion is non-circular or non-planar are implicated in many astrophysical scenarios and lie at the interface between celestial mechanics and fluid dynamics. Using a vector approach to celestial mechanics developed originally by Milankovitch, I will illustrate and interpret some aspects and applications of secular theory, which describes how eccentricity and inclination are communicated gravitationally between the members of a planetary system or multiple star system (for example) over very many orbits. This classical theory can be extrapolated into an approach to understanding distorted discs as systems in which eccentricity and inclination are continuously distributed and are communicated through pressure as well as gravity. Instead of solving the equations of fluid dynamics, we can include in the Hamiltonian the internal energy of the gas and its response to the orbital geometry. Together with a “columnar” view of the motion in a disc, this approach reveals some of the characteristic properties of warped and eccentric discs in linear and nonlinear regimes. I will describe progress towards a unified description of distorted discs, also incorporating dissipative processes, as well as some outstanding problems.