Planetary Tides: Theories

Abstract

Synthetic presentation of planetary tide theories in the simple case of a homogeneous primary rotating around an axis orthogonal to the orbital plane of the companion. The considered theories are founded on the dynamical equilibrium figure of the tidally deformed body, assumed as an ellipsoid whose rotation is delayed with respect to the motion of the companion. The orbital and rotational evolutions of the system are derived using standard physical laws. The main theory considered is the creep tide theory, a first-principles hydrodynamical theory where the dynamical tide is assimilated to a low-Reynolds-number flow and determined using a Newtonian creep law. The Darwin theories are also considered and are formally derived from the creep tide theory. The various rheologies used in Darwin theories are discussed, with emphasis on the CTL (constant time lag) and CPL (constant phase lag) theories. One introductory session is devoted to the main classical results on the hydrostatic figures of equilibrium of the celestial bodies (static tide).