In this talk I will present equations for the motion of linear viscoelastic bodies interacting under gravity. The equations are fully three dimensional and allow for the integration of the spin, the orbit, and the deformation of each body.The equations are obtained within a finite dimension Lagrangian framework with dissipation function. The main result is an “Association Principle” that stablishes a conection between any spring-dashpot rheological model and the rheology of the deformation variables in the time domain. The theory is applied to the Earth (solid part plus oceans) using a Wiechert rheological model.
Finally the effect of deformation inertia on tides will be discussed.