The equations of motion for a system of two deformable bodies are analyzed with a view toward describing orbital evolution. These bodies are modeled as incompressible, viscoelastic solids. The mean tidal moment exerted by each body in a slightly eccentric orbit is obtained directly from the deformation induced by gravitational attraction. The corresponding orbital evolution is described analytically by determining a slowly varying solution to the equations of motion. Results for the earth-moon system indicate that the mean orbital angular velocity is decreasing more rapidly at present than in the distant past. This change in the angular velocity rate suggests a possible resolution of the time-scale problem for lunar orbital evolution. |