The local and total dissipation rate of mechanical energy is calculated for an incompressible, Kelvin-Voigt body in a circular orbit with finite obliquity. This material is characterized by a shear modulus and a viscosity. While in principle both of these material constants could be determined experimentally, only the shear modulus is known. The variation of the total dissipation rate with the viscosity is studied. For 'small' values of the viscosity the Kelvin--Voigt material approximates the behavior of an elastic solid. In this range, results for the earth-moon system are similar to those obtained by Peale and Cassen (1978) using a modified form of the elastic solution. For 'large' values of the viscosity the results are qualitatively different from those in the 'elastic' range, as viscous effects dominate the material response.