Rotational dynamics of celestial deformable bodies

In a previous paper of this series (Tokis, 1974b), we have discussed the solution of the Eulerian equation which governs the axial rotation, applied to the effects of viscous friction exhibited in binary systems which consist of a close pair of fluid bodies of arbitrary structure. The aim of the present paper will be to give an application of those results to the Earth-Moon system. It is shown that synchronism between the axial rotation of the Earth and the revolution of the Moon will occur at the value of 650 h, in a time scale which depends strongly on the value of the mean viscosity of the Earth (regarded as spherical or spheroidal). In particular, the variation of rotational angular velocity of the Earth over the next ten centuries commencing from 1900 A.D., depends sensitively on the value of viscosity. On the other hand, the time for synchronism of axial rotation of the Moon is not affected by the viscosity for values between 10²⁴g cm^?1 s^?1 and 10²⁷g cm^?1 s^?1.