ON THE HISTORY OF THE LUNAR ORBIT.

A frequency-dependent model of tidal friction is used in the development of equations for the time rate of change of the lunar orbital elements and the angular velocity of the earth. While the inclination of the lunar orbit and obliquity of the earth remain small, a linearized solution, employing complex variables, of the equations governing the precession of the polar axis of the earth and normal axis to the lunar orbit plane is found. It is shown analytically and numerically that in the vicinity of the predicted close approach of the moon to the earth the precessional motion of both bodies occurs about a common axis. This allows the derivation of a nonlinearized solution for the precessional motion when the precession angles become large.