Abstract: The rule of angular momentun conservation for Earth-Moon system iscorrect to a great extent. The Earth-Moon distance is affected mainly by thelunar tidal friction, therefore according to lunar mean motion and itssecular acceleration, the energy dissipated by lunar tides could becalculated. Oceans are the main region for the tidal energy dissipation. Asthe gravitational force between the moon and oceanic tidal bulge isproportional to the oceanic tide height, which leads to the total tidalfriction is proportional to the square of lunar mean motion. If adopting asmaller value of lunar acceleration -20.72'\cdotcy^-2, the evolution ofdistance between Earth-Moon and the length of day can be extrapolated up to3.5 billion years ago. The theoritical number of days in a tropical year andin a synodic month is consistent with the data of the paleontological clockfossils.