Estimation of the frictional dissipation of lunisolar tide †*

Lunisolar tidal friction and variation in the earth's moment of inertia are the major factors for the long-term change in the length of day (lod). This article uses the latest geophysical and paleontological clock data to study and compare numerically the lunisolar tidal friction, variation in the terrestrial moment of inertia and long-term change in the lod for the past 1500 Ma. Two important conclusions are obtained: 1) the variation in J2 can not be explained solely by the rotational deformation of the earth, which shows that gravitational differentiation still exists in the earth; 2) tidal friction was much greater a few hundred million years ago than it is now. If it is assumed that tidal dissipation is inversely proportional to the cube of the distance between the earth and the moon, then the theoretical results of the numbers of days in a tropical year and in a synodic month accord rather well with the paleontological clock data.