Re-estimation of Earth spin rotational energy decrease due to tidal friction

Abstract

The Earth undergoes tidal deformation due to the Moon and the Sun, and its spin angular velocity is being gradually reduced by the tidal friction, while the Earth-Moon distance is slowly increasing accordingly. The amount of this energy loss has been formerly estimated by simplified two-dimensional model of the Earth-Moon system. In this study, we repeated the same kind of estimation with the latest data for the lunar recession rate. For more accurate estimation, we further developed a three-dimensional model by taking into account the Earth’s obliquity angle and lunar orbital inclination and eccentricity. The Earth spin rotational energy loss estimated from the three-dimensional model amounts to 3.54×1012 Watt, slightly greater than that (3.28×1012 Watt) from the two-dimensional model which tends to underestimate it due to oversimplification of the orbital geometry. About 97% of the energy loss is being transformed into heat of 3.42×1012 Watt, which is about the total human expenditure of electric power. The quality factors of the Earth’s body tide estimated from the energy loss, assuming that the body tidal dissipation is 5 to 10% of the total tidal dissipation, range from 90 to 190.