New treatment of tidal braking of Earth rotation

Abstract

We estimate the tidal braking of the Earth rotation by calculating the tidal torque on the Moon and the Sun exerted by the tidal potential of the Earth. Using this simple method and the tidal parameters estimated from modern satellite tracking data, we derive the tidal secular change in the Earth rotation with a high accuracy. The results from three sets of tidal parameters from satellite tracking data are in good agreement. The average value of Ω ̇ t equals (−6.01±0.02)×10 −22 rad s −2. Based on the results of tidal braking of the Earth rotation and the astronomical records from 700 BC to 1600 AD, we obtain the non-tidal acceleration of the Earth rotation at Ω ̇ nt =(1.5±0.1)×10 −22 rad s −2. This result corresponds to J ̇ 2 =(−3.2±0.2)×10 −11/a which can be explained by the anelastic Earth responding to the post-glacial rebound. Our result of J ̇ 2 agrees very well with J ̇ 2 estimated directly from satellite tracking data.