Variation of the instantaneous angular velocity of the rigid Earth in the lunar–solar gravitational field

The variation of the instantaneous rotational angular velocity of the rigid Earth in the lunar-solar gravitational field is studied. The formula is derived for variation of the instantaneous angular velocity of the rigid oblate Earth using the potential function from Euler’s dynamic equations. The theoretical results show that under the influence of the gravitational field of the Moon and the Sun the Earth instantaneous angular velocity varies with periodic terms, but without secular variations. Amplitudes of the periodic terms and their periods are calculated and discussed.