Indirect perturbation influence of planets on the variation of the instantaneous angular velocity of the rigid Earth in the lunar-solar gravitational field

Abstract

The differential equation and its solution for indirect influence of the planetary perturbation on the variation of the rotational angular velocity of the rigid Earth in the lunar-solar gravitational field are obtained by using Euler’s dynamic equations. The theoretical results show that the angular velocity of the Earth varies with the periodic and mixed periodic variation under the lunar and solar gravitational field due to the planetary perturbation on the Earth orbit. The numerical results for the amplitudes of the periodic terms and the coefficient of the mixed periodic terms are presented.