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Tidal effects in the earth–moon system and the earth's rotation

G. A. Krasinsky

Celestial Mechanics and Dynamical Astronomy, 75(1), 39-66 (1999)

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Analytical expressions for tidal torques induced by a tide‐arising planet which perturbs rotation of a nonrigid body are derived. Corresponding expressions both for secular and periodic perturbations of the Euler's angles are given for the case of the earth's rotation. Centennial secular rates of the nutation angle θ and of the earth's angular velocity ω, as well as the centennial logarithmic decrement ν of the Chandler wobble are evaluated: θ˙θ˙ mas, ω˙/ω=−5.08 mas = −24.6 × 10−9, v=−12.3 masω˙/ω=−5.08 mas = −24.6 × 10−9, v=−12.3 mas. In the Universal Time (UT) a large out‐of‐phase (sine) dissipative term with the period 18.6 years and the amplitude 2.3 ms is found. Corrections to nutation coefficients, which presumably have not been taken into account in IAU theory, are given.