Volume 648, April 2021
|Number of page(s)||9|
|Section||Celestial mechanics and astrometry|
|Published online||15 April 2021|
Secular changes in length of day: Effect of the mass redistribution
Department of Sciences, University Centre of Defence at the Spanish Air Force Academy,
Santiago de la Ribera,
2 Department of Aerospace Engineering, University of León, 24071 León, Spain
3 Department of Applied Mathematics, University of Alicante, PO Box 99, 03080 Alicante, Spain
Accepted: 5 March 2021
In this paper the secular change in the length of day due to mass redistribution effects is revisited using the Hamiltonian formalism of the Earth rotation theories. The framework is a two-layer deformable Earth model including dissipative effects at the core–mantle boundary, which are described through a coupling torque formulated by means of generalized forces. The theoretical development leads to the introduction of an effective time-averaged polar inertia moment, which allows us to quantify the level of core–mantle coupling throughout the secular evolution of the Earth. Taking advantage of the canonical procedure, we obtain a closed analytical formula for the secular deceleration of the rotation rate, numerical evaluation of which is performed using frequency-dependent Love numbers corresponding to solid and oceanic tides. With this Earth modeling, under the widespread assumption of totally coupled core and mantle layers in the long term response, a secular angular acceleration of − 1328.6′′ cy−2 is obtained, which is equivalent to an increase of 2.418 ms cy−1 in the length of day. The ocean tides and the semidiurnal band of the mass-redistribution-perturbing potential, mostly induced by the Moon, constitute the main part of this deceleration. This estimate is shown to be in very good agreement with recent observational values, and with other theoretical predictions including comparable modeling features.
Key words: celestial mechanics / methods: analytical / reference systems / Earth
© ESO 2021
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