Secular changes in length of day induced by the redistribution potential

The secular change in the length of day due to mass redistribution effects is revisited using the Hamiltonian formalism of the rotation of a two-layer deformable Earth. The dissipative effects at the core-mantle boundary are described through a coupling torque formulated by means of generalized forces. Taking advantage of the canonical procedure, a closed analytical formula for the secular deceleration of the rotation rate is obtained, which can be evaluated using frequency-dependent Love numbers corresponding to solid and oceanic tides.

Under the widespread assumption of totally coupled core and mantle layers in the long-term response, a secular angular deceleration of 1328.6 as/cy² is calculated, equivalent to an increase of 2.418 ms/cy in the length of day. Such an estimate is in very good agreement with recent observational values and theoretical predictions based on comparable modeling features. The complete research work can be consulted in the paper by Baenas, T., Escapa, A., and Ferrándiz, J. M. (2021), entitled “Secular changes in length of day: Effect of the mass redistribution” (A&A 648, A89).

This work has been partially supported by the Spanish projects PID2020-119383GB-I00 funded by Ministerio de Ciencia e Innovación (MCIN/AEI/10.13039/501100011033/) and  PROMETEO/2021/030 funded by Generalitat Valenciana.