The time series of northern hemisphere (NHSI) and southern hemisphere (SHSI) sea-ice extent are submitted to singular spectral analysis (SSA). The spectral components are analyzed with Laplace's formulation of the Liouville-Euler system of differential equations. Laplace assumes that all masses on and in Earth are set into motion by astronomical forces. As already shown in a previous work (see Le Mouël et al., (2021b), figure 03), the trends observed in the time series are quasi linear, decreasing for NHSI (by 58.300 km 2 /yr) and increasing for SHSI (by 15.400 km 2 /yr). The amplitude of annual variations in the Antarctic is double that in the Arctic, they are in phase opposition and modulated, with a flat trend for SHSI, a decreasing trend for NHSI and a sub-decadal modulation of the envelopes. The semi-annual components are in quadrature. The first three oscillatory components of both NHSI and SHSI at 1, 1/2 and 1/3 yr account for more than 95% of the signal variance. The trends are respectively 21 (Antarctic) and 4 times (Arctic) less than the amplitudes of the annual SSA components. Following Laplace's views, we complement previous analyses of variations in pole position (PM for polar motion, with coordinates m 1 , m 2 ) and length of day (lod). Whereas SSA of lod is dominated by the same first three components as sea-ice, SSA of PM contains only the 1 yr forced annual oscillation and the Chandler ∼1.2 yr components. The 1 yr component of NHSI is in phase with that of lod and in phase opposition with m1. The reverse holds for the 1 yr component of SHSI. We note that the semi-annual component appears in lod not in m 1 . The annual and semi-annual components of NHSI and SHSI are much larger than the trends observed since 1978, that leads us to test whether a first order geophysical or astronomical forcing should not be preferred to the mechanisms generally suggested as a forcing factor of the trends. The lack of modulation of the largest (SHSI) forced component suggests an alternate mechanism. In Laplace's paradigm, the torques exerted by the Moon, Sun and planets play the leading role as the source of forcing (modulation) of many geophysical phenomena. These forces (and torques) lead to changes in the inclination of the Earth's rotation axis, transferring stresses to the Earth's solid and fluid envelopes, setting Earth masses in motion and resulting in thermal dissipation: more than variations in eccentricity, it is variations in inclination of the rotation axis that lead to the large annual components of melting and re-freezing of sea-ice.
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