Gravitational waves (GWs) are ripples in space-time that propagate deformations caused by compact bodies throughout the Universe. As an elastic body, the Earth responds to passing GWs much like a resonant sphere. This interaction produces a redistribution of mass, which results in perturbations of the Earth’s tensor of inertia. By conservation of angular momentum, such perturbations lead to a displacement of the rotation axis within the mantle (polar motion) and to changes in the spin rate, directly linked to variations in the length of day (LOD). In this work, we compute for the first time the perturbations of the Earth’s rotation induced by GWs emitted by compact white-dwarf binaries, using a normal mode summation approach applied to an elliptical, rotating, radially stratified Earth model. Our results indicate maximal amplitudes of approximately ${10}^{-15}\mathrm{\mu }\mathrm{s}$ in the LOD and ${10}^{-15}$ mas for the polar motion—values that remain far below current instrumental sensitivities. These findings highlight the extreme difficulty of detecting GWs through their rotational effects on the Earth, yet the methodology developed here offers a framework that could be extended to other astrophysical bodies.

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• Gravitational wave detection
• Gravitational waves
• Seismology