The kinematical mechanism for the perturbation of the rotational axis in the rotation of the elastic Earth |
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Authors: | Yoshio Kubo |
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Institution: | (1) Royal Observatory of Belgium, B 1180 Bruxelles, Belgium, e-mail |
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Abstract: | Kubo (Celest Mech Dyn Astron 110:143–168, 2011) investigated the kinematical structure of the perturbation in the rotation of the elastic Earth due to the deformation caused
by the outer bodies. In that paper, while the mechanism for the perturbation of the figure axis was made clear, that for the
rotational axis was not shown explicitly. In the present study, following the same method, the structure of the perturbation
of the rotational axis is investigated. This perturbation consists of the direct perturbation and the convective perturbation.
First the direct perturbation is shown to be (A − C)/A times as large as that of the figure axis, coinciding with the analytical expressions obtained in preceding studies by other
authors. As for the convective perturbation, which appears only in the perturbation of the rotational axis but not in that
of the figure axis, it is shown to be (A − C)/A times the angular separation between the original figure axis and the induced figure axis produced by the elastic deformation,
A and C being the principal moments of inertia of the Earth. If the perturbing bodies are motionless, the conclusion of Kubo (Celest
Mech Dyn Astron 105:261–274, 2009) holds strictly, i.e. the sum of the direct and the convective perturbations of the rotational axis coincides with the perturbation
of the figure axis. |
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