Kinematical modeling of the Earth rotation, focusing on the Oppolzer terms in a rigid Earth and the Oppolzer-like terms in an elastic Earth

Author: Kubo, Yoshio

Source: Celestial Mechanics and Dynamical Astronomy, Volume 110, Number 2, June 2011 , pp. 143-168(26)

Publisher: Springer

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Under perturbations from outer bodies, the Earth experiences changes of its angular momentum axis, figure axis and rotational axis. In the theory of the rigid Earth, in addition to the precession and nutation of the angular momentum axis given by the Poisson terms, both the figure axis and the rotational axis suffer forced deviation from the angular momentum axis. This deviation is expressed by the so-called Oppolzer terms describing separation of the averaged figure axis, called CIP (Celestial Intermediate Pole) or CEP (Celestial Ephemeris Pole), and the mathematically defined rotational axis, from the angular momentum axis. The CIP is the rotational axis in a frame subject to both precession and nutation, while the mathematical rotational axis is that in the inertial (non-rotating) frame. We investigate, kinematically, the origin of the separation between these two axes—both for the rigid Earth and an elastic Earth. In the case of an elastic Earth perturbed by the same outer bodies, there appear further deviations of the figure and rotational axes from the angular momentum axis. These deviations, though similar to the Oppolzer terms in the rigid Earth, are produced by quite a different physical mechanism. Analysing this mechanism, we derive an expression for the Oppolzer-like terms in an elastic Earth. From this expression we demonstrate that, under a certain approximation (in neglect of the motion of the perturbing outer bodies), the sum of the direct and convective perturbations of the spin axis coincides with the direct perturbation of the figure axis. This equality, which is approximate, gets violated when the motion of the outer bodies is taken into account.

Keywords: Angular momentum axis; Convective terms; Earth rotation; Elastic Earth; Figure axis; Oppolzer terms; Poisson terms; Precession and nutation; Rigid Earth; Rotational axis

Document Type: Research Article


Affiliations: 5-8-3 Higashi-gotanda, Shinagawa-ku, Tokyo, 141-0022, Japan, Email:

Publication date: June 1, 2011

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