A Search for the Earth's ‘Nearly Diurnal Free Wobble’

Summary The existence of the Earth's liquid core, besides affecting the period of the Chandler wobble, gives rise to a second free wobble mode, with period short of a sidereal day by a factor of the order of the ellipticity of the coremantle boundary. Seen from space this nearly diurnal geographic motion of the pole should appear as a nutation of the Earth's rotation axis, with a period theoretically calculated to be about 460 days, and (as pointed out by Toomre) an amplitude correspondingly 460 times larger than that of the associated wobble. The curious history of the ‘nearly diurnal wobble’ problem is reviewed, and the relevant dynamics derived and described in terms of Poinsot's scheme. A special method developed for harmonic analysis of non-equispaced data, applied to a 20-year record of observations with Loomis Polar Telescope of Yale University Observatory, sets an upper limit of 0"·12–0"·26 on the amplitude of any free nutation in obliquity in the frequency range 0–4 cpy, i.e. an upper limit of 0"·0003–0"·0006 on the amplitude of the nearly diurnal free wobbble. This supports Toomre's contention that earlier reports of observations of this wobble, with amplitudes in the range 0"·01–0"·02, cannot be correct.

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