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Earth and Space Sciences · 术语表

什么是 Reference ellipsoid？

Definition 3.5 University Earth and Space Sciences — Year 3 · 第 3 章 — Gravity and the Figure of the Earth

A reference ellipsoid is an ellipsoid of revolution, of equatorial semi-axis $a$ and flattening $f$ , chosen so that it is itself a level surface of a model potential: the potential of a rotating body of mass $M$ with the angular velocity $\omega$ and the dynamical form factor $J_2$ of the Earth. Four constants define it; the Geodetic Reference System 1980 takes

\begin{gather*} a = 6\,378\,137\,\mathrm{m},\qquad GM = 3.986\,005 \times 10^{14}\,\mathrm{m}^{3}\,\mathrm{s}^{-2},\\ J_2 = 1.082\,63 \times 10^{-3},\qquad \omega = 7.292\,115 \times 10^{-5}\,\mathrm{rad}\,\mathrm{s}^{-1}, \end{gather*}

and derives from them the flattening $f = 0.003\,352\,810\,68$ ( $1/f = 298.257\,222$ ) and the semi-minor axis $b = 6\,356\,752.3141\,\mathrm{m}$ .

The flattening of a fluid planet with the Earth’s rotation, against its moment-of-inertia factor, from the Darwin–Radau relation (computed from the Geodetic Reference System 1980). The more the mass is concentrated towards the centre, the rounder the planet. At the Earth’s 0.3308 the hydrostatic flattening is 1/299.9, a little less than the observed 1/298.26. — The flattening of a fluid planet with the Earth’s rotation, against its moment-of-inertia factor, from the Darwin–Radau relation (computed from the Geodetic Reference System 1980). The more the mass is concentrated towards the centre, the rounder the planet. At the Earth’s $0.3308$ the hydrostatic flattening is $1/299.9$ , a little less than the observed $1/298.26$ .

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