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oblate spheroid : ウィキペディア英語版
Spheroid

A spheroid, or ellipsoid of revolution, is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters.
If the ellipse is rotated about its major axis, the result is a prolate (elongated) spheroid, like an American football or rugby ball. If the ellipse is rotated about its minor axis, the result is an oblate (flattened) spheroid, like a lentil. If the generating ellipse is a circle, the result is a sphere. A spheroid has circular symmetry.
Because of the combined effects of gravity and rotation, the Earth's shape is not quite a sphere but instead is slightly flattened in the direction of its axis. For that reason, in cartography the Earth is often approximated by an oblate spheroid instead of a sphere. The current World Geodetic System model uses a spheroid whose radius is 6,378.137 km at the equator and 6,356.752 km at the poles.
The word ''spheroid'' originally meant an ''approximately spherical body'',
admitting irregularities even beyond the bi- or tri-axial ellipsoidal shape,
and that is how it is used in some older papers on geodesy
(for example, referring to truncated spherical harmonic expansions of the Earth〔Torge, Geodesy, p.104()〕).
==Equation==

The equation of a tri-axial ellipsoid centred at the origin with semi-axes ''a'', ''b'' and ''c'' aligned along the coordinate axes is
:::\frac+\frac+\frac = 1
The equation of a spheroid with ''z'' as the symmetry axis is given by setting ''a=b'':
:::\frac+\frac=1.
The semi-axis ''a'' is the equatorial radius of the spheroid, and ''c'' is the distance from centre to pole along the symmetry axis. There are two possible cases:
:::
*   ''c < a''  :  oblate spheroid
:::
*   ''c > a''  :  prolate spheroid
The case of ''a=c'' reduces to a sphere.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Spheroid」の詳細全文を読む



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