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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 ::: The equation of a spheroid with ''z'' as the symmetry axis is given by setting ''a=b'': ::: 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 スポンサード リンク
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