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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Great-circle distance ： ウィキペディア英語版 Great-circle distance The great-circle or orthodromic distance is the shortest distance between two points on the surface of a sphere, measured along the surface of the sphere (as opposed to a straight line through the sphere's interior). The distance between two points in Euclidean space is the length of a straight line between them, but on the sphere there are no straight lines. In non-Euclidean geometry, straight lines are replaced with geodesics. Geodesics on the sphere are the ''great circles'' (circles on the sphere whose centers coincide with the center of the sphere). Through any two points on a sphere which are not directly opposite each other, there is a unique great circle. The two points separate the great circle into two arcs. The length of the shorter arc is the great-circle distance between the points. A great circle endowed with such a distance is the Riemannian circle. Between two points which are directly opposite each other, called ''antipodal points'', there are infinitely many great circles, but all great circle arcs between antipodal points have the same length, i.e. half the circumference of the circle, or $\backslash pi\; r$, where ''r'' is the radius of the sphere. The Earth is nearly spherical (see Earth radius) so great-circle distance formulas give the distance between points on the surface of the Earth (''as the crow flies'') correct to within 0.5% or so. A ''great circle'' arc, is together with the rhumb line and the isoazimuthal, one of the three lines that can be drawn between any two points on the earth's surface. ==Formulas== Let $\backslash phi\_1,\backslash lambda\_1$ and $\backslash phi\_2,\backslash lambda\_2$ be the geographical latitude and longitude of two points 1 and 2, and $\backslash Delta\backslash phi,\backslash Delta\backslash lambda$ their absolute differences; then $\backslash Delta\backslash sigma$, the central angle between them, is given by the spherical law of cosines: :$\backslash Delta\backslash sigma=\backslash arccos\backslash bigl(\backslash sin\backslash phi\_1\backslash cdot\backslash sin\backslash phi\_2+\backslash cos\backslash phi\_1\backslash cdot\backslash cos\backslash phi\_2\backslash cdot\backslash cos(\backslash Delta\backslash lambda)\backslash bigr).$ The distance ''d'', i.e. the arc length, for a sphere of radius ''r'' and $\backslash Delta\backslash sigma$ given in radians :$d\; =\; r\; \backslash ,\; \backslash Delta\backslash sigma.$ 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「Great-circle distance」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.