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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 ellipse ： ウィキペディア英語版 Great ellipse A great ellipse is an ellipse passing through two points on a spheroid and having the same center as that of the spheroid. Equivalently, it is an ellipse on the surface of spheroid and centered at the origin, or the curve formed by intersecting the spheroid by a plane through its center.〔 .〕 For points which are separated by less than about a quarter of the circumference of the earth, about $10\backslash ,000\backslash ,\backslash mathrm$, the length of the great ellipse connecting the points is close (within one part in 500,000) to the geodesic distance.〔 〕〔 〕〔 〕 The great ellipse therefore is sometimes proposed as a suitable route for marine navigation. == Introduction == Assume that the spheroid, an ellipsoid of revolution, has an equatorial radius $a$ and polar semi-axis $b$. Define the flattening $f=(a-b)/a$, the eccentricity $e=\backslash sqrt$, and the second eccentricity $e\text{'}=e/(1-f)$. Consider two points: $A$ at (geographic) latitude $\backslash phi\_1$ and longitude $\backslash lambda\_1$ and $B$ at latitude $\backslash phi\_2$ and longitude $\backslash lambda\_2$. The connecting great ellipse (from $A$ to $B$) has length $s\_$ and has azimuths $\backslash alpha\_1$ and $\backslash alpha\_2$ at the two endpoints. There are various ways to map an ellipsoid into a sphere of radius $a$ in such a way as to map the great ellipse into a great circle, allowing the methods of great-circle navigation to be used: * The ellipsoid can be stretched in a direction parallel to the axis of rotation; this maps a point of latitude $\backslash phi$ on the ellipsoid to a point on the sphere with latitude $\backslash beta$, the parametric latitude. * A point on the ellipsoid can mapped radially onto the sphere along the line connecting it with the center of the ellipsoid; this maps a point of latitude $\backslash phi$ on the ellipsoid to a point on the sphere with latitude $\backslash theta$, the geocentric latitude. * The ellipsoid can be stretched into a prolate ellipsoid with polar semi-axis $a^2/b$ and then mapped radially onto the sphere; this preserves the latitude—the latitude on the sphere is $\backslash phi$, the geographic latitude. The last method gives an easy way to generate a succession of way-points on the great ellipse connecting two known points $A$ and $B$. Solve for the great circle between $(\backslash phi\_1,\backslash lambda\_1)$ and $(\backslash phi\_2,\backslash lambda\_2)$ and find the way-points on the great circle. These map into way-points on the corresponding great ellipse. 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 ellipse」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.