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Great-circle navigation is the practice of navigating a vessel (a ship or aircraft) along a great circle. A great circle track is the shortest distance between two points on the surface of a sphere; the Earth isn't exactly spherical, but the formulas for a sphere are simpler and are often accurate enough for navigation (see the numerical example). ==Course and distance== The great circle path may be found using spherical trigonometry; this is the spherical version of the ''inverse geodesic problem''. If a navigator begins at ''P''1 = (φ1,λ1) and plans to travel the great circle to a point at point ''P''2 = (φ2,λ2) (see Fig. 1, φ is the latitude, positive northward, and λ is the longitude, positive eastward), the initial and final courses α1 and α2 are given by formulas for solving a spherical triangle : where λ12 = λ2 − λ1〔In the article on great-circle distances, the notation Δλ = λ12 and Δσ = σ12 is used. The notation in this article is needed to deal with differences between other points, e.g., λ01.〕 and the quadrants of α1,α2 are determined by the signs of the numerator and denominator in the tangent formulas (e.g., using the atan2 function). The central angle between the two points, σ12, is given by :} The distance along the great circle will then be ''s''12 = ''R''σ12, where ''R'' is the assumed radius of the earth and σ12 is expressed in radians. Using the mean earth radius, ''R'' = ''R''1, yields results for the distance ''s''12 which are within 1% of the geodesic distance for the WGS84 ellipsoid. 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 navigation」の詳細全文を読む スポンサード リンク
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