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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 Gauss' Method ： ウィキペディア英語版 Gauss' Method In orbital mechanics (subfield of celestial mechanics), Gauss' method is used for preliminary orbit determination from at least three observations (more observations increases the accuracy of the determined orbit) of the orbiting body of interest at three different times. The required information are the times of observations, the position vectors of the observation points (in Equatorial Coordinate System), the direction cosine vector of the orbiting body from the observation points (from (Topocentric ) Equatorial Coordinate System) and general physical data. Carl Friedrich Gauss developed important mathematical techniques (summed up in Gauss' methods) which were specifically used to determine the orbit of Ceres. The method shown following is the orbit determination of an orbiting body about the focal body where the observations were taken from, whereas the method for determining Ceres' orbit requires a bit more effort because the observations were taken from Earth while Ceres orbits the Sun. == Observer position vector == The observer position vector (in Equatorial Coordinate System) of the observation points can be determined from the latitude and local sidereal time (from Topocentric Coordinate System) at the surface of the focal body of the orbiting body (e.g., Earth) via either: $\backslash mathbf\; =\; \backslash left\; (\}+\backslash sin\backslash theta\_n\backslash mathbf\}+H\_n\; \backslash right)\; \backslash sin\backslash phi\_n\backslash mathbf\; =\; R\_e\backslash cos\backslash phi\text{'}\_n\backslash cos\backslash theta\_n\backslash mathbf\}+R\_e\backslash sin\backslash phi\text{'}\_n\backslash mathbf\{\backslash hat\{K\}\}$ where, :Rn is the respective observer position vector (in Equatorial Coordinate System) :Re is the equatorial radius of the body (e.g., Earth's Re is 6,378 km) :f is the oblateness (or flattening) of the body (e.g., Earth's f is 0.003353) :φn is the respective geodetic latitude :φ'n is the respective geocentric latitude :Hn is the respective altitude :θn is the respective local sidereal time 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「Gauss' Method」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.