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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 Theoretical gravity ： ウィキペディア英語版 Theoretical gravity In geodesy and geophysics, theoretical gravity or normal gravity is an approximation of the true gravity on the Earth's surface by means of a mathematical model representing (a physically smoothed) Earth. The most common model of a smoothed Earth is an Earth ellipsoid, or, more specifically, an Earth spheroid (i.e., an ellipsoid of revolution). Various, successively more refined, formulas for computing the theoretical gravity are referred to as the International Gravity Formula, the first of which was proposed in 1930 by the International Association of Geodesy. The general shape of that formula is: :$g(\backslash phi)=\; \backslash mathbb\_e\backslash left(\; 1\; +\; A\; \backslash sin^2(\backslash phi)\; -\; B\; \backslash sin^2(2\; \backslash phi)\; \backslash right),$ in which (''φ'') is the gravity as a function of the geographic latitude ''φ'' of the position whose gravity is to be determined, $\backslash mathbb\_e$ denotes the gravity at the equator (as determined by measurement), and the coefficients and are parameters that must be selected to produce a good global fit to true gravity. Using the values of the GRS80 reference system, a commonly used specific instantiation of the formula above is given by: :$g(\backslash phi)=\; 9.780327\; \backslash left(1+0.0053024\backslash sin^2(\backslash phi)\; -\; 0.0000058\backslash sin^2(2\; \backslash phi)\; \backslash right)\backslash ,\backslash mathrm^.$〔 Using the appropriate double-angle formula in combination with the Pythagorean identity, this can be rewritten in the equivalent forms : &=9.780327\left(1.0053024-.0053256\cos^2(\phi)+.0000232\cos^4(\phi)\right)\,\mathrm^,\\ &=9.780327\left(1.0026454-0.0026512\cos(2\phi)+ .0000058\cos^2(2\phi)\right)\,\mathrm^ .\end\,\! Up to the 1960s, formulas based on the Hayford ellipsoid (1924) and of the famous German geodesist Helmert (1906) were often used. The difference between the semi-major axis (equatorial radius) of the Hayford ellipsoid and that of the modern WGS84 ellipsoid is ; for Helmert's ellipsoid it is only . A more recent theoretical formula for gravity as a function of latitude is the International Gravity Formula 1980 (IGF80), also based on the WGS80 ellipsoid but now using the Somigliana equation: : *$a,b$ are the equatorial and polar semi-axes, respectively; *$e^2=\backslash frac$ is the spheroid's eccentricity, squared; *$\backslash mathbb\_e,\backslash mathbb\_p$ is the defined gravity at the equator and poles, respectively; *$k=\backslash frac\_e\}$ (formula constant); providing, : : ==See also== *Gravity anomaly *Reference ellipsoid *EGM96 (Earth Gravitational Model 1996) *Standard gravity : 9.806 65 m/s2 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「Theoretical gravity」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.