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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 Equation of the center ： ウィキペディア英語版 Equation of the center ''For further closely related mathematical developments see also Two-body problem, also Gravitational two-body problem, also Kepler orbit, and Kepler problem'' The equation of the center, in astronomy and elliptical motion, is equal to the true anomaly minus the mean anomaly, i.e. the difference between the actual angular position in the elliptical orbit and the position the orbiting body would have if its angular motion was uniform. It arises from the ellipticity of the orbit, is zero at pericenter and apocenter, and reaches its greatest amount nearly midway between these points. The "equation" in the present sense comes from astronomy. It was specified and used by Kepler, as that variable quantity determined by calculation which must be added or subtracted from the mean motion to obtain the true motion. It is based on ''aequatio, -onis, f.'' in Latin. In the expression "equation of time" used in astronomy, the term "equation" has a similar meaning. ==Analytical expansions== For small values of orbital eccentricity, $e$, the true anomaly, $\backslash nu\backslash$, may be expressed as a sine series of the mean anomaly, $M$. The following shows the series expanded to terms of the order of $e^3$: :$\backslash nu\; =\; M\; +\; (2\; e\; -\; \backslash frac\; e^3)\; \backslash sin\; M\; +\; \backslash frac\; e^2\; \backslash sin\; 2\; M\; +\; \backslash frac\; e^3\; \backslash sin\; 3\; M\; +\; ...$ Related expansions may be used to express the true distance $r$ of the orbiting body from the central body as a fraction of the semi-major axis $a$ of the ellipse, :$\backslash frac\; =\; (1\; +\; e^2\; /2)\; -\; (e\; -\; \backslash frace^3)\; \backslash cos\; M\; -\; \backslash frac\; e^2\; \backslash cos\; 2\; M\; -\; \backslash frac\; e^3\; \backslash cos\; 3\; M\; -\; ...$ ; or the inverse of this distance $a/r$ has sometimes been used (e.g. it is proportional to the horizontal parallax of the orbiting body as seen from the central body): :$\backslash frac\; =\; 1\; +\; (e\; -e^3/8)\; \backslash cos\; M\; +\; e^2\; \backslash cos\; 2\; M\; +\; \backslash frac\; e^3\; \backslash cos\; 3\; M\; +\; ...$ . Series such as these can be used as part of the preparation of approximate tables of motion of astronomical objects, such as that of the moon around the earth, or the earth or other planets around the sun, when perturbations of the motion are included as well. 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「Equation of the center」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.