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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 Laplace limit ： ウィキペディア英語版 Laplace limit In mathematics, the Laplace limit is the maximum value of the eccentricity for which the series solution to Kepler's equation converges. It is approximately : 0.66274 34193 49181 58097 47420 97109 25290. Kepler's equation ''M'' = ''E'' − ε sin ''E'' relates the mean anomaly ''M'' with the eccentric anomaly ''E'' for a body moving in an ellipse with eccentricity ε. This equation cannot be solved for ''E'' in terms of elementary functions, but the Lagrange reversion theorem yields the solution as a power series in ε: :$E\; =\; M\; +\; \backslash sin(M)\; \backslash ,\; \backslash varepsilon\; +\; \backslash tfrac12\; \backslash sin(2M)\; \backslash ,\; \backslash varepsilon^2\; +\; \backslash left(\; \backslash tfrac38\; \backslash sin(3M)\; -\; \backslash tfrac18\; \backslash sin(M)\; \backslash right)\; \backslash ,\; \backslash varepsilon^3\; +\; \backslash cdots$ Laplace realized that this series converges for small values of the eccentricity, but diverges when the eccentricity exceeds a certain value. The Laplace limit is this value. It is the radius of convergence of the power series. ==See also== *Orbital eccentricity 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「Laplace limit」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.