翻訳と辞書 Words near each other ・ Aquarium of Genoa ・ Aquarium of Niagara ・ Aquarium of Rhodes ・ Aquarium of the Americas ・ Aquarium of the Bay ・ Aquarium of the Pacific ・ Aquafresh ・ Aquagen ・ Aquagenic pruritus ・ Aquagenic urticaria ・ AquaGib ・ Aquagirl ・ Aquagirl (Lorena Marquez) ・ Aquagrill ・ Aquajogging ・ AQUAL ・ Aqualad (Kaldur'ahm) ・ Aqualand ・ Aqualandia ・ Aqualate Hall ・ Aqualate Mere ・ Aqualignicola ・ Aqualillies ・ Aqualina Tower ・ AquaLoop ・ Aqualung ・ Aqualung (Aqualung album) ・ Aqualung (Jethro Tull album) ・ Aqualung (musician) ・ Aqualung (software) Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク AQUAL ： ウィキペディア英語版 AQUAL AQUAL is a theory of gravity based on Modified Newtonian Dynamics (MOND), but using a Lagrangian. It was developed by Jacob Bekenstein and Mordehai Milgrom in their 1984 paper, "Does the missing mass problem signal the breakdown of Newtonian gravity?". "AQUAL" stands for "A QUAdratic Lagrangian". The gravitational force law obtained from MOND, :$m\; \backslash mu(a/a\_0)\; a\; =\; GMm/r^2$, has a serious defect: it violates Newton's third law of motion, and therefore fails to conserve momentum and energy. To see this, consider two objects with $m\; \backslash neq\; M$; then we have :$\backslash mu(a\_m/a\_0)\; m\; a\_m\; =\; GmM/r^2\; =\; GMm/r^2\; =\; \backslash mu(a\_M/a\_0)\; M\; a\_M$ but the third law gives $m\; a\_m\; =\; M\; a\_M$, so we would get $\backslash mu(a\_m/a\_0)\; =\; \backslash mu(a\_M/a\_0)$ even though $a\_m\; \backslash neq\; a\_M$, and $\backslash mu$ would therefore be constant, contrary to the MOND assumption that it is linear for small arguments. This problem can be rectified by deriving the force law from a Lagrangian, at the cost of possibly modifying the general form of the force law. Then conservation laws could then be derived from the Lagrangian by the usual means. The AQUAL Lagrangian is: :$\backslash rho\; \backslash Phi\; +\; (8\; \backslash pi\; G)^\; a\_0^2\; F(|\backslash nabla\backslash Phi|^2/a\_0^2)$; this leads to a modified Poisson equation: :$\backslash nabla\; \backslash cdot\; (\backslash mu(|\backslash nabla\backslash Phi|/a\_0)\; \backslash nabla\backslash Phi)\; =\; 4\; \backslash pi\; G\; \backslash rho$. Here, $\backslash mu(x)\; =\; dF(x^2)/dx$ and the predicted acceleration is $-\backslash nabla\backslash Phi\; =\; a$. These equations reduce to the MOND equations in the spherically symmetric case, although they differ somewhat in the disc case needed for modelling spiral or lenticular galaxies. However, the difference is only 10-15%, so does not seriously impact the results. ==References== * * * 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「AQUAL」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.