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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 Mattig relation ： ウィキペディア英語版 Mattig formula Mattig's formula is one of the most important formulae in observational cosmology and extragalactic astronomy which gives relation between radial coordinate and redshift of a given source. It depends on the cosmological model being used and is needed to calculate luminosity distance in terms of redshift.〔(Observations in Cosmology ), Cambridge University Press〕 ==Without dark energy== Derived by W. Mattig in a 1958 paper, the mathematical formulation of the relation is,〔Bradley M. Peterson, "An Introduction to Active Galactic Nuclei", p. 149〕 $r\_1\; =\; \backslash frac\; \backslash frac$ Where, $r\_1=\backslash frac=\backslash frac$ is the radial coordinate distance (proper distance at present) of the source from the observer while $d\_p$ is the proper distance and $d\_c$ is the comoving distance. :: $q\_0=\backslash Omega\_0/2$ is the deceleration parameter while $\backslash Omega\_0$ is the density of matter in the universe at present. :: $R\_0$ is scale factor at present time while $R$ is scale factor at any other time. :: $H\_0$ is Hubble's constant at present and :: $z$ is as usual the redshift. This equation is only valid if $q\_0\; >\; 0$. When $q\_0\; \backslash le\; 0$ the value of $r\_1$ cannot be calculated. From this radius we can calculate luminosity distance using the following formula, : $D\_L\; \backslash \; =\; \backslash \; R\_0r\_1(1+z)\; =\; \backslash frac\; \backslash left()$ When $q\_0=0$ we get another expression for luminosity distance using Taylor expansion, : $D\_L\; =\; \backslash frac\backslash left(z+\backslash frac\backslash right)$ But in 1977 Terrell devised a formula which is valid for all $q\_0\; \backslash ge\; 0$, : $D\_L\; =\; \backslash fracz\backslash left()$ 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「Mattig formula」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.