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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 Angular diameter distance ： ウィキペディア英語版 Angular diameter distance The angular diameter distance is a distance measure used in astronomy. The angular diameter distance to an object is defined in terms of the object's actual size, $x$, and $\backslash theta$ the angular size of the object as viewed from earth. $$ d_A= \frac The angular diameter distance depends on the assumed cosmology of the universe. The angular diameter distance to an object at redshift, $z$, is expressed in terms of the comoving distance, $\backslash chi$ as: $$ d_A = \frac Where $r(\backslash chi)$ is defined as: $$ r(\chi) = \begin \sin \left( \sqrt H_0 \chi \right)/\left(H_0\sqrt\right) & \Omega_k < 0\\ \chi & \Omega_k=0 \\ \sinh \left( \sqrt H_0 \chi \right)/\left(H_0\sqrt\right) & \Omega_k >0 \end Where $\backslash Omega\_k$ is the curvature density and $H\_0$ is the value of the Hubble parameter today. In the currently favoured geometric model of our Universe, the "angular diameter distance" of an object is a good approximation to the "real distance", i.e. the proper distance when the light left the object. Note that beyond a certain redshift, the angular diameter distance gets smaller with increasing redshift. In other words, an object "behind" another of the same size, beyond a certain redshift (roughly z=1.5), appears larger on the sky, and would therefore have a ''smaller'' "angular diameter distance". ==Angular size redshift relation== The angular size redshift relation describes the relation between the angular size observed on the sky of an object of given physical size, and the objects redshift from Earth (which is related to its distance, $d$, from Earth). In a Euclidean geometry the relation between size on the sky and distance from Earth would simply be given by the equation: $\backslash tan\backslash left\; (\; \backslash theta\; \backslash right\; )=\; \backslash frac$ where $\backslash theta$ is the angular size of the object on the sky, $x$ is the size of the object and $d$ is the distance to the object. Where $\backslash theta$ is small this approximates to: $\backslash theta\; \backslash approx\; \backslash frac$. However, in the currently favoured geometric model of our Universe, the relation is more complicated. In this model, objects at redshifts greater than about 1.5 appear larger on the sky with increasing redshift. This is related to the angular diameter distance, which is the distance an object is calculated to be at from $\backslash theta$ and $x$, assuming the Universe is Euclidean. The actual relation between the angular-diameter distance, $d\_A$, and redshift is given below. $q\_0$ is called the deceleration parameter and measures the deceleration of the expansion rate of the Universe; in the simplest models, corresponds to the case where the Universe will expand for ever, $q\_0>0.5$ to closed models which will ultimately stop expanding and contract $q\_0=0.5$ corresponds to the critical case – Universes which will just be able to expand to infinity without re-contracting. $d\_A=\backslash cfrac\; \backslash cfrac$ The Mattig relation yields the angular-diameter distance as a function of redshift for a universe with ΩΛ = 0.〔(An introduction to the science of cosmology, Chapter 6:2 ) by Derek J. Raine & Edwin George Thomas (2001)〕 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「Angular diameter distance」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.