Angular diameter distanceとは 意味・読み方・使い方

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 θ the angular size of the object as viewed from earth.

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, χ as:

Where r(χ) is defined as:
<img class="tex" alt=" r(\chi) = \begin{cases} \sin \left( \sqrt{-\Omega_k} H_0 \chi \right)/\left(H_0\sqrt{|\Omega_k|}\right) & \Omega_k < 0\\ \chi & \Omega_k=0 \\ loading="lazy" \sinh \left( \sqrt{\Omega_k} H_0 \chi \right)/\left(H_0\sqrt{|\Omega_k|}\right) & \Omega_k >0 \end{cases} " src="http://upload.wikimedia.org/math/1/5/d/15d6cd06c3077bf1a8e3cd9f86708f4c.png" >
Where Ω_k is the curvature density and H₀ is the value of the Hubble parameter today.