# Angular diameter distance

- 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 $heta$ the angular size of the object as viewed from earth.

$d\_A=\; frac\{x\}\{\; heta\}$

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, $chi$ as:

$d\_A\; =\; frac\{r(chi)\}\{1+z\}$

Where $r(chi)$ is defined as:

$r(chi)\; =\; egin\{cases\}sin\; left(\; sqrt\{-Omega\_k\}\; H\_0\; chi\; ight)/left(H\_0sqrt\; ight)\; Omega\_k\; 0\backslash chi\; Omega\_k=0\; \backslash sinh\; left(\; sqrt\{Omega\_k\}\; H\_0\; chi\; ight)/left(H\_0sqrt\; ight)\; Omega\_k\; 0\; end\{cases\}$

Where $Omega\_k$ 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. However, beyond a certain redshift it gets "smaller" with increasing redshift. In other words an object "behind" another of the same size, beyond a certain redshift, appears larger on the sky, and would therefore have a "smaller" "angular diameter distance".

** Related Links **

[*http://icosmos.co.uk/ iCosmos: Cosmology Calculator (With Graph Generation )*]

* Angular size redshift relation

* Distance measures (cosmology)

*Wikimedia Foundation.
2010.*

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