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| '''Luminosity distance''' ''D<sub>L</sub>'' is defined in terms of the relationship between the [[absolute magnitude]] ''M'' and [[apparent magnitude]] ''m'' of an astronomical object.
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| :<math> M = m - 5 (\log_{10}{D_L} - 1)\!\,</math>
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| which gives:
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| :<math> D_L = 10^{\frac{(m - M)}{5}+1}</math>
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| where ''D<sub>L</sub>'' is measured in [[parsec]]s. For nearby objects (say, in the [[Milky Way]]) the luminosity distance gives a good approximation to the natural notion of distance in [[Euclidean space]].
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| The relation is less clear for distant objects like [[quasar]]s far beyond the [[Milky Way]] since the apparent magnitude is affected by [[spacetime]] [[curvature]], [[redshift]], and [[time dilation]]. Calculating the relation between the apparent and actual luminosity of an object requires taking all of these factors into account. The object's actual luminosity is determined using the inverse-square law and the proportions of the object's apparent distance and luminosity distance.
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| Another way to express the luminosity distance is through the flux-luminosity relationship. Since,
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| :<math> F = \frac{L}{4\pi D_L^2}</math>
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| where ''F'' is flux (W·cm<sup>−2</sup>), and ''L'' is luminosity (W), or where ''F'' is flux (erg·s<sup>−1</sup>·cm<sup>−2</sup>), and ''L'' is luminosity (erg·s<sup>−1</sup>). From this the luminosity distance can be expressed as:
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| :<math> D_L = \sqrt{\frac{L}{4\pi F}}</math>
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| The luminosity distance is related to the "comoving transverse distance" <math>D_M</math> by the Etherington's reciprocity relation:
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| :<math> D_L = (1 + z) D_M</math> | |
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| where ''z'' is the [[redshift]]. <math>D_M</math> is a factor that allows you to calculate the [[comoving distance]] between two objects with the same redshift but at different positions of the sky; if the two objects are separated by an angle <math>\delta \theta</math>, the comoving distance between them would be <math>D_M \delta \theta</math>. In a spatially flat universe, the comoving transverse distance <math>D_M</math> is exactly equal to the radial comoving distance <math>D_C</math>, i.e. the comoving distance from ourselves to the object.<ref>{{cite book| author = Andrea Gabrielli| coauthors = F. Sylos Labini, Michael Joyce, Luciano Pietronero| title = Statistical Physics for Cosmic Structures| url = http://books.google.com/?id=nYHRdjxKOEMC&pg=PA377| date = 2004-12-22| publisher = Springer| isbn = 978-3-540-40745-4| page = 377 }}</ref><ref>http://www.mpifr-bonn.mpg.de/staff/hvoss/DiplWeb/DiplWebap1.html {{dead link|date=January 2013}}</ref>
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| ==See also==
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| * [[Distance measures (cosmology)]]
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| * [[distance modulus]]
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| == Notes ==
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| {{reflist}}
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| ==External links==
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| * [http://www.astro.ucla.edu/~wright/CosmoCalc.html Ned Wright's Javascript Cosmology Calculator]
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| * [http://icosmos.co.uk/ iCosmos: Cosmology Calculator (With Graph Generation )]
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| [[Category:Observational astronomy]]
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| [[Category:Physical quantities]]
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| {{relativity-stub}}
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Oscar is how he's called and he completely loves this name. To collect coins is what his family members and him enjoy. She is a librarian but she's always wanted her personal business. Her spouse and her reside in Puerto Rico but she will have to transfer 1 day or another.
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