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This question came to my mind when I read on NASA's website that an explosion (gamma ray burst, GRB 080913) took place 12.8 billion light years away from us. How do they measure such large distances?

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Did you mean 12.8 billion light years away?

If so, in this case the distance was estimated by measuring a rough spectrum for the GRB. The NASA article I've linked says:

In certain colors, the brightness of a distant object shows a characteristic drop caused by intervening gas clouds. The farther away the object is, the longer the wavelength where this fade-out begins.

This technique is used where it's hard to get a detailed spectrum and calculate the red shift.

If you're asking a more general question then this is covered in the question How is distance measured to far away stars and galaxies? and your question would be a duplicate.

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  • $\begingroup$ So, in essence, this is a rather fuzzy redshift calculation? $\endgroup$ – M.Herzkamp Jul 18 '14 at 13:18
  • $\begingroup$ @M.Herzkamp: yes, exactly. $\endgroup$ – John Rennie Jul 18 '14 at 14:00
  • $\begingroup$ @JohnRennie: yes sir i meant 12.8 billion light years. sorry for omitting billion there. $\endgroup$ – syed_ali_mousvi Jul 18 '14 at 18:00
  • $\begingroup$ I think that characteristic drop would be the beginning of the "Lyman-$\alpha$ forest". So really this is a lower limit on the distance (which, at 12.8 Gly, still tells you it's pretty darn far away). $\endgroup$ – Kyle Oman Jul 18 '14 at 18:24
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For relatively close objects, the distance can be measured through measurements of parallax (http://en.wikipedia.org/wiki/Parallax ).

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  • $\begingroup$ And also using Variable stars in a star cluster. $\endgroup$ – ja72 Jul 18 '14 at 18:09
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    $\begingroup$ Note this was a reasonable answer to the question as stated at the time of the answer (I almost downvoted until I noticed). $\endgroup$ – Kyle Oman Jul 18 '14 at 22:13

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