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  1. The universe is around 13.8 billion years old.
  2. We know how fast the light is.
  3. We also know how fast our galaxy moving around inside observable universe.

Is it possible to calculating distance between Earth and the place where The Big Bang happened ? If so how far away our planet ? and is there a something special about this place ? (A black hole or something else really crazy?)

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The distance to where the big bang theoretically happened would be "0" (and this should be true for any point within the universe). The entire universe was theoretically produced in the big bang, with every point in space being "inside" the big bang. The whole universe is very special, it is amazing what is out there (including black holes, earth, stars, planets, nebulae, etc...).

Whether or not there is even a "center" to the big bang / the universe, however is another related interesting question. Current models seem to indicate that there is no center. It would be interesting if there is a true center of the universe, and would be interesting to know if there is anything special about the center if it exists.

The question of whether or not there is a center of the universe is addressed in the following links:

What is in the center of the universe?

http://www.spaceanswers.com/deep-space/is-there-a-centre-of-the-universe/

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    $\begingroup$ "It would be interesting if there is a true center of the universe, and would be interesting to know if there is anything special about the center if it exists." - that's pure speculation, and it doesn't even make much sense within the current models $\endgroup$ – Florin Andrei Dec 5 '14 at 19:28
  • $\begingroup$ @FlorinAndrei You're right. Jonathan, there is no center. $\endgroup$ – HDE 226868 Dec 5 '14 at 23:54

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