Are You Using the Correct Formula to Convert Redshift to Megaparsecs?

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The formula z x c = H x d is being used to convert redshift to megaparsecs, with H set at 71 km/s/Mpc and c as 299,792.46 km/s. While the calculations yield reasonable results for lower redshift values, higher values like z=10 produce excessively large distances, raising questions about the method's validity. The linear relation v=cz is not suitable for larger distances due to the universe's expansion dynamics. A more accurate approach is recommended, focusing on light travel time distance rather than comoving distance. For a comprehensive understanding, a referenced review article is suggested for further reading.
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z x c = H x d is the formula I am using to try to convert redshift to megaparsecs, where H I'm taking to be 71km/s/Mpc and c as 299,792.46 km/s. When I plug in .1 for z I get 1.377 Billion Light years (422.2429 Mpc), which sounds right. But when I plug in 10 for z I get the huge distance of 137.717 Billion Light years. Is that because of the comoving universe? I'm really just after the light travel time distance, not really where the galaxy is now. Am I using the wrong formula?
 
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You are using linear relation v=cz, which is not good at larger distances. Try here, just plug redshift value and you will have light travel time distance.
 
To expand a little on Calimero's response:
The equation you are using is the linear approximation of the full expression for the expansion of the universe (given a particular cosmology). Here is an excellent review article which should answer your question in detail http://arxiv.org/abs/astro-ph/9905116
 

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