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

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SUMMARY

The formula z x c = H x d is used to convert redshift to megaparsecs, with H set at 71 km/s/Mpc and c at 299,792.46 km/s. When using a redshift value of 0.1, the calculation yields 1.377 billion light years (422.2429 Mpc), which is accurate. However, a redshift value of 10 results in an implausible distance of 137.717 billion light years due to the limitations of the linear approximation v=cz at larger distances. For accurate light travel time distance calculations, a more comprehensive model of cosmic expansion should be utilized.

PREREQUISITES
  • Understanding of redshift and its significance in cosmology
  • Familiarity with the Hubble constant (H = 71 km/s/Mpc)
  • Knowledge of the speed of light (c = 299,792.46 km/s)
  • Basic grasp of cosmological models and their implications on distance calculations
NEXT STEPS
  • Research the full expression for cosmic expansion beyond the linear approximation
  • Study the implications of comoving distance in cosmology
  • Explore the use of cosmological calculators for redshift to distance conversions
  • Read the review article on cosmic expansion at http://arxiv.org/abs/astro-ph/9905116
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Astronomers, astrophysicists, and students studying cosmology who are interested in accurate distance measurements related to redshift and cosmic expansion.

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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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