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Calculating distance using redshift

  1. Feb 26, 2012 #1
    Hi. I have pretty rudimentary math skills, and am hoping someone can explain this formula for me, found online a number of places including:


    for calculating distance (d) in megaparsecs using redshift (z), the speed of light (c), and Hubble's constant (H).

    d = c z/H

    It's the (units in) Hubble's constant that have me confused. In the example from the link, "we see that objects with a redshift of 0.1 are about 4.6 gigaparsecs [a]way", assuming an H of 65 km s-1 Mpc-1. So I assumed c here would be in km/s, but:

    300000 * (0.1/65) = 461

    Which is 0.46 gigaparsecs, not 4.6. What is it about the units/Hubble's constant here that I don't get?

    Here's what I guessing: units ^ -1 mean 65 should be multiplied by 0.1, which is different than 65 ^ -1. This would make H 6.5, and the result would be correct. Is that right? If so, why is the notation km/s-1/Mpc-1? How would that be different from km/s/Mpc-1?
  2. jcsd
  3. Feb 26, 2012 #2
    I think your calculation (as it was) is correct. Your guess about the units is definitely not right---the units are separate from the number attached to them.
    Maybe their result is just a typo...
  4. Feb 26, 2012 #3
    Yeah, you're right. The next thing I tried this on was the Large Magellanic Cloud, which produced even more bizarre results, but I found a calculator for this online:


    And eventually got some data to match up (it seems the LMC's redshift is an anomaly, so my first test case was a typo and my second anomalous -_-).
    Last edited: Feb 26, 2012
  5. Feb 26, 2012 #4
    Haha, just some bad luck I guess!
    Way to be thorough---good job
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