Hi Scott,

That question sounded vaguely familiar. I dug through old e-mails
and found that I'd answered it for somebody back in 2005. So I'll
recycle my answer.

The only additional comment I'd make is that the Hubble Constant,
and therefore the age of the universe, is now known to within about
one percent (as opposed to the five percent error in 2005). The
improvement is mostly due to WMAP measurements. To me, it's pretty
amazing that we can know how old the universe is to that level of precision.

-- Bill

---------------------------------

(Pause to do some on-line research... I'm not all that knowledgeable
about cosmology; does that mean I'm not a cosmopolitan kind of guy?)

Unfortunately, Guide can't tell you that. I ought to add in some code
to enable it to compute new numbers using those found in a catalog... but
at present, it can just take the redshift and spit that out at you.
However, there's another way to do it, as follows.

I eventually found some formulae (more on that below) which, with a
modest bit of effort, could be turned into the following table. You can
interpolate within the table as needed. For example, an object with
z=.4 is receding from us at about one-third of the speed of light, and
is about 1400 million parsecs or 4.5 billion light-years away. (Please
ignore the meaningless precision! If the Hubble Constant really is
known to within about one part in twenty, then these distances should
also be good to within one part in twenty.)

z vel distance
(% of c) Mpc Mlightyears
0.1 9.5 401 1308
0.2 18.0 761 2482
0.3 25.7 1083 3530
0.4 32.4 1369 4464
0.5 38.5 1624 5294
0.6 43.8 1850 6031
0.7 48.6 2051 6687
0.8 52.8 2230 7272
0.9 56.6 2390 7793
1.0 60.0 2533 8259
1.5 72.4 3057 9967
2.0 80.0 3377 11012
3.0 88.2 3725 12145
4.0 92.3 3897 12706
5.0 94.6 3994 13021
6.0 96.0 4053 13214
7.0 96.9 4092 13341
8.0 97.6 4119 13429
9.0 98.0 4138 13492
10.0 98.4 4153 13539

Anyway. My on-line research turned up a relationship between the velocity
v of the galaxy and its redshift z:

1 + z = sqrt( (1+v/c) / (1-v/c))

which, after a bit of algebra, can be solved for v:

k = (z+1)^2
v = c (k-1) / (k+1)

Then you can solve for the distance to the object using Hubble's Law:

D = v / H

where D = distance in megaparsecs, v = velocity in km/second, and
H = Hubble's constant, currently thought by at least some to be about
71+/-3.5 km/sec/Mpc.

-- Bill