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Originally Posted by Fr. Wayne
I think I understand your effort: to simply. But multiplying by 1/x/y is not the same as dividing by 1/y/x. I do like your train of thought but the switch to ppt still baffles me. Give me some time to re-think your proposal- 12 hours.
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Re-hashing this a couple of times will not hurt, because the misconception regarding the expansion rate is so deeply ingrained. Here is the conversion, one more time:
1)
H = 72 km/sec/Mpc = 72 km/(Mpc-sec)
(seconds and megaparsecs are both "down-stairs")
2) [72 km/(Mpc-sec)] * [1 Mpc/(3.09 x10^19 km)] = 23 x 10^-19/sec
(km & Mpc are both cancelled out)
3) [23 x 10^-19/sec] * [3.15 x 10^7 sec/yr] = 73 x 10^-12/yr
(seconds are cancelled out)
4) 73 x 10^-12/yr = 73 ppt/yr
Again, to a first approximation, 1 km/sec/Mpc = 1 ppt/yr. They are, for all intents and purposes, the same, but "kilometers per second" creates the totally wrong impression of what is going on. The expansion rate is truly infinitesimal, and using "parts per trillion per year" paints more "accurate" picture.
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typo removed for clarity}