[quote="Jim_Baur, post:17, topic:291548"]
Thanks for the help.
Concerning our knowledge of the size of the universe in 1945, how much larger is it than we thought it was in 1945? (If we include the dark matter and dark energy.)
That is a tough question because the universe is expanding. I do not know the value, however, we can certainly estimate it. Assume that the universe expands linearly with time (i.e., R[sub]Universe[/sub]=ct). From here, we can see that:
[list]*]50 years = 1.58x10[sup]9[/sup] seconds
*]using c=2.9979x10[sup]10[/sup] cm/s, then R[sub]50 years[/sub] = 4.76x10[sup]19[/sup] cm
*]using V=4*pi*R[sup]3[/sup]/3, then V[sub]50 years[/sub]=4.52x10[sup]59[/sup] cm[sup]3[/sup] [/list]
That is a pretty big number! However, we really need to compare this value to the linearly-interpolated volume of the universe.
[list]*]13.7 billion years = 4.32x10[sup]17[/sup] s
*] R[sub]Universe[/sub]=ct=1.30x10[sup]28[/sup] cm
*] V[sub]Universe[/sub]=4*pi*R[sup]3[/sup]/3=2.90x10[sup]84[/sup] cm[sup]3[/sup][/list]
This is an even bigger number! The difference of 50 years seems like a lot, but compared to the entire universe, it is rather insignificant!
Also: the expansion rate was determined via observations and is independent of the existence/non-existence of dark matter and/or dark energy.