--->DIFFICULT<--- question

[afterburner]

This is actually a few related questions.

What is the estimated mass of the universe? Assuming its not infinitely big. Or at least the visible universe.

How big of a "ball" could you make with all of this stuff. The diameter. Assuming it doesnt completely collase into nothing (but similar to a black hole).

[Ken G]

Interesting questions. The way to get a rough estimate of the mass is to assume the critical density over a volume with about 10 million LY radius. The critical density is then found by using the constant G and the age of the universe until you get units of mass density, which is 1/(G age^2), or 10 to the minus 27 grams per cc. Then multiply that by the volume, which is about 10 to the 84 cc, giving about 10 to the 57 grams in the observable universe, very roughly. That's about 10 to the 24 solar masses, but it counts dark matter and dark energy as mass energy. A black hole with that mass would have a radius of about G M/ c^2, which comes out to 10 to the 28 cm, or just about the visible horizon of the universe. This is not a coincidence-- the critical density is of order the density inside the event horizon of a universe-sized black hole. Inside the event horizon, the black hole singularity might have infinite density, so you can't really answer that part. If we made a "ball" made of that much water, and ignored the spectacular pressure, it would be 10 to the 19 cm in radius, or only about the space between each star in our galaxy.

[Grey]

Interesting questions. The way to get a rough estimate of the mass is to assume the critical density over a volume with about 10 million LY radius.

You mean billion light years of course, though looking at your actual calculations, the numbers look right there.

[Jeff Root]

If we made a "ball" made of that much water, and ignored the
spectacular pressure, it would be 10 to the 19 cm in radius,
or only about the space between each star in our galaxy.

I haven't tried to analyze how you arrived at this figure,
but I get 10 to the 19 cm = just over 100 light-years.
The average distance between nearest star systems in our
neighborhood is a bit less than ten light-years.

-- Jeff, in Minneapolis

[Ilya]

10^19 cm = 10^17 m = 10^14 km

1 light-year = 9.6 * 10^12 km

Yes, 10^19 cm ~ 10 ly

[Jeff Root]

I see what I did wrong. Ken said the ball of water would be
"10 to the 19 cm in radius". But I repeatedly put "10 Exp 19"
into my calculator, when I should have put in "1 Exp 19".

-- Jeff, in Minneapolis

[Ken G]

I was just trying to put the number in perspective, not be too accurate. It seemed a little surprising to me that we could fit all the matter in the universe into that small of a space at a density of 1 g/cc, but so it is with volumes. And yes, I did mean billion LY, that was a typo. Oops.

[RussT]

Interesting questions. The way to get a rough estimate of the mass is to assume the critical density over a volume with about 10 million LY radius. The critical density is then found by using the constant G and the age of the universe until you get units of mass density, which is 1/(G age^2), or 10 to the minus 27 grams per cc. Then multiply that by the volume, which is about 10 to the 84 cc, giving about 10 to the 57 grams in the observable universe, very roughly. That's about 10 to the 24 solar masses, but it counts dark matter and dark energy as mass energy. A black hole with that mass would have a radius of about G M/ c^2, which comes out to 10 to the 28 cm, or just about the visible horizon of the universe. This is not a coincidence-- the critical density is of order the density inside the event horizon of a universe-sized black hole. Inside the event horizon, the black hole singularity might have infinite density, so you can't really answer that part. If we made a "ball" made of that much water, and ignored the spectacular pressure, it would be 10 to the 19 cm in radius, or only about the space between each star in our galaxy.

[That's about 10 to the 24 solar masses, but it counts dark matter and dark energy as mass energy.]

This is the 70% Dark Energy
26% Dark Matter Non-Baryonic
and 4% Baryonic Matter

Isn't Critical Density all about figuring out Omega and what that means for the universes expansion or contraction?

So, if Omega =1 exactly, and could stay that way, balanced forever, we could live in a static universe...highly unlikely.

So before 1998, what was the critical density?
How does the missing Baryonic Matter (not for the rotation curves for the galaxies or the clusters) factor into this?

[which comes out to 10 to the 28 cm,] to the visible horizon
[would be 10 to the 19 cm in radius,] space between stars in our galaxy

These figures seem off to me, the top one = 13 billion light years
The bottom one = about 4 light years