3 ms·
So I quickly did a back-of-envelope calculation using [0] for source of mass and diameter of the universe. Then I used the formula given in [1]: r = (2 G M) /
by grandchild 6y ago
So I quickly did a back-of-envelope calculation using [0] for source of mass and diameter of the universe.
Then I used the formula given in [1]: r = (2 G M) / (c^2).
You have: (2 * G * 1.5 * 10^56 grams ) / (c^2)
You want: lightyears
* 2.3548373e+10
So about 23,548,373,000 ly of SR, while the radius of the observable universe is given as ~46,500,000,000 ly. So the ordinary-matter ratio is about half the density of a black hole. Not quite there, but still _much_ closer than I would have thought!
If we account for not just ordinary matter but dark matter (a ratio of 4.9% to 26.8%) the picture is different:
You have: (2 * G * (1.5 * 10^56 grams + (1.5/4.9*26.8) * 10^56 grams) ) / (c^2)
You want: lightyears
* 1.5234355e+11
So the SR then would be about 5 times larger. But I have no idea whether dark matter would count towards the black hole mass and SR, and I don't know if anyone does.
[0] https://en.wikipedia.org/wiki/Observable_universe https://en.wikipedia.org/wiki/Observable_universe
[1] https://en.wikipedia.org/wiki/Schwarzschild_radius https://en.wikipedia.org/wiki/Schwarzschild_radius
(The scientific calculator I used, which is awesome every day is "units" btw: https://linux.die.net/man/1/units https://linux.die.net/man/1/units)
- gnramires 6y agoYes, dark matter has mass, this is its defining characteristic: it seems to be a detectable mass, just doesn't interact electromagnetically. In any case, it's important to note the Schwarzchild model is a spherically symmetrical ball. Mass in our Universe seems more or less uniformly dispersed (with some anisotropy). Without a center for mass to collapse, I suspect the black hole dynamics don't apply.