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Q & A: How large do you have to get to be a black hole?

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Most recent answer: 08/22/2013
Q:
How big could a blob of water get in space before it crushed itself and became a black hole?
- Fred (age 30)
Tampa, FL
A:

Hi Fred,

Good question. I read once that if you filled the solar system with air, it would be a black hole. I never checked that statement until today (see below).

If you look at the wikipedia page on Schwartzchild radius, you can easily see that (for a ball of uniform mass), the schwartzchild radius is rs = Sqrt(8 * pi * G * d / (3 * c2)), where G is the gravitational constant, d is the uniform density, and c is the speed of light.

Just plugging in to wolfram alpha, I find that a ball of water would need a radius of about 2.7 AU. So, if you started at the sun and filled the space in all directions with ordinary water for a radius 2.7 times larger than the earth's orbit, you'd get a black hole!

If you used air, you'd need to make a sphere with radius of around 75 AU, or 7 billion miles. This is about twice the radius of Plutos orbit.

It's pretty amazing to me that a ball of air with similar density to our atmosphere can have enough mass to become a black hole! (For the record, an object with any density can become a black hole, if you have enough of it.)

Cheers!

David Schmid

p.s. I think David will be getting back to this soon with a modification. That ball of water at ordinary density would  already be a black hole at 2.7 A.U. size. However, a much smaller ball would soon collapse under its own gravity and form a near-black hole because its R would go down while keeping the same M.  These were the sorts of calculations done by Chandrashekar, Oppenheimer, et al. many years ago. I think, and David will be checking this to make it accurate, that starting with a ball just a few times bigger than the Sun would be enough to collapse toward forming a black hole. My weasel words about "near" black holes are just a reminder that, from the point of view of a distant observer, the gravitational redshift prevents one from ever quite making the last little step to form a genuine black hole. / mw


(published on 08/22/2013)

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