[Rich]

Could you survive being hit by a thousand million tonne black hole travelling at half a million miles an hour?

If yes would you even notice?

If no how far away would you have to be to survive?

[quetzalcoatl]

K.E. = 1/2 m v2.

If the mass has units of kilograms and the velocity of meters per second, the kinetic energy has units of kilograms-meters squared per second squared. Kinetic energy is usually measured in units of Joules.

Assuming we're talking metric tonnes, 10^9 tonnes = 10^3 X 10^9 = 10^12 kg.
500,000 miles per hour = 22.4 X 10 ^4 mps
K.E. = 1/2 X 10^12 X (22.4 X 10^4)^2 = 2.6 X 10^22 joules, if I've done the math right.

10^17 joules Tsar Bomba
10^23 joules Estimated output of Chicxulub Impact

You wouldn't want to be anywhere close. Maybe not on the same planet.

------------------------

EDIT: I was calculating the damage from a standard rock. Just noticed you were talking about a black hole.

So, the big difference is that a big rock striking the earth has virtually all it's K.E. transformed into heat, shock, and radiation. A black hole passing this fast through the earth might have only a tiny fraction of its K.E. converted. So maybe nothing would happen?

[Prosthetic Conscience]

Just thinking of the gravitational effect of that mass, the field strength is (GM/(R*R)), which is 6.7*10^11 * 10^12/(R*R), or 67/(R*R). So at 1 metre distance, it's 6.7g. This would, presumably, be drawing in some mass from the atmosphere as it falls, with much of that converting to X rays as it approaches the (tiny) event horizon. Though it's moving at 140 miles per second, which means it'll pass before most things have a chance to react. If it got to your body, it would, I suppose, drill a precise tiny hole through you (since the Schwarzschild radius for such a small black hole will be tiny - according to this, 1.4*10-15 metres) and your atoms would experience a sudden jerk of acceleration toward the drilled cylinder, that lasts an incredibly short time.

I guess that means it might do more damage if it were slower.

After that, I guess it might get slowed down by having to go through the much greater mass of the Earth. Still, it starts at well above escape velocity (but within a couple of orders of magnitude of it), so perhaps it'd make it to the other side. Would you get a lot of heat energy, but spread out over a few thousand km in a line, and so not that disruptive?

[Ter]

I saw some black holes in Africa.
They were not so deadly as you guys describe them.
Pretty pleasant I dare say.

[Rich]

After that, I guess it might get slowed down by having to go through the much greater mass of the Earth. Still, it starts at well above escape velocity (but within a couple of orders of magnitude of it), so perhaps it'd make it to the other side. Would you get a lot of heat energy, but spread out over a few thousand km in a line, and so not that disruptive?

How much volume of matter would the Black Hole have to displace /absorb to pass through the earth. If we say the Black Hole has a diameter of 10 to -15 m, then

Volume = 10 to -15m * 10 to - 15m * 8 * 10 to 6m //For the diameter of the Earth
= 8 * 10 to -24 cubic meters
= 8 * 10 to -15 cubic milimetres

That's an incredibly small volume with an incredibly small mass, so its effect on the Black Hole's velocity's is going to be incredibly negligible. I calculate the Black Hole will enter your head and pass out through your feet in about a millionth of a second, so although it will create some high gs it will be very short lived.

I'm not sure but I think you're biggest problem might be the Hawking Radiation. My Physics soon gets quite rocky, am I right in saying that Hawking Radiation actually increases absolutely as the Black Hole gets smaller.

[Prosthetic Conscience]

I did look for formulae for Hawking radiation; what I found seemed to say that a black hole of this magnitude would have a life of something like 10 billion years (it's around the size that they say would be 'primordial, but dying now'). So I suspect the momentary radiation, even over a few minutes inside the Earth, won't be huge.

Everything I say is a huge uneducated guess, of course. I suppose that every time it 'hit' a nucleus in the Earth, it would annihilate it (though how do black holes interact? By gravity, we know; do they react to the strong nuclear force in some way? Way, way over my head...). But yeah, perhaps not that much would happen, in the grand scheme of things.

[Potemkin]

I did look for formulae for Hawking radiation; what I found seemed to say that a black hole of this magnitude would have a life of something like 10 billion years (it's around the size that they say would be 'primordial, but dying now'). So I suspect the momentary radiation, even over a few minutes inside the Earth, won't be huge.

Everything I say is a huge uneducated guess, of course. I suppose that every time it 'hit' a nucleus in the Earth, it would annihilate it (though how do black holes interact? By gravity, we know; do they react to the strong nuclear force in some way? Way, way over my head...). But yeah, perhaps not that much would happen, in the grand scheme of things.

Black holes do not interact via the strong nuclear force. As the saying has it, "a black hole has no hair". Once its mass has collapsed into the singularity, and it is cloaked in an event horizon, the black hole exerts and feels only the gravitational force. And since the black hole would not and could not be stopped by any matter it encountered, it would actually do surprisingly little damage, since its kinetic energy would not be converted into heat and radiation. It would likely just bore a microscopic tunnel through you and then the Earth, and then continue on its merry way. You might not even notice it had hit you. Lol.

[ness31]

I do it all the time

[Ter]

I do it all the time

You do WHAT all the time?

[ness31]

get hit by black holes, duh..

[Prosthetic Conscience]

Black holes do not interact via the strong nuclear force. As the saying has it, "a black hole has no hair". Once its mass has collapsed into the singularity, and it is cloaked in an event horizon, the black hole exerts and feels only the gravitational force. And since the black hole would not and could not be stopped by any matter it encountered, it would actually do surprisingly little damage, since its kinetic energy would not be converted into heat and radiation. It would likely just bore a microscopic tunnel through you and then the Earth, and then continue on its merry way. You might not even notice it had hit you. Lol.

Interesting - I thought that since black holes can have electrical charge, it would still interact via the electromagnetic force, and so the strong nuclear force might be possible too.

[Potemkin]

Interesting - I thought that since black holes can have electrical charge, it would still interact via the electromagnetic force, and so the strong nuclear force might be possible too.

The strong nuclear force falls off so rapidly with distance that I don't see how the matter at the singularity could exert any such force beyond the event horizon. I could be wrong, however - I am by no means an expert on black holes.

[Rich]

Its little appreciated that Stephen Hawking, saved the world, saved the Galaxy, in fact saved the universe as we know it. If a billion tonne was somehow to be captured by the Earth, was inside the Earth and didn't have the escape velocity to get out, then I think we would have problems. We are only relatively safe because Black Holes are likely to be travelling at enormous speeds. Any Black Hole that comes from outside the Solar system must have a minimum velocity relative to the Earth of the order of a 100,000 Km/h.

In 1974 in Britain, we were on a three day week the light were going out. However Stephen Hawking realised that Black Holes were an even greater existential threat than the National Union of Miners, threatening to put the lights out permanently. The fear was that tiny microscopic Black Holes would form from some sub atomic event, possibly from a man made particle accelerator and then it would just grow and grow over time until it consumed the earth. Similarly every star in the universe could get eaten in time by a single microscopic Black Hole. So the purpose of the Hawking Radiation was to blow up any tiny Black Holes that might come into existence.

[Potemkin]

Hawking radiation is one of those things which, at the time it was suggested, sounded crazy, but which in retrospect must obviously be true, for the reasons Rich has outlined. Cosmic rays striking the Earth's atmosphere produce far more energetic collisions than anything puny humans can achieve in our laboratories, and there are undoubtedly microscopic black holes being formed and almost instantly evaporating all the time.

[Rich]

Contributions appreciated. I've been trying to work towards an appropriate Daily Mail headline. I was thinking of something along the lines of:

We could be by hit by a billion ton black hole travelling at half a million mph, but "experts" say don't worry.

[Prosthetic Conscience]

If the person who wrote Wikipedia's "crude analytic estimate" is right, then the power of Hawking radiation for it is considerable after all. They think it's

which, for a mass of 10^12 kg, should be 3.56*10^8 W - 356 MW, or a respectable power station. Can you work that into your Mail headline? Especially if we say 'nuclear'.

[Rich]

Just to add a few notes.

1. Billion tonne black holes are massive enough and hence the Hawking Radiation low enough that large numbers of primordial black holes of around this size, could have survived since or soon after the Big Bang. Yet they are small enough that the fact of their existence in large numbers could have eluded observation so far.

2. So it seems that it is plausible that billion tonne black holes could be passing through the earth without us noticing them. At the very least, even if they would be noticed by modern instrumentation they could have passed through in historical time, without leaving a historical record.

3. As I understand it the root of these counter-intuitive effects, or rather counter-intuitive lack of effects, is that the diameter of a black hole's event horizon is proportional to the mass, when intuitively, we might expect it to vary with the cube root of the mass.