First, this is just amazingly unlikely. There are far fewer black holes than there are stars, and the sun is a far bigger target, or Jupiter. But there’s almost no chance even of a star getting as close as Neptune never mind the inner solar system. And the Earth is a tiny target in the inner solar system. Even Jupiter, even the Sun is absolutely minute compared to the vast distances between stars. Basically it’s not going to happen.
That’s for stellar sized black holes. As for mini black holes, they can’t be common either, or else we’d spot stars blinking out as a result of getting hit by black holes. And again a star is far more likely to be hit than any planet.
But let’s go with the idea. Suppose it’s a mini black hole and it’s created and then fired at us for reasons obscure by some advanced creatures (even ourselves?)
First, note - despite popular ideas, black holes don’t “suck you in” unless you are inside the event horizon - so close that the escape velocity is more than the speed of light. That’s really close except for black holes so large they mass thousands or millions of suns.
If it has the mass of the sun, the event horizon is 3 km away so you have to get that close to get sucked in. Of course you’d get many consequences of a solar mass object passing close to Earth, we don’t want that to happen but we won’t get sucked in. For even smaller black holes the event horizon radius is cms or less. For instance for an Earth mass black hole it is less than a centimeter. Schwarzschild radius - Wikipedia
HOW MUCH DELTA V DO WE NEED TO MISS EARTH
With the 120 years we need to deflect it by 6,371,000 meters in total (radius of the Earth assuming it’s a direct hit) or 6,371,000 /(100*365*24*69) meters per hour or about 10 centimeters per hour. to miss Earth. Or if it takes a while to get to it, say 60 years to reach it, then double that, 20 cm per hour.
So let’s run with that, delta v of 20 cm per hour to miss Earth. It would be much less if it did a close flyby, say, of the Sun, or Jupiter on the way, as tiny changes in velocity before a close flyby make big changes in the trajectory after a flyby, but we can’t assume that.
WHAT SIZE OF BLACK HOLE COULD WE DEFLECT EASILY?
Now suppose we can hit it at a relative velocity of 20 km / sec. for sake of argument. That’s reasonably feasible with flyby’s of Jupiter especially to increase the velocity of our mass, after all Voyager 1‘s 17 km / sec is not far off that. Then to achieve a 20 cm / hour change in velocity for the black hole, that’s 20/(100*60*60) meters per second, so it’s 20*1000*100*60*60/20 or 360 million for the ratio of velocity applied to velocity achieved. So we need a ratio of masses of 360 million too (by conservation of momentum)
If it is a 360 million ton black hole, a one ton impactor at 20 km / second will do the trick. So, we could deflect black holes of up to several billion tons fairly easily given 120 years of warning.That’s not a lot though. That’s like a really small asteroid turned into a black hole.
COULD WE DEFLECT A STELLAR MASS BLACK HOLE?
If it is stellar mass, then you are talking about 2,000,000,000,000,000,000,000,000,000 tons for the Sun. Divide by 3600 and it hardly makes any difference. There’s no way we’d deflect it even by cms / second.
COULD WE DEFLECT A MOON MASS BLACK HOLE?
If it’s a smaller black hole. say the mass of the Moon, 7.35 × 10^19 tons, again far too massive to shift. We’d need an impactor with a mass of about 200 billion tons for our 360 million ratio of masses. (7.35 × 10^19/(360 million))
Now, that’s not totally impossible. We couldn’t accelerate something that big to hit it directly, at least not with ordinary propulsion methods that we have today. But we could do it with “comet billiards” if we are lucky.
What we’d need to do is to try to find an asteroid or comet with mass about 200 billion tons. At density of 2 tons per cubic meter that would be cube root(200 billion*3/(4*pi)) or about 3 km in radius. There are many of those. So if we are lucky, we find one that is going to miss our black hole, but only just, way out in the Oort cloud. We would need to know our local neighbourhood very well to do that.
So then we can give this a gentle nudge with our 20 km / sec rocket, which now has to mass around 500 tons, not impossible (though a major challenge, launching lots of rockets of 10 tons perhaps) we can use it to deflect the black hole long before it reaches Earth.
STELLAR MASS BLACK HOLE - NO WAY
Basically your only option is to evacuate Earth, if it is a large stellar mass black hole. It would be very obvious from a distance due to its accretion disk and you’d want to evacuate long before it got to Earth. Light from behind the black hole would be absorbed by it. So it should seem black. But - it is likely to be surrounded by matter continually falling into it, in an accretion disk - and that can get very bright.
And then gravitational lensing lets you see the far side of the accretion disk, which is actually behind the black hole, warped above it. This is what the black hole of Interestellar would look like, to naked eye taking account of colour shifting.
Though the movie makers thought that would confuse the audience so simplified it to the more symmetrical: The Truth Behind Interstellar's "Scientifically Accurate" Black Hole
If we truly had a stellar mass black hole approaching Earth, then evacuating Earth would be only the first of our problems. It would disturb the whole solar system with its gravity. The accretion disk of hot matter swirling into it would be devastating also. Hard to see how we could survive, perhaps by hiding deep below the ice of an ice moon or comet, carefully selected so that it doesn’t get caught up in the accretion disk?
Luckily this scenario is vanishingly unlikely. It’s for all practical purposes for a star to do this and black holes are much rarer than stars. See last section for details.
SMALL FAST MOVING MICRO BLACK HOLE
If it is a small and fast moving black hole, maybe we don’t need to worry, it would just go straight through the Earth and out the other side. After all it is approaching Earth at the solar escape velocity or more.
There’s a useful black hole properties calculator here:
So a black hole of mass the same as the Earth would be less than a cm in radius. The main effects would be tidal due to its immense gravity, focused on a single spot, passing through the Earth.
If the Hawking radiation predictions are correct, the smallest black hole we can expect to find would be about the mass of the Moon as smaller ones would evaporate quickly.
Frank Heile, says that a black hole with the mass larger than the Moon would actually be gaining in mass because its temperature would be lower than the 2.7 degrees background radiation. So instead of radiating, net effect is it absorbs radiation.
Presumably closer to a star like us, with higher ambient radiation levels and equilibrium temperatures due to influence of the sun and the materials from the solar wind and galactic material - then somewhat smaller black holes could also be stable, or gaining in mass. All supposing the Hawking calculations are correct, which is a theoretical prediction that has to be confirmed by experiment or observation before we can be sure about it.
From outside its event horizon then a black hole behaves gravitationally like any other object - you can orbit it with a stable orbit for instance. A planet could have a mini black hole Moon, and so on.
A small black hole with the mass of the Moon would be only 1 mm in radius. That’s the radius of its event horizon (it doesn’t have a well defined surface, as the inside is just a mathematical point according to current ideas). You could put miniature spacecraft in orbit around a Moon mass black hole at distances of centimeters, even millimeters.
It’s only when you enter the event horizon - so closer than 1 mm in the case of a Moon mass black hole - that you get caught. All future timelines end up at its center and unless you have faster than light travel there is then no possibility of escape.
The galaxy can’t really have mini black holes like that, or if there are any they must be very rare indeed, or for some reason they must be harmless, or we’d see stars blinking out. But let’s continue with the idea and see what happens.
WHAT IF HAWKING IS WRONG IN HIS PREDICTION?
But if Hawking’s hypothesis / prediction of black hole radiation is incorrect (it hasn’t yet been confirmed), small black holes may be stable. If so, it takes a long time for a black hole to absorb the Earth and we could even have mini black holes inside our Earth. A ten billion ton black hole would take 700 times the age of our universe to absorb the Earth. A small black hole like that could pass all the way through the Earth with no noticeable effects. We could even have mini black holes orbiting inside all the planets and the sun, and we’d not notice. This is one, probably unlikely, explanation of some of the “dark matter” in the universe.
It could even perhaps create mini “atoms” “Gravitational Equivalent of Atoms” with conventional atoms orbiting a mini black hole according to this paper [1105.0265] Structure and Mass Absorption of Hypothetical Terrestrial Black Holes
However a micro black hole could cause minor earthquakes through tidal effects passing through the Earth.
“This is a hypothetical form of a black hole that could have been created in the very early stage of the universe, shortly after the big bang, when the Universe was still very dense. That's why they are also called primordial black holes. They have not yet been discovered and their existence is just speculation. However, if they exist they are very small (of the order of the size of an atom and smaller, their event horizon is just a few nanometres) and they would have the weight of a medium sized asteroid. They would pass right through the Earth with almost no effect in less than one minute. Some research from the Max Planck Institute in Germany has revealed that a micro black hole with a mass of a billion tons would penetrate through the Earth causing minor earthquakes of magnitude 4. The form of the waves would be unique and different from all forms a normal earthquake could cause. Measuring such waves would be strong evidence for this kind of black hole. At the moment we cannot completely dismiss the possibility that these primordial black holes may even be the famous dark matter itself. But until further evidence emerges this scenario seems very unlikely.”
I can’t find that paper at present (do say if you know where it is) but I found another paper here about effects of a billion ton black hole
What Would Happen if a Small Black Hole Hit the Earth? - Universe Today
It concludes that it would create a narrow hole through the Earth that “It creates a long tube of heavily radiative damaged material, which should stay recognizable for geological time” but its other effects would be negligible.
Worldbuilding stack exchange has a discussion here: On the immediate effects of a small, short term black hole
ALL THIS IS VERY UNLIKELY AND JUST FOR FUN
Just to reassure those who worry about such things. All this is so very very unlikely that it’s just for fun, this calculation. Ain’t going to happen. If it could happen with micro black holes, we’d see stars blinking out. While stellar sized black holes are much rarer than stars, so again, those are so incredibly unlikely to even come into our solar system that we don’t need to worry about those either.
Black holes are dangerous - especially the very large one thought to exist in the center of our galaxy. But we are in a quiet “suburb” of our galaxy and though there are black holes, or things that look like them at least, out here, the stars are so far apart we don’t need to worry about them either,
The chances of any celestial object even getting as close as Neptune in any one million year time period are minute:
- 1 in 1.4 million for a rogue planet
- 1 in 2.8 million for a star
- 1 in 48 million for a neutron star
- 1 in 2.8 billion for a black hole.
The chances of any of these getting as close to the sun as Earth, hitting Earth or hitting the Sun are vanishingly small.
For the calculation see Debunk: Our Sun or Earth could be hit by a neutron star, black hole or star
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