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I have been thinking about the moon becoming a black hole. I was thinking about how much it would eat a day. How much mass would it suck in in 24 hours on average?

I am writing a story where the moon becomes a black hole.

Qmechanic
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Number File
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6 Answers6

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It'd suck in very little mass.

One thing to understand about black holes is that they have super-strong gravity, but only when you are very close to their event horizon. Otherwise they're just normal objects. If the Moon became a black hole, it would have a radius of about 0.1 millimeters. You need to get pretty close to this distance before you notice anything special, and even closer to get sucked in. Further out (especially beyond the current Moon radius of 1737 km) it's completely normal.

Since space is mostly a vacuum and you have to get so close (compare that size of a millimeter to the distance from the Earth to the Moon, which is about 380,000 kilometers) to be sucked in, the Moon would not eat much a day.

Allure
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    further out it's completely normal Yes, but with extremely strong Newtonian gravity. For example, if you got within a kilometer of this millimeter-sized thing your body would be torn apart by tidal forces. This is not what most people think of as completely normal. – G. Smith Jul 28 '20 at 06:59
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    @G.Smith You are right, but a distance of 1km is tiny by astronomical standards. Imagine you put a big balloon around the Moon, so you couldn't see the Moon. Then you replace the Moon with a BH of the same mass. From outside the balloon, you wouldn't notice any difference. So from the POV of us on Earth, nothing would change. You would only notice the extreme gravity as you approached to ranges inside the Moon's current radius. – Oscar Bravo Jul 28 '20 at 07:45
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    @G.Smith if you got within 1km of the centre of the Moon right now you'd also die. – OrangeDog Jul 28 '20 at 09:30
  • Actually, it would have a radius of $0,1mm$. Or is my caclulation wrong? – jng224 Jul 28 '20 at 09:44
  • @Jonas indeed, I edited it to a more precise value. – Allure Jul 28 '20 at 09:50
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    @G.Smith .. "Yes, but with extremely strong Newtonian gravity" that's totally wrong. It would have identical "Gravity". Gravity is a function of one thing, Mass. There would be absolutely no difference at all in the moon if it's density/radius changed to any value. Black holes have no higher gravity than any other mass. – Fattie Jul 28 '20 at 10:50
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    @OrangeDog, Die from what cause? If you drilled a hole down to within 1km of the center of the moon, and if you were provided with adequate life support, you could descend to the bottom of the hole and feel no ill effect. – Solomon Slow Jul 28 '20 at 11:10
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    @SolomonSlow extreme pressure or temperature or both. No such "adequate life support" currently exists. – OrangeDog Jul 28 '20 at 11:12
  • You would only be "sucked in" if the loss of kinetic energy from radiating gravitational waves decreases your speed below escape velocity. – Peter - Reinstate Monica Jul 28 '20 at 11:19
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    @OrangeDog, I did not know that the interior of the Moon was still hot. Learn something new every day. But when I said "hole," I was picturing,... um,... a hole —an open space. There might be immense pressure on whatever structure enabled you to keep the hole open, but if you could do it, then inside that space, there would be no pressure at all. – Solomon Slow Jul 28 '20 at 11:19
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    @SolomonSlow that's not how holes work in massive bodies. The deepest ever on earth reached 12km, and that's with a bore in it - not empty space (or even air). In comparison the moon has a radius of 1700km. – OrangeDog Jul 28 '20 at 11:22
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    @OrangeDog, You said, "If you got within 1km of the centre of the Moon..." I guess I thought you were talking about a hypothetical situation in which somebody could get within 1km of the center of the Moon. My mistake. Sorry. – Solomon Slow Jul 28 '20 at 11:40
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    @OrangeDog , I'm sorry, what you're saying makes no sense. If you take a submarine/bathyscape to a very low depth, the pressure outside on the hull is enormous. But the pressure inside is normal. – Fattie Jul 28 '20 at 12:00
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    @OrangeDog if you drilled a hole, say 10 feet across, right through the moon or earth, assuming it didn't collapse obviously, you could float right through it with no ill effects. Since the moon has no atmosphere there would not even be any air pressure through the middle. – Fattie Jul 28 '20 at 12:01
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    @Fattie Uhh... Gravity is a function of two things: mass and distance. Right now you can't get within 1km of the center of mass of the moon, and even if you could, some of it would be behind you. If the moon were a black hole, you could get within 1km of it, and all of it would be in one direction. If your feet were facing a black hole with the mass of the moon, you were 1km away, and you were 1.75 m tall, you'd experience a tidal force of about 1e6 N (238700 lbs, or 108272 kg on Earth). – Vaelus Jul 28 '20 at 14:44
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    hi @Vaelus - sure, I meant at normal astronomical distances (like "other planets" etc) - but many have now made the point! cheers! thanks for the cool tidal calculation. (For the OP, tides on Earth would be completely unchanged.) – Fattie Jul 28 '20 at 15:57
  • I’m sorry that my comment seems to have confused many people. I was talking about the gravity inside, not outside, the pre-collapse lunar radius. I thought my example of the tidal force one kilometer away from the black hole made this clear, but obviously it didn’t. – G. Smith Jul 28 '20 at 16:34
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It would suck in basically nothing. If the mass of the moon were concentrated in a black hole, you could draw a sphere around that black hole the size of the moon, and for everything outside that sphere, nothing would have changed. The gravity field would be just the same as it is now.

Now, black holes are tiny. At the mass of the moon, the radius is on the order of $\frac{1}{10}mm$. The effects of the strong gravity gradient will be significant within a larger radius, but anything that is supposed to end up within the black hole must eventually hit this $\frac{1}{10}mm$ sphere. Matter that's on direct collision course will hit, of course. And some matter that passes really close and looses enough momentum due to Bremsstrahlung (gravitational or electro-magnetical) or collision with other matter will become bound to the black hole, circle it while radiating away its energy, until it comes close enough to get sucked in. But the radius where this effect works is also rather small. Most matter that passes by simply gets deflected a bit towards the black hole, and that's it.

Secondly, if you hit the black hole with a stone, and it catches some stuff for feeding, the fall into the black hole will release enormous amounts of energy. This energy will heat up the stuff that's circling the black hole, and it will blow other matter away. So, even if you hit your black hole with a slow stone, almost nothing of that stone will actually end up being sucked into the black hole. Most of it will explode with the force of a nuke.

Thirdly, tiny black holes radiate energy via Hawking Radiation. They are not black at all. I don't know the exact amount of radiation that a black hole with the weight of our moon would emit. That's more radiation that tends to heat up matter before it gets a chance at being sucked in. The Hawking Radiation of a black hole with the mass of the moon is negligible and has no effect on its ability to accrete matter. G. Smith has thankfully provide the link to an answer on this site that lists the radiation power of tiny black holes against their respective mass.

Bottom line: A moon-sized black hole won't suck in any appreciable amounts of matter. Nevertheless, random encounters with asteroids may happen, in which case the asteroid would explode in a blinding flash.

cmaster - reinstate monica
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  • A black hole with the mass of the moon has negligible Hawking radiation... probably measurable in femtowatts. – G. Smith Jul 28 '20 at 03:04
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    But I recall reading in a Hawking book that smallet blackholes emit more radiation. Which is why he had suggested that studying black holes using primordial black holes would prove highly suggestive. Is it not true that Hawking radiation of a black hole increases with decreasing radius? – Richard Kiddman Jul 28 '20 at 03:23
  • What would happen to a solid object like a stone, that is bigger then the BH itself? The stone would pass through the BH (or better yet, the BH would pass through the stone), but that means that the singularity is passing through the stone, which means that part of the stone's matter must cease to exist (it must end up and stay in the singularity). – Árpád Szendrei Jul 28 '20 at 03:53
  • @RichardKiddman Yes, Hawking radiation increases with decreasing radius, but the radius must become extremely small for the radiated power to become significant. See this answer for some rough numbers. – G. Smith Jul 28 '20 at 05:00
  • @ÁrpádSzendrei Like any black hole the stone would be crushed and stretched as it was pulled into the black hole. At 1 mile from the center of the black hole the acceleration due to gravity would be 1 million times higher than the 1.6 meters per second squared at the moons surface now. That’s an extreme amount and you still have a mile to go before you get there. Imagine taking a vacuum with a 2 inch round nozzle and pulling the same amount of air into a 1 mm inch nozzle. The suction could be dangerous. – Bill Alsept Jul 28 '20 at 05:05
  • @G.Smith Thanks. I've edited my answer accordingly. – cmaster - reinstate monica Jul 28 '20 at 07:05
  • @ÁrpádSzendrei In addition to what Bill Alsept said, yes, the about $1mm$ cross section cylinder that's on the path of the event horizon would be doomed. Most of the rest, albeit being accelerated with insane force, would fly past the black hole and be deflected towards it. Behind the black hole, this matter will meet, again at relativistic speeds, turning into an extremely hot and dense plasma and start radiating gamma radiation. Matter that was further away will be blown apart by that gamma flash. It's like a nuke. It's not the nuke material that forms the shockwave, it's the air around it. – cmaster - reinstate monica Jul 28 '20 at 07:17
  • @ÁrpádSzendrei Forget the $1mm$, it's smaller. It's on the order of $\frac{1}{10}mm$. – cmaster - reinstate monica Jul 28 '20 at 07:25
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    Regarding Hawking Radiation, the Hawking temperature of a black hole with the mass of the moon is about 1.67 K, this is less than (but close to) the 2.7 K of the CMB. Consequently, the black hole would gain slightly more more from absorbing CMB radiation, than it loses by emitting Hawking radiation. It also means that its Hawking radiation would be nearly indistinguishable from the CMB. – TimRias Jul 28 '20 at 07:40
  • @ÁrpádSzendrei There's a point, close enough to the black hole, at which the chemical bonds holding the stone together are weaker than the tidal forces generated by the black hole. The stone would essentially be atomized before it gets to the event horizon. – probably_someone Jul 28 '20 at 14:49
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Right now, it already eats a fair amount of mass, as tiny meteors (and occasional big ones) rain down on it every day. Once it became a black hole, it would eat far less. Gravitationally, meteors would behave exactly the same while they're outside the moon's former radius. This is because the gravitational field of a spherical shell is exactly the same as for a tiny object of the same mass. And a body like the moon can be seen as a series of concentric spherical shells. This makes calculating orbits very simple, because you can treat a planet as a point object of the same mass.

Once the moon becomes a black hole, any meteors that would have crashed into its surface are now more likely to just whiz by the black hole, then continue on their orbit of the sun. Only a few, which are headed straight for for the smaller black hole at the center would be at risk of getting sucked in. Meteors that just pass near it, even within a few miles, would undergo a different deflection than predicted by Newton's theory, but probably wouldn't get eaten. Meteors would pretty much have to hit it directly. It would swallow up a tiny portion of the solar wind, but that wouldn't amount to much at all. Your basically asking how much matter currently gets eaten by a given 0.01 square millimeters of today's lunar surface.

MiguelMunoz
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About 32 femtograms per day

As others have explained, a black hole doesn't really suck in matter. It uses gravity to pull matter in, but that is not any different from how the moon acts now. Only matter that is on a direct collision course with the black hole will actually get eaten up, any other matter will just pass by and fly off into space again.

A black hole with the same mass of the moon would have a frontal area about $3.4 * 10^{21}$ smaller than Earth. So our black hole would also get hit by $3.4 * 10^{21}$ times less particles. Earth gets hit by about 400,000 tons of interstellar dust per year. Combining these numbers would mean that a black hole the size of the moon would eat about $32$ femtograms or $7.1 * 10 ^{-17} lbs$ worth of interstellar dust per day.

Jelmer Nauta
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  • Well, that's not true. Some stuff passing by would be captured in orbit around it and shredded, making tiny accretion disk. If something big hit it, things could get interesting. – Mithoron Jul 28 '20 at 15:27
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Probably much less than its present rate.

Moon has a lot of surface to "catch" meteorites and convert their kinetic energy into heat (so they won't bounce back into space). If made a black hole, most of these will pass in a parabolic/hyperbolic orbit around the black hole and leave for good.

In order to get something into the black hole (less than a 1mm for the Moon case), one has to target it pretty much exactly. If the object is a larger solid body, it will be converted to sand/dust by tidal force and most of it expelled back in pretty much all directions - all particles going in their very own parabolic/hyperbolic orbits.

p.s. I am not sure how much of actually sucked matter will convert into radiation. Larger black holes are pretty good and cocnvert 20-40% of the mass into light, that's how quazars work. If so, a collision with an ordinary meteorite could be pretty spectacular.

fraxinus
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It has everything to do with distance as you can see in the formula g=G*M/R2 . If the moon became a black hole it would still have the same mass. Right now the moon has a radius of about 1000 miles which equates to an acceleration due to gravity of 1.6 m/s squared at the surface. If the moon were a black hole its radius would be tiny and you would be able to get a lot closer then 1000 miles to the center. If you got within 1 mile of the center your acceleration due to gravity would be much much higher. For example radius squared at the surface of the moon is 1000×1000 = 1,000,000. The equation above would be divided by 1 million to get the 1.6 m/s squared. If you were 1 mile away from the black hole the radius squared would be 1 mile times 1x1=1. Then the acceleration due to gravity would be divided by 1 instead of 1 million and your acceleration would be a million times greater that where the surface is now.

Bill Alsept
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