How long would the Earth last if the sun became a black hole?

[the_david]

From our point of view, time dilation included, how long would we last if the Sun became a black hole?

We'd all be dead from the supernova that comes first, wouldn't we? Is there any way that wouldn't happen?

[Sermil]

Depends a little on how exactly you assume this happens.

The sun won't go supernova, it doesn't have the mass, so regardless, we're talking about something that's theoretical.

If you assume "All the mass of the sun is suddenly *boop* in a singularity in the current center-of-mass of the sun" then Earth, the planet, would be fine. We would last a few days or weeks before the Earth cooled off enough to become uninhabitable. People might be able to survive for quite a while if they were in insulated, completely-sealed, perfect-recycling buildings with a long-lasting power source.

If you assume a slightly more realistic scenario like "a very small black hole wanders in from outside the solar system, hits the sun perfectly, somehow stops while inside the sun, and starts eating it from the inside out" -- I believe the accretion disk radiation would fry us pretty quick, but I'm not sure how to calculate that.

(Which brings up a point -- if a very small black hole did fall directly towards the sun from interstellar space, would it actually stop? Concepts like friction don't really apply to black holes. I guess the singularity would get more inflowing momentum from its direction of travel, so it would slow down somewhat...)

[Manga Shoggoth]

Gravitationally, quite a long time - pretty much the same amount of mass would be anchoring the Earth in orbit.

For other things...

The shortest answer is "approximately 8 minutes", which is the time light would take to reach us from the sun.

If there are any radiation-based effects they will hit at the speed of light (Gamma rays and other photons) and shortly thereafter (for the very small bits that have rest mass).

If we survive that, we are looking at something simillar to the What If Earth got Kicked Out of the Solar System? Rogue Earth scenario described by Kurzgesagt (the relevent stuff starts around 3:58 - the first bit is discussing how the planet would be ejected).

[Chronos]

The most plausible scenario would be a black hole coming in at initially just over escape speed, and then getting a momentum transfer from the matter it plows into, enough to bring it to just under escape speed. It'd go through the Sun, come out the other side, and head back out into space... but would then eventually slow down, stop, and fall back in, on an orbit around the Sun with its perihelion inside the surface of the Sun. Every time it passed through, it'd lose a little more momentum, and rise to a little lower aphelion, and come back a little sooner, until, after many such passes, it'd eventually be orbiting entirely inside the Sun.

But yeah, the accretion process would release a lot of energy. Maybe not initially, while the hole is still tiny, but at some point, eventually, you'd have a hole that's an appreciable fraction of the mass of the Sun, surrounded by another appreciable portion of a solar mass, and that's going to get hot. I'm not sure we have a name for the resulting phenomenon, but it'd definitely be something in the general ballpark of a supernova.

[Maat Mons]

From our point of view, time dilation included, how long would we last if the Sun became a black hole?

If the resulting black hole is the same mass as the sun and we're the same distance from it, there won't be any more time dilation than there already is.

[Mastikator]

Really depends on what you mean "the Sun became a black hole".

If the process involves a supernova then we'd last 8 minutes. Because that's how long it takes light to reach the Earth.

If the process does not involve a supernova but simply rapidly squishing the Sun until it becomes a black hole then it'd be maybe a year before the last person dies of cold. This is because all that would be different is that we'd lose all of our precious sunlight, the Earth would cool down, eventually all the way down to about 2-3 Kelvin. We'd be dead long before that though, most would die within a month, a few survivors in underground bunkers could last as long as they have fuel, food and water.
This scenario is the same as just removing the Sun as far as our survival is concerned.

If the process means putting a stellar mass black hole in the sun's place then we'd go into a highly eccentric orbit and potentially the Earth would be torn apart by tidal forces as it approaches periapsis (perihelios? periblackholeius?).

If the process means putting a supermassive black hole in the sun's place then we'd die more or less instantly.

[Fat Rooster]

The most plausible scenario would be a black hole coming in at initially just over escape speed, and then getting a momentum transfer from the matter it plows into, enough to bring it to just under escape speed. It'd go through the Sun, come out the other side, and head back out into space... but would then eventually slow down, stop, and fall back in, on an orbit around the Sun with its perihelion inside the surface of the Sun. Every time it passed through, it'd lose a little more momentum, and rise to a little lower aphelion, and come back a little sooner, until, after many such passes, it'd eventually be orbiting entirely inside the Sun.

But yeah, the accretion process would release a lot of energy. Maybe not initially, while the hole is still tiny, but at some point, eventually, you'd have a hole that's an appreciable fraction of the mass of the Sun, surrounded by another appreciable portion of a solar mass, and that's going to get hot. I'm not sure we have a name for the resulting phenomenon, but it'd definitely be something in the general ballpark of a supernova.

I'm not entirely convinced that is what would happen. The issue is that the amount of material actually 'eaten' by the black hole would be pretty tiny, so the momentum it would get from that would be quite small. Meanwhile a huge amount of energy would be radiating out, blowing out a bubble of very hot material behind it. Material in front of it would be cooler and higher density than the hotter material behind it, so I think gravity might actually accelerate it! The sun might just spit it back out again.

If it came close to the sun without actually consuming any mass then tidal effects would definitely slow it, but the two effects might not cancel in any sort of stable way. The issue is that the forward force would be strictly prograde, while the tidal forces would be just resisting in the angular direction. I think it would get increasingly eccentric until the black hole was just kicked out of the solar system completely.

The energy available from material infalling into a black hole is absolutely absurd, to the point that solar escape velocity is barely a rounding error. You cannot just assume that friction will behave like you would expect any more than you would expect friction on a bullet to work as expected when it hits dynamite. Friction is intuitive because contact usually reduces energy available, but when a black hole contacts matter you end up with far more energy floating about than you started with. The first instinct might be wrong. Would need proper modelling to be sure though, and I haven't been able to find any (please point me at some if you know of any).

If the sun were suddenly replaced with a stellar mass black hole, the initial impact would be panic, because there would be no other initial impact. Then we would get cold. If material started infalling we might get hit by massive x-ray doses, but largely the solar system would keep on turning. Orbital mechanics doesn't care what the object at the centre is, just that it is near spherical of a certain mass.

[Lord Torath]

If the process means putting a stellar mass black hole in the sun's place then we'd go into a highly eccentric orbit and potentially the Earth would be torn apart by tidal forces as it approaches periapsis (perihelios? periblackholeius?).

When you say "stellar mass" black hole, do you mean a black hole with the mass of the sun? Or one with several to several-dozen times the mass of the sun? My first impression when you say 'stellar mass' is the mass of the sun, but in that case we wouldn't notice anything other than the sun has stopped shining. If you mean "several to several-dozen" solar masses, then yeah, our orbit will rapidly decay and we'll get ripped apart when we hit the black hole's roche limit.

[Lord Torath]

If the process means putting a stellar mass black hole in the sun's place then we'd go into a highly eccentric orbit and potentially the Earth would be torn apart by tidal forces as it approaches periapsis (perihelios? periblackholeius?).

When you say "stellar mass" black hole, do you mean a black hole with the mass of the sun? Or one with several to several-dozen times the mass of the sun? My first impression when you say 'stellar mass' is the mass of the sun, but in that case we wouldn't notice anything other than the sun has stopped shining. If you mean "several to several-dozen" solar masses, then yeah, our orbit will rapidly decay and within a few months at most we'll get ripped apart when we hit the black hole's roche limit.

[Mastikator]

When you say "stellar mass" black hole, do you mean a black hole with the mass of the sun? Or one with several to several-dozen times the mass of the sun? My first impression when you say 'stellar mass' is the mass of the sun, but in that case we wouldn't notice anything other than the sun has stopped shining. If you mean "several to several-dozen" solar masses, then yeah, our orbit will rapidly decay and we'll get ripped apart when we hit the black hole's roche limit.

I'm just copying NASA's nomenclature to be honest. It's a black hole that formed when a sufficiently large star undergoes supernova. The remaining black hole is at least 3 times more massive than the sun, but probably 5-8 times the mass of the sun.

Plopping down such a black hole on top of the Sun would possibly rip the Earth apart from the sudden gravitational wave, possibly atomize the Earth from the ensuing explosion. If neither of that happens then the resulting higher gravity would pull on the Earth 3-8 times stronger. That would change the orbit, wherever the Earth is would become the new apoapsis, the periapsis would be significantly closer, possibly within the roche limit.

https://www.nasa.gov/image-article/s...ss-black-hole/
https://en.wikipedia.org/wiki/Stellar_black_hole

[Lord Torath]

Gotcha. Thanks for the clarification!

[Quizatzhaderac]

if a very small black hole did fall directly towards the sun from interstellar space, would it actually stop? Concepts like friction don't really apply to black holes. I guess the singularity would get more inflowing momentum from its direction of travel, so it would slow down somewhat...)

If it's small enough and fast enough it wouldn't stop. It's even been theorized that the Earth has been hit by several black holes.

That would change the orbit, wherever the Earth is would become the new apoapsis, the periapsis would be significantly closer, possibly within the roche limit

If I calculated it correctly, Earth would not be in the Roche limit. Although Venus and Mercury would enter it.

The Earth-Sun Roche limit is only about 110% of the sun's radius (the sun is not dense). If we octuple the Sun's mass¹, we double the Roche limit. Assuming the new periapsis is no less than an 8th of an AU, that still leaves a fair distance.

¹ The Roche limit equations from wikipedia use the sun's radius and density, but those exactly cancel out if you keep the mass constant.

Edited for math mistake

[Bohandas]

https://www.youtube.com/watch?v=Q6kJaMf3Lgo

[DavidSh]

If I calculated it correctly, Earth would not be in the Roche limit. Although Venus and Mercury would enter it.

The Earth-Sun Roche limit is only about 110% of the sun's radius (the sun is not dense). If we octuple the Sun's mass¹, we octuple the Roche limit. Assuming the new periapsis is no less than an 8th of an AU, that still leaves a fair distance.

¹ The Roche limit equations from wikipedia use the sun's radius and density, but those exactly cancel out if you keep the mass constant.

I see the equations as giving the Roche limit as in proportion to the cube root of the mass of the primary. So octupling the Sun's mass would double the Roche limit. (But maybe that's what you meant to say, otherwise why use "octuple".)

[Quizatzhaderac]

I see the equations as giving the Roche limit as in proportion to the cube root of the mass of the primary. So octupling the Sun's mass would double the Roche limit. (But maybe that's what you meant to say, otherwise why use "octuple".)

I made a math mistake, the Roche limit should double, as you said. I was octupling the Sun's mass, because that's approximately what would happen if a stellar mass black hole fell into it and stuck.

[Ionathus]

I think we're focusing too hard on the problems this scenario would cause.

Let's highlight some of the positives of this scenario!