Minimum safe distance to black hole

[berra]

I wonder what the minimum safe distance would be for a black hole with mass of a couple of billion solar masses. With that I mean at what distance would the gravitational pull be negligible, I guess. I am sorry if this is the wrong kind of question to ask in this forum.

 

[ghwellsjr]

If the black hole were the only thing in the universe and you were not moving with respect to it, there would be no safe distance. The reason why the black hole at the center of our galaxy doesn't pose a threat is because we are orbiting it.

 

[PatrickPowers]

I wonder what the minimum safe distance would be for a black hole with mass of a couple of billion solar masses. With that I mean at what distance would the gravitational pull be negligible, I guess. I am sorry if this is the wrong kind of question to ask in this forum.

The most massive black hole yet found is eighteen billion times the mass of the sun. So how close could you get? In one sense the gravity doesn't matter: you are falling, so you don't feel anything as long as you don't bump into anything. The gravity could be a million times that of Earth and you wouldn't even be able to tell. The limit comes when the difference in gravity between different parts of your body becomes large enough that it is like being stretched on a rack. If you hang from your arms with your feet off the floor, that is called 1G of stretch. I figure about 1G per meter would be the most that anyone would care to tolerate for very long. Special compression body suits would help. You would have to be careful to perpendicular to the black hole, so that the stretching is along the small distance across the body instead of the large distance from head to toe. So with that universal-record-holding black hole, that would occur at a distance of seven million kilometers. That would be about as close as you could go.

 

[PAllen]

The most massive black hole yet found is eighteen billion times the mass of the sun. So how close could you get? In one sense the gravity doesn't matter: you are falling, so you don't feel anything as long as you don't bump into anything. The gravity could be a million times that of Earth and you wouldn't even be able to tell. The limit comes when the difference in gravity between different parts of your body becomes large enough that it is like being stretched on a rack. If you hang from your arms with your feet off the floor, that is called 1G of stretch. I figure about 1G per meter would be the most that anyone would care to tolerate for very long. Special compression body suits would help. You would have to be careful to perpendicular to the black hole, so that the stretching is along the small distance across the body instead of the large distance from head to toe. So with that universal-record-holding black hole, that would occur at a distance of seven million kilometers. That would be about as close as you could go.

Note that that is way inside the horizon. The horizon of this black hole completely dwarfs the solar system.

Or do you mean 7 million kilometers from the horizon? It is not clear from your description.

 

[PatrickPowers]

Note that that is way inside the horizon. The horizon of this black hole completely dwarfs the solar system.

Or do you mean 7 million kilometers from the horizon? It is not clear from your description.

OK, what's the radius of the horizon?

 

[PAllen]

OK, what's the radius of the horizon?

According to this:

http://www.nytimes.com/2011/12/06/science/space/astronomers-find-biggest-black-holes-yet.html

it dwarfs the solar system.

 

[PatrickPowers]

According to this:

http://www.nytimes.com/2011/12/06/science/space/astronomers-find-biggest-black-holes-yet.html

it dwarfs the solar system.

I the black hole event horizon radius as 50 billion kilometers. That's about nine times the furthest orbit of Pluto.

 

[Naty1]

...minimum safe distance would be for a black hole with mass of a couple of billion solar masses. With that I mean at what distance would the gravitational pull be negligible,

As you have probably figured out from the very nice replies already posted, these are two very different questions..."minimum safe distance" and "negligible"...and neither is well defined. For example, the gravitational strength is proportional to 1/r² so it gets asymptotically small, but never reaches zero in our universe.

 

[jtbell]

A better way to define "safe distance" would probably be, "how close can you get before tidal forces (different gravitational forces on different parts of your body) tear you apart?"

See for example Larry Niven's short story "Neutron Star" which has a nice description of traveling close to a very small but massive object, not a black hole, but the principles are the same.

http://en.wikipedia.org/wiki/Neutron_Star_(short_story)

 

[PAllen]

A better way to define "safe distance" would probably be, "how close can you get before tidal forces (different gravitational forces on different parts of your body) tear you apart?"

See for example Larry Niven's short story "Neutron Star" which has a nice description of traveling close to a very small but massive object, not a black hole, but the principles are the same.

http://en.wikipedia.org/wiki/Neutron_Star_(short_story)

Right, but for a massive black hole, you get way inside the event horizon before you feel tidal forces. Are you safe before this? Nope - you are long past the point of no return; nothing you do will even significantly slow down your arrival at the singularity.

Meanwhile, near the horizon, you feel nothing locally, but it would still take enormous fuel consumption to escape.

Here's a thought: there are two aspects to safety:

- ability to survive tidal forces
- ability to survive escape

The former has been discussed (e.g. force per meter of your body). The second might be based on the idea that you wouldn't want to experience more than e.g. 3 G acceleration for an extended period of time. So, it is not safe to get closer to the horizon than would require greater acceleration to escape.

 

[Passionflower]

It is actually difficult to fall into a black hole.

Even a little angular momentum could either swing you right past it, or have you enter into an orbit or even let you make a 360 turn around the black hole (even multiple times) and then travel away from it.

If you are on a radial collision course all you need to do is to calculate how much you have to accelerate laterally to avoid crashing into the black hole.

 

[PAllen]

It is actually difficult to fall into a black hole.

Even a little angular momentum could either swing you right past it, or have you enter into an orbit or even let you make a 360 turn around the black hole (even multiple times) and then travel away from it.

If you are on a radial collision course all you need to do is to calculate how much you have to accelerate laterally to avoid crashing into the black hole.

Good points! So you could safely pass close to a horizon and escape; only hovering close to a horizon would require excessive g force.

But you could never consider yourself safe once you've crossed.

 

[berra]

Thanks for all answers, I feel like I should explain my worries maybe hehe. The reason I asked was that I read a huge black hole is 300 million lightyears away. So let's say it takes 100 generations until its possible to evacuate earth, we wouldn't need to worry then until it is a couple of hundred "plutos" away ? :-)
Edit: ignore the generations thing, obviously it depends on the trajectory.

 

[Matterwave]

A huge black hole 300 million light years away will take at least 300 million years (probably much longer) to get here (if it's even heading here at all). There's a large black hole much closer to us at the center of our galaxy (~50,000 Light years away), but we are orbiting that one and there's no danger posed by that black hole.

 

[Tracer]

Right, but for a massive black hole, you get way inside the event horizon before you feel tidal forces. Are you safe before this? Nope - you are long past the point of no return; nothing you do will even significantly slow down your arrival at the singularity.

Meanwhile, near the horizon, you feel nothing locally, but it would still take enormous fuel consumption to escape.

Here's a thought: there are two aspects to safety:

- ability to survive tidal forces
- ability to survive escape

The former has been discussed (e.g. force per meter of your body). The second might be based on the idea that you wouldn't want to experience more than e.g. 3 G acceleration for an extended period of time. So, it is not safe to get closer to the horizon than would require greater acceleration to escape.

Or less fuel than required to reach escape velocity.

 

[George Jones]

How close can one get to a Schwarzschild black hole while staying freely falling? I think I know the answer.

 

[Tracer]

Thanks for all answers, I feel like I should explain my worries maybe hehe. The reason I asked was that I read a huge black hole is 300 million lightyears away. So let's say it takes 100 generations until its possible to evacuate earth, we wouldn't need to worry then until it is a couple of hundred "plutos" away ? :-)
Edit: ignore the generations thing, obviously it depends on the trajectory.

The escape velocity at a distance of "two hundred plutos" from an 18 billion solar mass black hole is close to a tenth of the speed of light. Any escape plans should have been exercised long before the black hole gets that close to the solar system. If you haven't taken a fast ship out of town by the time the black hole is "two hundred plutos" away, you will be subjected to an enormous and fatal amount of radiation from the acretion region activity long before you encounter the Event Horizon.

 

[Passionflower]

The escape velocity at a distance of "two hundred plutos" from an 18 billion solar mass black hole is close to a tenth of the speed of light. Any escape plans should have been exercised long before the black hole gets that close to the solar system. If you haven't taken a fast ship out of town by the time the black hole is "two hundred plutos" away, you will be subjected to an enormous and fatal amount of radiation from the acretion region activity long before you encounter the Event Horizon.

Does not make any sense to me, the chances are already very slim you would ever get trapped and if you happen to approach the black hole radially (if we take the simple view of a non rotating black hole) then all you need is some very small and short acceleration in the theta and phi direction.

 

[Tracer]

Does not make any sense to me, the chances are already very slim you would ever get trapped and if you happen to approach the black hole radially (if we take the simple view of a non rotating black hole) then all you need is some very small and short acceleration in the theta and phi direction.

I was responding to post #13 in which a black hole was approaching the Earth. The question in that post seemed to be how close can the black hole get to the Earth before
its presence become a serious concern to the Earth. The escape velocity at a distance of 200 times the average radius of Pluto's orbit from the center (not the Event horizon) of an 18 billion solar mass black hole is more than 0.22c. There is no way the Earth can be accelerated to miss the approaching black hole. A ship might still be able to accelerate radially from the black hole to reach escape velocity. Anything less than 0.22c would at best only put the ship in orbit around the black hole. Even if the ship could achieve an orbit around the black hole, the radiation from the acretion area of the black hole would be lethal.

 

[Passionflower]

A ship might still be able to accelerate radially from the black hole to reach escape velocity. Anything less than 0.22c would at best only put the ship in orbit around the black hole.

That is not correct, why do you think that is the case? It depends on the approach, some will 'smash' into the black hole, others might orbit, and yet others might be slung back after circumnavigating the lack hole one or more times. We can calculate this based on the so-called impact parameter.

There seems to be a myth that a black hole is something like pulling the plug in a bathtub full of water sucking everything in, but that is not the case.

 

[feathermoon]

Are there stable orbits within the event horizon of a black hole?

 

[Passionflower]

Are there stable orbits within the event horizon of a black hole?

There are no stable orbits passed the event horizon of a non-rotating black hole.
Also there are no stable (circular) orbits closer than 3 times the Schwarzschild radius of a non-rotating black hole.

Now in contrast for instance a charged or rotating black hole could, in theory, have stable orbits beyond the event horizon.

 

[pervect]

For an 18 billion solar mass black hole, GM/c^2 = 178 astronomical units. This makes the Schwarzschild radius at R=2GM/c^2= 356 au. The photon sphere is at r=3GM/c^2 which is the radius at which light has an unstable orbit around the black hole.

An object on a flyby trajectory will always be outside the photon sphere at closest approach. Because any material object must travel slower than light, a material object on a flyby orbit will always be further away than the photon sphere at it's closest approach. So you can consider this as sort of a limit on how close you can approach and expect to get away again if you are in an unpowered orbit, a limit you won't actually achieve.

The maximum stable circular orbit is at r=6GM/c^2, twice the above value. An unpowered flyby will approach closer than this without falling in.

The Earth's orbit would probably be moved outside the habitable zone by a close enough flyby without any of the planets (or the sun) falling into the black hole, however the calculation as to exactly when that would happen would be messy and would depend also on how one defined the "habitable zone".

Note that what has been specified here are r-coordinate values - they are not really distances.

The basic differential equations for orbits around black holes are presented on the WWW (without proof) at http://www.fourmilab.ch/gravitation/orbits/.

 

[feathermoon]

There are no stable orbits passed the event horizon of a non-rotating black hole.
Also there are no stable (circular) orbits closer than 3 times the Schwarzschild radius of a non-rotating black hole.

Now in contrast for instance a charged or rotating black hole could, in theory, have stable orbits beyond the event horizon.

I'm guessing anything landing in the stable orbits would be completely ripped apart? So the orbits might be filled with rings of matter like a planet?

I guess a slightly more interesting question for me is how big a black hole could pass near our solar system without disrupting our orbits around the sun? Does information on such a scenario?

 

[Passionflower]

I'm guessing anything landing in the stable orbits would be completely ripped apart? So the orbits might be filled with rings of matter like a planet?

Entirely depends on the mass of the black hole and the orbit.

I guess a slightly more interesting question for me is how big a black hole could pass near our solar system without disrupting our orbits around the sun? Does information on such a scenario?

Just in case you do not realize; it does not matter if the object is a black hole or simply some other mass, the effect simply depends on the mass, not on whether the object is a black hole or not.

 

[feathermoon]

Just in case you do not realize; it does not matter if the object is a black hole or simply some other mass, the effect simply depends on the mass, not on whether the object is a black hole or not.

Well, I only insist on that scenario because I assumed we could be sure a massive star wasn't approaching. I suppose a dwarf star or something will suffice, but a black hole wouldn't have to get as close undetected, right? I'm ignoring how unlikely any of this is, just curious.

 

[Tracer]

That is not correct, why do you think that is the case? It depends on the approach, some will 'smash' into the black hole, others might orbit, and yet others might be slung back after circumnavigating the lack hole one or more times. We can calculate this based on the so-called impact parameter.

There seems to be a myth that a black hole is something like pulling the plug in a bathtub full of water sucking everything in, but that is not the case.

The black hole encounter scenario being considered is that an 18 billion solar mass black hole is moving directly toward the sun and its center is presently at a distance of 200 times the average radius of Pluto's orbit around the sun. Pluto's average distance from the sun is 5.4E12 meters. Two hundred times pluto's average distance from the sun is 1.08E15 meters.

The Event horizon of the 18 billion solar mass black hole has a radius of 5.32E13 meters. The radius of the event horizon horizon is larger than Pluto's average distance from the sun. Therefore the sun and all of its planets will encounter the event horizon of the black hole.

Plans to move the people and resources of the Earth should have been made and executed many years earlier. The arrival of the enormous black hole should not have been a surprise. At the very least, astronomers should have noticed gravitational lensing effects while the black hole was at a great distance. They should have also noticed large amounts of radiation from the acretion area just outside of the event horizon. But earlier escape plans are left for discussion elsewhere.

Now there is no escape for the sun and planets of the solar system. They can't be accelerated and moved out of the path of the approaching black hole. However, the people of the Earth could build vehicles to propell themselves and some of their intellectual resources away from the black hole. There are two options. one option is to build ships capable of achieving escaape velocity from the black hole. A second option is to build ships capable of achieving a circular orbit around the black hole.

the first option should be the best since it offers the possibility of moving the Earth's people to a planet and physical resources of another distant solar system. The second option is less desireable since the only resources the people would have would be just whatever they could carry on their ships.

The question to be answered for option number two is whether or not a stable orbit can be achieved around the black hole. Is the Earth outside of three times the radius of the Event horizon? Three times the event horizon radius is 1.6E14 meters. That distance subtracted from the black hole's present distance from the sun is 9.2E14 meters. Therefore a stable orbit is still possible if a ship can accelerate to the necessary orbital speed at its present distance from the black hole. That orbital speed is 0.157c or 47000000 meters/second. Accelerating at one g, it would take more than seventy days to reach orbital velocity assuming that the ship starts from zero relative motion with the black hole. Even with a perfectly efficient matter/antimatter propulsion system the amount of mass needed to accelerate the ship to the necessary orbital velocity would be enormous. This option leaves the Earth's people permanently in the vicinity of the black hole and with no more resources than they could carry on their ship. It also leaves them in jeopardy from the radiation from the acretion zone surrounding the event horizon. This is not a satisfactory option.

To build ships capable of reaching escape velocity from the black hole from its present location would require the ability to accelerate the ships to a speed of 0.2217c or about 66500000 meters/second radially outward form the black hole. This would take more than 99 days if the ship could accelerate at a constant rate of one g from a starting zero relative velocity with the black hole. This option requires much more mass for conversion to energy than the option of orbiting the black hole. However, it offers a chance of permanently escaping from the vicinity of the black hole and finding a new home and safely relocating the people of earth.

 

[DrGreg]

Tracer, you seem to think the only options are to do a U-turn and reverse away from the black hole, or else go into orbit around it. Several people have already mentioned a third option, the most efficient one, a fly-by such as I've crudely sketched below.

If you were driving down the middle of a wide empty road and found a large truck heading straight towards you, would you slam on the brakes and go into reverse, or would you swerve round one side of it?

 

[Tracer]

Tracer, you seem to think the only options are to do a U-turn and reverse away from the black hole, or else go into orbit around it. Several people have already mentioned a third option, the most efficient one, a fly-by such as I've crudely sketched below.

If you were driving down the middle of a wide empty road and found a large truck heading straight towards you, would you slam on the brakes and go into reverse, or would you swerve round one side of it?

If there is enough time before the impending impact and enough room for swerving around then swerving would be a good thing to do. However, why not perform a sling shot manouver around the black hole such that your initial relative velocity is redirected toward a promising but distant destination. After years of free falling toward the black hole, the Earth's relative velocity with the black hole should be a significant fraction of light speed. Furthermore, almost of that relative velocity will be due to the motion of the Earth and not the black hole.

 

[PatrickPowers]

Plans to move the people and resources of the Earth should have been made and executed many years earlier.

"It's only a theory." :-)