# Blackhole Escape Velocity

I've heard it said that any object that wants to escape another object's gravitational pull must travel at the object's escape velocity. I assume this is incorrect, and would only apply to something with an initial velocity at the escape velocity (like a bullet from a gun would need to travel at the Earth's escape velocity to not fall back to earth.) Is it correct that if it gradually exerts force like a space elevator then something could travel much slower than the escape velocity?

1) So as a typical space shuttle or rocket does not expend all of its fuel at launch, but releases it gradually; does that mean that the space shuttle travel's much slower than the Earth's escape velocity.

2) If a black hole is defined as an object with an escape velocity equal to the speed of light, why could something gradually exerting force (like a space elevator) not "climb" its way out of the black hole's gravitational pull?

## Answers and Replies

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JesseM
1) So as a typical space shuttle or rocket does not expend all of its fuel at launch, but releases it gradually; does that mean that the space shuttle travel's much slower than the Earth's escape velocity.
Yes, powered flight allows you to escape Earth's pull without reaching escape velocity.
Good4you said:
2) If a black hole is defined as an object with an escape velocity equal to the speed of light, why could something gradually exerting force (like a space elevator) not "climb" its way out of the black hole's gravitational pull?
Some popular articles on black holes may define them this way but it isn't really accurate. The reason you can't escape a black hole doesn't really have any perfectly good analogy in terms of Newtonian forces and escape velocities, you really need the theory of general relativity to understand it. Are you familiar with the idea of a light cone in relativity? Basically if you pick an event, the "future light cone" of that event is all the points in spacetime that could receive a signal from the original event which travels at the speed of light or slower; since no signal can travel faster than light in relativity, no point in spacetime outside the future light cone can be influenced by the event in any way. In general relativity light cones can be "tilted" by the curvature of spacetime, and it works out that for an event at or inside the event horizon of a black hole, the entire future light cone is tilted to lie inside the event horizon, so that no signal from the event can ever reach the region outside the horizon. Here's a diagram showing the future light cones of various events on the path of a particle falling into a black hole (its event horizon represented by a cylinder, the vertical dimension of the diagram standing for the time dimension), from the textbook Gravitation by Misner/Thorne/Wheeler:

http://www.valdostamuseum.org/hamsmith/DFblackIn.gif [Broken]

http://www.etsu.edu/physics/plntrm/relat/blackhl.htm has some similar diagrams at the bottom, one showing more clearly how for an event exactly on the horizon, the light cone has tilted over enough so it becomes impossible for anything in the future light cone to be outside the horizon:

http://www.etsu.edu/physics/plntrm/relat/eventho2.gif

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Because the force of gravity would be much greater than the force of the "space elevator" or anything gradually applying a force. For example, the required force to escape a blackhole would be about 50,000 N. But the gradually applying the force would not be enough to escape the blackhole.

According to the Schwarzschild coordinates of a distant observer, for an observer stationary at r, the local acceleration would be (G M / r^2) / sqrt(1 - r_s / r), so the acceleration required to remain stationary at the Schwarzschild radius is infinite and below that, there can be no stationary observers and no finite amount of acceleration can be applied to hover or escape.

bcrowell
Staff Emeritus
Gold Member
JesseM has done a good job of pointing out that this is all ultimately about limits on cause and effect, not limits on mechanical processes. However, it may be helpful to spell out the mechanical stuff a little more concretely.

Suppose that you wanted to lift an elevator out past the event horizon of a black hole. One can show that this would require a certain tension in the cable, and that tension would be such that the speed at which vibrations would travel in the cable would be greater than c. But the atoms in the cable are held together by electromagnetic forces, so disturbances can only propagate at c or less. Therefore the cable would break. In other words, relativity places fundamental limits on the strengths of materials.

Good4:

Escape velocity has a specific definition...and within the context of that definition is "correct",,or accurate....

Wiki explains it this way:

In physics, escape velocity is the speed at which the kinetic energy plus the gravitational potential energy of an object is zero. It is the speed needed to "break free" from a gravitational field without further propulsion.

http://en.wikipedia.org/wiki/Escape_velocity

It's usually referenced to the surface of, say, a planet like earth, and a since a typical rocket takes a while to develop velocity, defined "escape velocity" may be greater than the actual velocity required to "escape"...

And JesseM captured the essential concept answering your black hole "escape velocity" question:

"The reason you can't escape a black hole doesn't really have any perfectly good analogy in terms of Newtonian forces and escape velocities, you really need the theory of general relativity to understand it."

Black hole "escape velocity" has a different meaning....a different context.....you cannot bypass this "escape velocity" as you can in the Newtonian definition.

In fact, it seems a bit of a misnomer???

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Because the force of gravity would be much greater than the force of the "space elevator" or anything gradually applying a force. For example, the required force to escape a blackhole would be about 50,000 N. But the gradually applying the force would not be enough to escape the blackhole.
I took elementary physics from Prof. Leonard at U. Illinois/CU and he would always say that you can derive any physics equation starting with F=ma.

If you apply a force to an object using that equation, the object would indeed accelerate until it exceeds the escape velocity, but that's only if you ignore the reality of Special Relativity.

The space elevator is actually a really, really stupid idea. The notion that you could apply a simple parallel force to a vehicle attached to a tether that reaches all the way to a geosynchronous AND geostationary center of mass is ludicrous.

As you go up the tether you would also need to apply an ever increasing tangential force to the vehicle. That's just one of the many problems with this idea.

Even worse, what can you do with this vehicle until you actually reach the center of gravity of the tether system? If you "let go" of the tether before that you would simply fall back to earth. Why? Because your tangential velocity will not be high enough to maintain orbit - so that means you have to either use a PAM module to get into orbit OR go the full 22,000 miles to get to the center of mass of the Geostationary orbit. Even in that case - you're not in a useful orbit because you are too close to the space elevator.

There is no advantage to a space elevator since it would require exactly the same amount of energy to get something into orbit as it does any other way (minus losses due to fighting air pressure at low altitudes.)

Even if there were some advantage, you'd still have an extremely long pay off period because you have to get 22,000 miles+ of tether up there somehow. This idea is useful only to hit up governments and philanthropic organizations for research money.

I work professionally with CNT's at the University of Pennsylvania, so I know a little more than average about this Space Elevator crap.

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bcrowell
Staff Emeritus
Gold Member
Zentrails, I think you missed the fact that this thread is about black holes.

Zentrails, I think you missed the fact that this thread is about black holes.
You're talking about the OLD part of the thread, as in 2009.

PAllen
2019 Award
Well we should revive old threads with a new topic. Open a new thread.

bcrowell
Staff Emeritus
Gold Member
You're talking about the OLD part of the thread, as in 2009.
All the 2011 posts, up until yours, were also about black holes. If you want to talk about space elevators to earth orbit, a good subforum to post in would be either Classical Physics or General Astronomy.

All the 2011 posts, up until yours, were also about black holes. If you want to talk about space elevators to earth orbit, a good subforum to post in would be either Classical Physics or General Astronomy.
OK, sorry. delete it, please.

DaveC426913
Gold Member
There is no advantage to a space elevator since it would require exactly the same amount of energy to get something into orbit as it does any other way (minus losses due to fighting air pressure at low altitudes.)
Can't resist...

Among some of the many things you haven't accounted for in considering a space elevator is the rather huge one that you don't have to carry all your fuel with you.
This means
a] What leaves the ground is 100% payload, rather than 99% delivery mechanism and 1% payload.
b] You don't waste even more fuel lifting your fuel.
c] You can keep all your fuel on the ground in some cheap safe and convenient reservior, such as a hydrodam, and elvier it as necessary, rather than storing in underfoot in the form of a highly pressu...

...oh you get the idea. The list goes on and on...

Can't resist...

Among some of the many things you haven't accounted for in considering a space elevator is the rather huge one that you don't have to carry all your fuel with you.
This means
a] What leaves the ground is 100% payload, rather than 99% delivery mechanism and 1% payload.
b] You don't waste even more fuel lifting your fuel.
c] You can keep all your fuel on the ground in some cheap safe and convenient reservior, such as a hydrodam, and elvier it as necessary, rather than storing in underfoot in the form of a highly pressu...

...oh you get the idea. The list goes on and on...
Sorry, I was told to post my elevator stuff in a different thread.
Your points are correct.

I've heard it said that any object that wants to escape another object's gravitational pull must travel at the object's escape velocity. I assume this is incorrect, and would only apply to something with an initial velocity at the escape velocity (like a bullet from a gun would need to travel at the Earth's escape velocity to not fall back to earth.) Is it correct that if it gradually exerts force like a space elevator then something could travel much slower than the escape velocity?

1) So as a typical space shuttle or rocket does not expend all of its fuel at launch, but releases it gradually; does that mean that the space shuttle travel's much slower than the Earth's escape velocity.

2) If a black hole is defined as an object with an escape velocity equal to the speed of light, why could something gradually exerting force (like a space elevator) not "climb" its way out of the black hole's gravitational pull?
Yes, a push would make you escape a gravitational field. But the escape velocity of earth also means that the velocity is required to orbit the earth, so spaceships usually do that in order to orbit freely.

You can do that when you are near the event horizon, just eject flame towards the black hole and remain at the same position. However, when you reach the event horizon it is vastly different. At that point, it is where speed of light cannot escape, which means even if you are accelerated near the speed of light you would be absorbed by B H.

It's similar that you cannot reach some distance from earth, and you can travel less distance from sun under the same condition. In the case of the B H you are never able to reach the position outside E H. (Similar to the light cone in the previous poster)

Sorry for my stupid English, I'm not native.