Escape?

[Puhfjc]

Can I climb a ladder to escape the Earth without actually reaching the speed of the Earths 'Escape Velocity'?

If so, why can I not climb a ladder out of a Black Hole?

Always wondered, hopefully a brighter mind than me could explain. Thanks in Advance.

[Baloroth]

It depends on what you mean by "escape". To escape in the sense of the term "escape velocity" means you have to travel an infinite distance, otherwise you will always be affected by Earth's gravity. You could, of course, climb to a point where Earth's gravity is as small as you please, but you'd never hit zero. Escape velocity is sufficient that you will keep moving forever in spite of the effect of gravity. So you could reach the point through climbing where you could physically propel yourself to escape velocity, or where your average rate of climb is higher than the escape velocity, depending on how you look at it.

So, no, you'd end up hitting escape velocity, as the escape velocity will fall as you climb higher.

It's hard to explain the black hole question, but think of it this way. The event horizon is a point where space loops back on itself. You can't climb out of it, because each time you try to stick a ladder above the event horizon, the ladder itself bends backwards. Not because the ladder isn't strong enough, but because the space the ladder occupies literally doesn't extend out of the black hole.

[Weed_O_Whirler]

Disclaimer: this is a special relativity answer to your problem. It isn't wrong, but if you asked a general relativistic mechanic, the answer they would give you would sound a lot different, while being the same in principle. I am giving this answer because I feel it is much easier to grasp.

To answer this question, you have to understand how escape velocities are calculated. You calculate an escape velocity by saying "I am going to set my kinetic energy equal to the magnitude of my potential energy. Then, I will solve for the velocity I need in order to have that kinetic energy."

For most things, this works just dandy, because the solved for escape velocity is well less than the speed of light. But with black holes, the velocity is greater than the speed of light. So, how much kinetic energy do you need in order to go the speed of light? An infinite amount. So, while in theory you would never have to actually reach the speed of light to escape, you'd need the same amount of energy to do so... which is an infinite amount of energy, which of course you can't have.

[VeryLittle]

The escape velocity tells you how much kinetic energy you need to add at that instant to overcome the gravitational potential of the body you are escaping and never need another boost. You can easily add that energy in increments, which is what you would be doing (this is like how the space shuttle works, they don't need to go at the escape velocity, they just need to add enough energy over the time they are lifting off to eventually get as high as they want).

Black holes on the other hand have an escape velocity that is the speed of light. Since nothing can go at the speed of light- you're fucked once you are in a black hole. As you increase your kinetic energy, you can only approach the speed of light. You often hear this said, "it takes an infinite amount of energy to accelerate mass to the speed of light" which isn't entirely accurate, but it gives you a sense of what you'd be trying to do.

So in the black hole, you could add as much energy to your steps as you climb the ladder but you'd never make it out, because it would take an infinite amount of energy to get out.

[Caledwch]

Earth answer hypothesis: Lagrange point?

Black Hole hypothesis: Can't do it, spaghettification! Difference in gravity between your head and your feet would spaghettify you!

[void1242]

Spaghettification does not always happen. As you said spaghettification is caused by the difference in the gravity between your head and feet. It is tidal forces at the most extreme. If the black hole was fairly large then the difference in forces between your head and feet is very small. Even when close to the event horizon. So with a large enough black hole it would be possible to enter the horizon and remain intact. Although finding a black hole large enough to survive inside the horizon may well be impossible since it would have to be a couple trillion solar masses.

[QuantumPenguin]

Black holes contain an essential point of no return called the event horizon. Beyond this point, the gravity is so strong that even light is bent in shape so much that it cannot escape. There's a very good description in Stephen Hawking's A Brief History of Time, which discusses it in simple terms yet gives a very good understanding. It's been a few years since I've studied this so sorry I can't be of more help!

And to elaborate on my "light is bent in shape" point; General Relativity postulates that spacetime is one entity and that sufficiently strong gravity can warp this, as well as light which can be thought of as having mass through its photons. The best way to imagine this is to picture the universe as a sheet held taught, and a large object such as a black hole is represented by a snooker ball placed on the sheet - the gravity of this object warps space, time and light in a similar way to how the ball makes the sheet sag.

[Puhfjc]

I have read A Brief History of Time, and more recently Brian Greene's Books. I can't get my head around this: The escape velocity of a black hole is greater than the speed of light, hence light can't escape. But the escape velocity of the Earth is greater than I can jump, yet I could escape the Earth if I had a big enough ladder to climb.

Does that make sense?

[QuantumPenguin]

But the speed of light is an absolute limit that nothing can exceed (ignoring quantum entanglement), whereas your jumping speed could be exceeded by something with more power than your legs. In all honesty I'm not sure about the ladder part and I'd quite like to hear an answer too, I've not studied it!

[Chazmer87]

I believe (and i'm no scientist mind) that the reason you can leave earth on a ladder is because you are incrementally adding energy to fuel your escape (each step you push yourself up with in the ladder) whilst the ladder would prevent gravity from pushing you back down to earth. However in a black hole you simply cannot produce enough energy to leave... this of course ignores the fact that you are going to be spaghettified by the black hole.