# Physics Question

• But you need an “initial thrust” that will get you off of the Earth.

A Rocket at rest which then blasts off to only 100 MPH will not have enough Acc to escape the Earth’s Gravity.

However, if you blast it off with enough of an “initial thrust” (initial acc), then you can.Â  Your speed there after may or may not matter.Â  I don’t remember.  Actually I think Falk answered the speed part.

With a Black Hole, this initial thrust must be greater than the speed of light, which is not possible.

• Mary,

I’d think of it in terms where you are “falling” into the black hole, you are not at a standstill (even on a surface like the floor you are standing on, we are still “falling” towards the center of the earth.  Its just that the surface provides an equal force in the opposite direction which counteracts this fall).  Therefore, you must first attain a speed greater than the rate at which you are “falling” before you can make any progress towards the event horizon.  However, this speed is greater than the speed of light in the case of a black hole.

Another way to look at it is in terms of the energy required and convert this energy to velocity.  By the time you climb out of earths gravity well at 10 mph, you have used the same amount of energy as if you had started at escape velocity.  In the case of a black hole, you would need the equivalent energy as if you started faster than the speed of light (which you won’t have).

F_alk, I may be somewhat incorrect with my description above as I’ve tried to make the explaination simple, so feel free to correct/clarify.

• I’d think of it in terms where you are “falling” into the black hole, you are not at a standstill (even on a surface like the floor you are standing on, we are still “falling” towards the center of the earth.Â  Its just that the surface provides an equal force in the opposite direction which counteracts this fall).

Yes, it’s being in a gravity well. And I realize that you “fall” into a black hole as well and that the gravity well in a black hole is too steep for light to escape from.

Therefore, you must first attain a speed greater than the rate at which you are “falling” before you can make any progress towards the event horizonÂ

This is what I have a problem with. Certainly the speed of “descent” into Earth’s gravity well is greater than 1 m.p.h., yet I can get out of the gravity well by going 1 m.p.h if I do it long enough (straight up, for 300 hours).

Another way to look at it is in terms of the energy required and convert this energy to velocity.Â  By the time you climb out of earths gravity well at 10 mph, you have used the same amount of energy as if you had started at escape velocity.

This seems right. Lets assume the energy of accelerating to 17,000 mph is the same as the energy required to go 10 mph for 50 or so hours.

In the case of a black hole, you would need the equivalent energy as if you started faster than the speed of light (which you won’t have)

So it goes back to infinite energy. But there’s not infinite gravity! Let’s say we’re in the gravity well of an object that requires an escape velocity of C-1 (speed of light -1). Given enough time and energy, we can escape the gravity well going at a very slow speed. And it woudn’t require anything close to infinite energy (or would it? I wouldn’t think so…). However, you are saying that once escape veolicty reaches C, there is no going back out. It doesn’t seem logical that a one mile per second difference is going to require an infinite amount of energy.

• Quote
Therefore, you must first attain a speed greater than the rate at which you are “falling” before you can make any progress towards the event horizon

This is what I have a problem with. Certainly the speed of “descent” into Earth’s gravity well is greater than 1 m.p.h., yet I can get out of the gravity well by going 1 m.p.h if I do it long enough (straight up, for 300 hours).

Well, we should really be talking acceleration, not velocity here.  Therefore the “descent” is not necessarily greater than 1 mph.  I’ve used velocity to try to make it simple to understand.

Quote
In the case of a black hole, you would need the equivalent energy as if you started faster than the speed of light (which you won’t have)

So it goes back to infinite energy. But there’s not infinite gravity!

Einsteins relativity theory states that particles gain mass as they approach the speed of light (infinite mass at the speed of light).  This is why a massless light particle still falls into the black hole, infinity times 0 equals something.  Therefore you do not need infinite gravity in a black hole to require infinite energy required to escape.

So as you speed up, you actually make it more difficult to escape the gravity as your mass increases.

• Edit:  Baker snuck in another post

But it is not necessarily your speed that matters, it is your acceleration.

For example, all the cars on the Earth don’t go flying off into space because they constantly go 50 MPH, or race cars that go 200MPH.

Your initial Acceleraion must be greater than the escape velocity OR

You must continue to accelerate past the escape velociy.

Either way works. Â Falk is this right?

So, in the case of a Black Hole you need to initially accelerate to the speed of light OR
gradually increase your speed upto and past the speed of light.

Both are impossible.

• From Wiki:

Not sure what is says, I didn’t have time to read the whole thing but it does have the equations and mentions energy.

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

• **Edit:**Â  Baker snuck in another post

But it is not necessarily your speed that matters, it is your acceleration.

For example, all the cars on the Earth don’t go flying off into space because they constantly go 50 MPH, or race cars that go 200MPH.

Your initial Acceleraion must be greater than the escape velocity OR

You must continue to accelerate past the escape velociy.

Either way works. Â Falk is this right?

So, in the case of a Black Hole you need to initially accelerate to the speed of light OR
gradually increase your speed upto and past the speed of light.

Both are impossible.

That’s not true. You can get into space from Earth without ever reaching 17,000 Mph, which is roughly the escape velocity.

• That’s not true. You can get into space from Earth without ever reaching 17,000 Mph, which is roughly the escape velocity.

Space is not necessarily escape from the earth.  The moon is in space, but it does not have this escape velocity required, therefore it orbits the earth.  If you want to place a satelite you don’t need escape velocity.  If you want to go elsewhere (other than orbit and the moon) in the solarsytem or universe you do need escape velocity.

• Yeah, as you get further off the Earth the escape velocity required is reduced.

So, if you are already 50 miles off the Earth you may be able to escape by going less than 17,000 MPH or whatever it is, BUT if you are on the Earth you will at some point have to have an accelation that will translate into being greater than the 17,000.Â  You need a certain amount of an initial thrust just to get off the planetary body.

Acceleration does not equal velocity.

• @221B:

That’s not true. You can get into space from Earth without ever reaching 17,000 Mph, which is roughly the escape velocity.

Space is not necessarily escape from the earth.Â  The moon is in space, but it does not have this escape velocity required, therefore it orbits the earth.Â  If you want to place a satelite you don’t need escape velocity.Â  If you want to go elsewhere (other than orbit and the moon) in the solarsytem or universe you do need escape velocity.

How is this true? What is to stop me from heading in the direction of Pluto at 100 m.p.h for a thousand years? Eventually I will get there at a very slow speed. Escape velocity simply refers to the speed at which no further accleration is required. As I said before, you DON’T have to go 17,000 mph to get into space and you wouldn’t have to go that fast to get beyond the moon.

• Back to the energy used, Mary.  To spend 1000 years maintaining 100 mph will require the same energy than what it would take to reach 17,000 mph in an initial burst of speed.  Either way, you are going to need a certain amount energy to accomplish this.

• @221B:

Back to the energy used, Mary.Â  To spend 1000 years maintaining 100 mph will require the same energy than what it would take to reach 17,000 mph in an initial burst of speed.Â  Either way, you are going to need a certain amount energy to accomplish this.

Right, I get that part. The energy required is the same, even if the speed differs. And your claim is that you would need an infinite amount of energy to get past the event horizon, correct? I like your illustration of accleration falling into a black hole. Objects approach C and you would have to have enough energy to halt your own accleration towards the singularity. Could you do that with enough energy?

• Ahh, I get you now, Baker. If the escape velocity is C, than you would either need to go C or have the equivalent energy of reaching C, but it would take an infinite amount of energy.

I’m in over my head now. This sounds right though.

• … The energy required is the same, even if the speed differs. And your claim is that you would need an infinite amount of energy to get past the event horizon, correct? I like your illustration of accleration falling into a black hole. Objects approach C and you would have to have enough energy to halt your own accleration towards the singularity. Could you do that with enough energy?

Can you accelerate out of a black hole, no, not once you are past the event horizon. Â As Einstein proved, you would need an infinite amount of energy for any object with mass to reach the speed of light…which still isn’t enough as light particles can’t escape.

The only ways out of a black hole according to current theory would be to either be a Hawking radiation particle, or wait inside until the black hole evaporates (approx. 10 ^ 64 years according to Wiki). Â Neither of these are proven, B.T.W.

Edit: Mary posted before I could get this in, and I think you have the concept, but I’ll submit it anyway.

• E = MC2

:-D

• I’ll wait for the lab results.  The black holes of today must be doubly better or more than the ones from Einstein’s day.

• For mary and her escape velocity question:
Suppose that you are standing on the surface of a planet. You throw a rock straight up into the air. Assuming you don’t throw it too hard, it will rise for a while, but eventually the acceleration due to the planet’s gravity will make it start to fall down again. If you threw the rock hard enough, though, you could make it escape the planet’s gravity entirely. It would keep on rising forever. The speed with which you need to throw the rock in order that it just barely escapes the planet’s gravity is called the “escape velocity.” As you would expect, the escape velocity depends on the mass of the planet: if the planet is extremely massive, then its gravity is very strong, and the escape velocity is high. A lighter planet would have a smaller escape velocity. The escape velocity also depends on how far you are from the planet’s center: the closer you are, the higher the escape velocity. The Earth’s escape velocity is 11.2 kilometers per second (about 25,000 m.p.h.), while the Moon’s is only 2.4 kilometers per second (about 5300 m.p.h.).

What happens when you get too close to the black hole:
Let’s suppose that you get into your spaceship and point it straight towards the million-solar-mass black hole in the center of our galaxy. (Actually, there’s some debate about whether our galaxy contains a central black hole, but let’s assume it does for the moment.) Starting from a long way away from the black hole, you just turn off your rockets and coast in. What happens?

At first, you don’t feel any gravitational forces at all. Since you’re in free fall, every part of your body and your spaceship is being pulled in the same way, and so you feel weightless. (This is exactly the same thing that happens to astronauts in Earth orbit: even though both astronauts and space shuttle are being pulled by the Earth’s gravity, they don’t feel any gravitational force because everything is being pulled in exactly the same way.) As you get closer and closer to the center of the hole, though, you start to feel “tidal” gravitational forces. Imagine that your feet are closer to the center than your head. The gravitational pull gets stronger as you get closer to the center of the hole, so your feet feel a stronger pull than your head does. As a result you feel “stretched.” (This force is called a tidal force because it is exactly like the forces that cause tides on earth.) These tidal forces get more and more intense as you get closer to the center, and eventually they will rip you apart.

For a very large black hole like the one you’re falling into, the tidal forces are not really noticeable until you get within about 600,000 kilometers of the center. Note that this is after you’ve crossed the horizon. If you were falling into a smaller black hole, say one that weighed as much as the Sun, tidal forces would start to make you quite uncomfortable when you were about 6000 kilometers away from the center, and you would have been torn apart by them long before you crossed the horizon. (That’s why we decided to let you jump into a big black hole instead of a small one: we wanted you to survive at least until you got inside.)

What do you see as you are falling in? Surprisingly, you don’t necessarily see anything particularly interesting. Images of faraway objects may be distorted in strange ways, since the black hole’s gravity bends light, but that’s about it. In particular, nothing special happens at the moment when you cross the horizon. Even after you’ve crossed the horizon, you can still see things on the outside: after all, the light from the things on the outside can still reach you. No one on the outside can see you, of course, since the light from you can’t escape past the horizon.

How long does the whole process take? Well, of course, it depends on how far away you start from. Let’s say you start at rest from a point whose distance from the singularity is ten times the black hole’s radius. Then for a million-solar-mass black hole, it takes you about 8 minutes to reach the horizon. Once you’ve gotten that far, it takes you only another seven seconds to hit the singularity. By the way, this time scales with the size of the black hole, so if you’d jumped into a smaller black hole, your time of death would be that much sooner.

Once you’ve crossed the horizon, in your remaining seven seconds, you might panic and start to fire your rockets in a desperate attempt to avoid the singularity. Unfortunately, it’s hopeless, since the singularity lies in your future, and there’s no way to avoid your future. In fact, the harder you fire your rockets, the sooner you hit the singularity. It’s best just to sit back and enjoy the ride.

• “For mary and her escape velocity question:
Suppose that you are standing on the surface of a planet. You throw a rock straight up into the air. Assuming you don’t throw it too hard, it will rise for a while, but eventually the acceleration due to the planet’s gravity will make it start to fall down again. If you threw the rock hard enough, though, you could make it escape the planet’s gravity entirely. It would keep on rising forever. The speed with which you need to throw the rock in order that it just barely escapes the planet’s gravity is called the “escape velocity.” As you would expect, the escape velocity depends on the mass of the planet: if the planet is extremely massive, then its gravity is very strong, and the escape velocity is high. A lighter planet would have a smaller escape velocity. The escape velocity also depends on how far you are from the planet’s center: the closer you are, the higher the escape velocity. The Earth’s escape velocity is 11.2 kilometers per second (about 25,000 m.p.h.), while the Moon’s is only 2.4 kilometers per second (about 5300 m.p.h.).”

yes, I know this. However, it is possible to “escape” from the gravity of an object without ever going close to the escape velocity. If you had enough power, and went 60, m.p.h. long enough, you could sail right through the solar system. What Baker’s point is that the energy expended to escape will be the same.

• OK but only if you were far enough away from the influence of any body that could tug to away from your course at that speed…

• It is all about the difference between potential energy and kinetic energy.

Potential energy = the distance one can fall = distance from your ship to the center of the earth/black hole Â Or to escape the earth or black hole, the distance from where you are to essentially infinity (since there is no known upper limit of distance to gravity waves).  Keep in mind that this distance is in gravity terms, most of the energy is real close to the earth/black hole.

Kinetic energy = the motion of your ship moving away from the center of the earth/black hole.

In order to escape the earth/black hole, you must apply enough kinetic energy (speed, velocity, motion…) to equal or exceed the potential energy (distance from effectively infinity to you…from the gravity standpoint). Â To better understand why the energy is the same regardless of whether it is done with a quick burst or with a slow push, simply look at the potential energy…the distance you have to move. Â It then is also apparent that the closer you get to the event horizon of a blackhole, the greater the potential energy becomes as you are deeper in the gravity well.

Outside the event horizon, this potential energy is small enough that the kinetic energy required to leave is possible to acheive, whether this is done in one quick burst of acceleration (escape velocity) or by a steady slow push. Â Once within the event horizon, the total kinetic energy required becomes equivalent to an escape velocity exceeding the speed of light. Â This is an infinite amount of energy which you can’t have and so you will become trapped.

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