1. I have a little question about the event horizon of a black-hole.
According to what I have heard even light cannot escape from past the event-horizon because the escape velocity is bigger than the velocity of light. And since the light-speed is the maximum achievable speed nothing can escape a black-hole.

Now consider a spaceship that is being lunched from earth. If this spaceship has its own engine it can escape without ever reaching the escape velocity required to escape from earth.

Why would this not work if the spaceship left from somewhere passed an event-horizon of a black-hole?

2.

3. Originally Posted by jan-pieterv
Now consider a spaceship that is being lunched from earth. If this spaceship has its own engine it can escape without ever reaching the escape velocity required to escape from earth.
No, it can't. This is why it is called "escape velocity". If a rocket or spacecraft does not reach at least this velocity, it will not leave the gravitational field of the earth and fall back to the surface (as soon as the fuel is depleted).

4. Instead of looking at it as an escape velocity that needs to be surpassed, since light can only travel at one speed, c, look at it in terms of 'red shift'. Light trying to escape a black hole is fighting a gravitational pull, which according to Gen Rel, is equivalent to an acceleration which implies a doppler shift towards longer wavelenths and lower frquencies. So the light is not trapped inside the event horizon endlessly circleing about, but rather its wavelength is shifted to infinity and its frequency to zero, ie. it ceases to exist, on exiting the event horizon.

5. Originally Posted by Dishmaster
Originally Posted by jan-pieterv
Now consider a spaceship that is being lunched from earth. If this spaceship has its own engine it can escape without ever reaching the escape velocity required to escape from earth.
No, it can't. This is why it is called "escape velocity". If a rocket or spacecraft does not reach at least this velocity, it will not leave the gravitational field of the earth and fall back to the surface (as soon as the fuel is depleted).
The article you linked says otherwise:
Misconception

Planetary or lunar escape velocity is sometimes misunderstood to be the speed a powered vehicle (such as a rocket) must reach to leave orbit; however, this is not the case, as the quoted number is typically the escape velocity at the body's surface, and vehicles need never achieve that speed. This barycentric escape velocity is the speed required for an object to leave the planet if the object is simply projected from the surface of the planet and then left without any more kinetic energy input: in practice the vehicle's propulsion system will continue to provide energy after it has left the surface.

In fact a vehicle can leave the Earth's gravity at any speed. At higher altitudes, the local escape velocity is lower. But at the instant the propulsion stops, the vehicle can only escape if its speed is greater than or equal to the local escape velocity at that position. As is obvious from the equation, at sufficiently high altitudes this speed approaches 0 as r becomes large.

6. Originally Posted by jan-pieterv
And since the light-speed is the maximum achievable speed nothing can escape a black-hole.
If you seek an exception to the rule, you might consider an electron. A black hole can gobble so many electrons that it repulses the next electron in line by a force equivalent to its gravitational attraction. An electron can thus simply ignore the event horizon, but of course at its own risk: An electrically neutral morsel increases the black hole's gravity and it can then grab the electron for desert.

7. Originally Posted by Twit of wit
The article you linked says otherwise:
Misconception

Planetary or lunar escape velocity is sometimes misunderstood to be the speed a powered vehicle (such as a rocket) must reach to leave orbit; however, this is not the case, as the quoted number is typically the escape velocity at the body's surface, and vehicles need never achieve that speed. This barycentric escape velocity is the speed required for an object to leave the planet if the object is simply projected from the surface of the planet and then left without any more kinetic energy input: in practice the vehicle's propulsion system will continue to provide energy after it has left the surface.

In fact a vehicle can leave the Earth's gravity at any speed. At higher altitudes, the local escape velocity is lower. But at the instant the propulsion stops, the vehicle can only escape if its speed is greater than or equal to the local escape velocity at that position. As is obvious from the equation, at sufficiently high altitudes this speed approaches 0 as r becomes large.
While this is technically true, leaving the Earth's gravity in this way uses more fuel than achieving escape velocity at a low an altitude as possible. (burning the fuel slowly means that you have to lift the mass of the remaining fuel, which in turn, requires burning more fuel.)

With a black hole, the escape velocity is c, and it would take an infinite amount of fuel to reach c. So if you burned all your fuel at once in an attempt to reach escape velocity, you would need an infinite fuel source.

Since trying to climb away slowly can't use any less fuel, you can't escape this way either.

8. If you say you would need infinite energy to leave the event horizon, why it doesn't work on things falling to it? Any tiniest particle falling to it should receive infinite energy.

Originally Posted by Janus
Since trying to climb away slowly can't use any less fuel,...
Why?

9. Originally Posted by Twit of wit
If you say you would need infinite energy to leave the event horizon, why it doesn't work on things falling to it? Any tiniest particle falling to it should receive infinite energy.
From the point of view of anyone watching the particle fall towards the black hole, it never reaches the event horizon.

Originally Posted by Janus
Since trying to climb away slowly can't use any less fuel,...
Why?
I already explained why. The more slowly you climb, the more fuel is needed just to lift the fuel that you'll need later. Carrying it to the extreme would be hovering at a constant altitude. You'd burn up all your fuel going nowhere. So at one extreme you have burning all your fuel in an instant to attain escape velocity, which is the most efficient, to just hovering, which is the least efficient. Any other climbing speed will fall in between.

10. Originally Posted by Janus
I already explained why. The more slowly you climb, the more fuel is needed just to lift the fuel that you'll need later. Carrying it to the extreme would be hovering at a constant altitude. You'd burn up all your fuel going nowhere. So at one extreme you have burning all your fuel in an instant to attain escape velocity, which is the most efficient, to just hovering, which is the least efficient. Any other climbing speed will fall in between.
Even with relativity effects? While accelerating to c needs an infinite amount of fuel, producing certain constant acceleration seems to need a finite amount of fuel.

Originally Posted by Janus
The more slowly you climb, the more fuel is needed just to lift the fuel that you'll need later.
Why just the fuel and not the whole thing?

11. Originally Posted by Twit of wit
Originally Posted by Janus
I already explained why. The more slowly you climb, the more fuel is needed just to lift the fuel that you'll need later. Carrying it to the extreme would be hovering at a constant altitude. You'd burn up all your fuel going nowhere. So at one extreme you have burning all your fuel in an instant to attain escape velocity, which is the most efficient, to just hovering, which is the least efficient. Any other climbing speed will fall in between.
Even with relativity effects? While accelerating to c needs an infinite amount of fuel, producing certain constant acceleration seems to need a finite amount of fuel.
You will always need fuel to keep a constant level of acceleration. If the fuel depletes on a spaceship the spaceship will remain at a constant velocity and will stop accelerating because there is no longer a constant force behind the spaceship pushing it forwards through space.

The fuel needed to get to c would be infinite because the closer towards c you get, the more your mass increases as given by m =m0y (I don't know TeX for this forum so I'll just spell it out):

m = relative mass of object
m0 = rest mass of object
y = the lorentz factor

The mass will increase closer to c and as a result will require more fuel, which will have more mass which will need more fuel.

Originally Posted by Twit of wit
Originally Posted by Janus
The more slowly you climb, the more fuel is needed just to lift the fuel that you'll need later.
Why just the fuel and not the whole thing?
The fuel that is needed extra to lift the object needs fuel to lift. For instance an extra 30 litres of fuel will need a certain amount of fuel to lift that fuel. So you'll need about 5 litres to lift 30 litres (random number there, you get the point).

The slower it lifts, the more fuel is needed.

I'm sure there is an equation that can be found here.

F = Fuel
t = time
m = mass of object
a = acceleration of object
r = resistance (air friction etc)

Hmm, that sounds a lot like some of newtons equations, go and have a look at them I don't know them off hand but you will see what we mean.

Oh, and add a variable equation to the extra fuel similar to how acceleration is worked out.

12. There's a TeX tutorial stickied in the Math section.

13. Originally Posted by Quantime
You will always need fuel to keep a constant level of acceleration. If the fuel depletes on a spaceship the spaceship will remain at a constant velocity and will stop accelerating because there is no longer a constant force behind the spaceship pushing it forwards through space.
?? Of yourse, but not an infinite amount!

Originally Posted by Quantime
The fuel needed to get to c would be infinite
Just as I said.

Originally Posted by Quantime

The fuel that is needed extra to lift the object needs fuel to lift. For instance an extra 30 litres of fuel will need a certain amount of fuel to lift that fuel. So you'll need about 5 litres to lift 30 litres (random number there, you get the point).
Of course. I'm not sure what are you trying to say here. But it doesn't depend on how quickly you burn it.

Originally Posted by Quantime
The slower it lifts, the more fuel is needed.
Yes, but because of the weight of the whole object, not just the fuel.

I was asking if it works even with relativistic effects. Accelerating to c needs infinite energy, but keeping a constant level of acceleration for some time does not need infinite energy.

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