## Breaking Earth's gravity well

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zmatt
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### Breaking Earth's gravity well

I was hoping for some clarification on this. Since Earth's gravity is 9.8m/s^2 give or take. Wouldn't one only need to overcome that to escape earth's gravity? Say 10m/s? Something like that is enough to get off the ground, so I don't understand why one has to be traveling so fast to get into space. Wouldn't 10m/s have the same effect on the edge of Earth's gravity well as it does at sea level? granted the rise in altitude would be slow, but why does one need to be going 11.2km/s?
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thoughtfully
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### Re: Breaking Earth's gravity well

"Earth's Gravity" is not 9.8 m/s2. That is the acceleration (which is proportional to force) felt near the surface. You get sufficiently far from the surface and it won't hold. Hint: F=GMm/r2.

It doesn't have all that much to do with escape velocity (which doesn't care where the surface is). The units don't even match.

Try Wikipedia for a more complete explanation.

Also, 10 m/s isn't very fast. It's a bit over 20 mph. I'm pretty sure elevators in high rise buildings and mines routinely exceed this.
Last edited by thoughtfully on Mon Mar 14, 2011 5:57 pm UTC, edited 1 time in total.

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zmatt
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### Re: Breaking Earth's gravity well

Just read the misconceptions bit, seems that actually traveling at a constant 10m/s would work as escape velocity refers to how fast I have to going at the surface give no more propulsion. Seems you only have to go stupid fast if you only have a second of fuel.
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Moose Hole
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### Re: Breaking Earth's gravity well

In order to maintain a constant 10m/s, you have to accelerate at a constant 9.8m/s^2 (give or take depending on height), which means you use more and more fuel.

zmatt
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### Re: Breaking Earth's gravity well

Yeah that bit I understand. The problem I had is that I thought that if you weren't going at 11.2km/s with constant thrust you would not break the gravity well. ie anything that isn't capable of a speed of 11.2km/s. Obviously I was wrong. Public edjumacation does a poor job of explaining this. It essentially amounts to "escape velocity is 11.2km/s." with no further explanation. Similar to that xkcd comic involving wings, if you ask how anything slower can lift off the ground, which you see all the time, you get a "we are moving on" response.
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### Re: Breaking Earth's gravity well

Moose Hole wrote:In order to maintain a constant 10m/s, you have to accelerate at a constant 9.8m/s^2 (give or take depending on height), which means you use more and more fuel.

Less, surely? Your mass is decreasing, since you're burning fuel, and so you need to burn fuel slower to maintain the acceleration.
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Moose Hole
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### Re: Breaking Earth's gravity well

Robert'); DROP TABLE *; wrote:
Moose Hole wrote:In order to maintain a constant 10m/s, you have to accelerate at a constant 9.8m/s^2 (give or take depending on height), which means you use more and more fuel.

Less, surely? Your mass is decreasing, since you're burning fuel, and so you need to burn fuel slower to maintain the acceleration.
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### Re: Breaking Earth's gravity well

To maintain 10 m/s, you should not be accelerating at all... Your thrusters might be applying enough force to maintain an acceleration of 9.8 m/s^2 (were it not for gravity) initially, but you could leave the earth's orbit at any velocity, be it 1 m/s or 10000 m/s. You just need to be able to provide enough thrust for the whole time, which would be quite a long time were you only going 1 m/s.
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douglasm
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### Re: Breaking Earth's gravity well

Sounds like you've at least mostly figured this out already, but the definition of escape velocity is the speed required to get into space and keep going with no additional propulsion on the way. Imagine some super-powered pitcher throwing a baseball straight up. Escape velocity is how fast the baseball would have to be going at the moment it leaves the pitcher's hand in order for the baseball to escape Earth's gravity and never come back down. Actually, the 11.2 km/s figure is probably the speed the baseball would need if the Earth's atmosphere spontaneously vanished first; the real number would be a bit higher because the air in the way would slow the ball down somewhat, and exactly how much of a difference that makes depends on the mass, size, and shape of the object.

If you have engines providing continuous thrust all the way, escape velocity is irrelevant - it's quite possible to get into outer space by moving a mere 1 meter per century, it'll just take a long time.

Tass
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### Re: Breaking Earth's gravity well

But the thing is that there is nothing to hold onto as you get up from the surface.

At the moment we therefore has to use rockets. And for rockets the hard currency is delta-v, and it needs to be least 11m/s to escape earth, regardless if the rocket never actually travels that fast.

The construction of the space elevator would change that. Then you could slowly climb to space at your 10m/s (or any other speed).

zmatt
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### Re: Breaking Earth's gravity well

Cool your posts have verified what I thought. Thanks for the clarification. otherwise a lot of things seemed pretty silly.
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Myria
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### Re: Breaking Earth's gravity well

The Schwarzschild radius of a black hole is the distance from the center within which the escape velocity is >= c. Why can't you escape from a black hole with continuous acceleration?

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### Re: Breaking Earth's gravity well

Outside of the Schwarzchild radius you can, provided you have enough thrust to overcome the pull of the black hole. (I...I think? It's been a few years since cosmology.)

Tass
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### Re: Breaking Earth's gravity well

Myria wrote:The Schwarzschild radius of a black hole is the distance from the center within which the escape velocity is >= c. Why can't you escape from a black hole with continuous acceleration?

Yes that confused me for years too. The simple answer is that classical physics are no longer relevant when you approach a black hole, you have to use general relativity instead. Time and space gets bend in a way that makes it impossible. You could regard it as just a coincidence that the Schwarzschild radius happens to be where you would classically expect the escape velocity to be c.

You could also argue that even though you can escape bodies without ever moving at escape velocity, you cannot get around the energy requirements. If escape velocity is c then the energy required is infinite. Since the escape velocity in finite right above it would take an infinite amount of energy even to move up ever so slightly at the event horizon.
Last edited by Tass on Fri Mar 18, 2011 2:19 pm UTC, edited 1 time in total.

zmatt
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### Re: Breaking Earth's gravity well

So don't park your star cruiser next to a black hole. got it!
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Technical Ben
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### Re: Breaking Earth's gravity well

zmatt wrote:So don't park your star cruiser next to a black hole. got it!

As you could be very far out, but not have the fuel supply to escape! Hows waiting 1000 years to even reach the event horizon...
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Turtlewing
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### Re: Breaking Earth's gravity well

Myria wrote:The Schwarzschild radius of a black hole is the distance from the center within which the escape velocity is >= c. Why can't you escape from a black hole with continuous acceleration?

Under Classical Mechanics black holes can't exist, basically for this reason. Also the speed of light in a vacume "c" isn't a universal constant.

Under General Relativity which is the theory that predicted the existence of black holes, c is a universal constant and the fastest anything can travel without breaking causality. Among the consequences of that is the strangeness that happens near a black hole. Most of which is over my head but from what I understand past the event horizon it no longer makes sense to discuss directions that aren't "towards the center of the black hole" so you can't escape by accelerating away from a black hole in much the same way as you can't escape by "accelerating towards purple"

zmatt
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### Re: Breaking Earth's gravity well

One thing I can't understand, black holes apparently give off radiation, which like like is electromagnetic (assuming gamma rays and such). How can that be emitted and not dragged back in? If it emits anything then it most not be impossible to escape.
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### Re: Breaking Earth's gravity well

It is emitted from the event horizon. (effectively) If it was emitted from the singularity, you wouldn't see it.
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zmatt
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### Re: Breaking Earth's gravity well

ok cool, where does it come from/how is it emitted? I mean obviously the event horizon isn't solid uranium. Or have we not figured that part out yet?
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gmalivuk
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### Re: Breaking Earth's gravity well

Turtlewing wrote:Also the speed of light in a vacume "c" isn't a universal constant.
Oh?

zmatt wrote:ok cool, where does it come from/how is it emitted? I mean obviously the event horizon isn't solid uranium. Or have we not figured that part out yet?

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### Re: Breaking Earth's gravity well

Turtlewing wrote:Under Classical Mechanics black holes can't exist, basically for this reason.

There's nothing in Classical Mechanics that prevents a body from having an escape velocity greater than the speed of light. Indeed, Laplace speculated on the possibility over a hundred years before General Relativity. What you get with GR is the sobering fact that nothing at all can escape.

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Soralin
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### Re: Breaking Earth's gravity well

gmalivuk wrote:
zmatt wrote:ok cool, where does it come from/how is it emitted? I mean obviously the event horizon isn't solid uranium. Or have we not figured that part out yet?

Hawking radiation doesn't cover what I think he's talking about, since for any star sized black hole or bigger, it would be extraordinarily small. This would be more applicable:

http://en.wikipedia.org/wiki/Accretion_disc
An accretion disc is a structure (often a circumstellar disk) formed by diffuse material in orbital motion around a central body. The central body is typically a star. Gravity causes material in the disc to spiral inward towards the central body. Gravitational forces compress the material causing the emission of electromagnetic radiation. The frequency range of that radiation depends on the central object. Accretion discs of young stars and protostars radiate in the infrared; those around neutron stars and black holes in the x-ray part of the spectrum.
The most spectacular accretion discs found in nature are those of active galactic nuclei and of quasars, which are believed to be massive black holes at the center of galaxies. As matter spirals into a black hole, the intense gravitational gradient gives rise to intense frictional heating; the accretion disc of a black hole is hot enough to emit X-rays just outside of the event horizon. The large luminosity of quasars is believed to be a result of gas being accreted by supermassive black holes. This process can convert about 10 percent of the mass of an object into energy as compared to around 0.5 percent for nuclear fusion processes.

Tass
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### Re: Breaking Earth's gravity well

gmalivuk wrote:
Turtlewing wrote:Also the speed of light in a vacume "c" isn't a universal constant.
Oh?

He meant in classical mechanics it is not.

andyisagod
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### Re: Breaking Earth's gravity well

zmatt wrote:One thing I can't understand, black holes apparently give off radiation, which like like is electromagnetic (assuming gamma rays and such). How can that be emitted and not dragged back in? If it emits anything then it most not be impossible to escape.

Even arbitrarily close to the horizon massless particles emitted in a particular direction will escape to infinity. As you get closer to the horizon the more directions will end up crossing the horizon. The physics of which particles escape and which end up getting sucked in gets even more interesting for rotating black holes. I recently finished a paper http://arxiv.org/abs/1101.4819 that has some graphs of the fraction of particles that can escape a black hole as a function of distance from the horizon.

zmatt
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### Re: Breaking Earth's gravity well

Thanks but understanding how that works is way over my head. I get that the closer you get the more directions end up with you falling in, but I'll have to take your word on the rest.
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Turtlewing
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### Re: Breaking Earth's gravity well

Tass wrote:
gmalivuk wrote:
Turtlewing wrote:Also the speed of light in a vacume "c" isn't a universal constant.
Oh?

He meant in classical mechanics it is not.

Yeah, though that's not as true as I made it sound either. If I recall classical mechanics did have a fixed speed of light (or at least was not incompatible with the idea), but it also had a preferred reference frame in which the speed of light was constant (the aether), and objects moving relative to that reference frame would observe differences in the speed of light based on the relative motion between the light and themselves. It should also be possible to accelerate to speeds higher than the speed of light.

The point however is that in Classical Mechanics you can't have a "black hole" because there's no reason you couldn't accelerate beyond the speed of light. Or simply apply a force equal and opposite the gravitational attraction to cancel out the "pull". However in General Relativity that's not the case. A perfect storm of time dilation, length contraction, and c being the same in all reference frames results in there being cases where not even a theoretical possibility of escape exists. Those cases are black holes.

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### Re: Breaking Earth's gravity well

zmatt wrote:ok cool, where does it come from/how is it emitted? I mean obviously the event horizon isn't solid uranium. Or have we not figured that part out yet?

Apparently, from fluctuations of void. I don't understand much, but what I've heard is that there are pairs of virtual particles/antiparticles that are created and destroyed constantly. If one pair is created near the horizon, one can be trapped, and the other freed. The captured particle does not add to the mass of the BH, because the mass of the two particles was kinda 'borrowed'.
It's probably very oversimplified, and maybe even plain wrong.
Can someone who really knows confirm or infirm?
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### Re: Breaking Earth's gravity well

Hawking Radiation has been chewed over and recontemplated more than a ruminant’s cud around here. Here, have a thread.

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