I know the answer to this, but I'm asking it here because it might be of interest to people (and, perhaps, as a kind of challenge in the vein of the "math challenges" thread).
When meteors fall onto the Earth, they might explode in mid-air while falling, releasing staggering amounts of energy. There have been famous examples recently, with such explosions having been estimated in the hundreds of kilotons range, and historic such events, such as the Tunguska event, estimated in the megatons range. (That's right, a falling meteor may explode in mid-air, with the same force as a thermonuclear blast.)
But what exactly are the mechanics behind this? How can a falling rock not only suddenly explode mid-air, without colliding with anything (well, anything other than air), but do it so violently that it's equivalent to a megaton-range thermonuclear blast? How can a rock explode? What exactly is happening? What makes it explode so violently, mid-air? What are the underlying mechanics behind it?
Meteors are rarely perfectly round and smooth. Given how fast a meteor is travelling say 8 miles/per second and how dense our atmosphere is. Especially when compared to the vacuum of space. It's not beyond reasoning that the air can pass through passages in a meteor and generate tremendous air pressure. Thus blow pieces off.
That may explain why they break apart in the atmosphere, but doesn't in itself explain how a meteor can suddenly explode in a megaton-range blast, as if it were a thermonuclear bomb.
There isn't a great deal of information on it sadly, but I still stand by it likely has something to do with the air pressure. After all, pressure = volume/area, and the faster you travel the greater the volume of air you'll be colliding with. An explosion is essentially highly compressed air particles that travel faster than the speed of sound.
You are not incorrect, but your explanation is a bit incomplete. In summary, the explanation is this:
An object traveling at enormous speeds through the atmosphere compresses the air in front of it, which makes it heat up (and it can heat up a lot in this manner). This is what happens to re-entering space capsules and meteors. The amount of air being compressed depends on the surface area of the object.
If the meteor breaks into pieces, its total surface area will increase, while its mass, and therefore momentum, remains the same. So in other words, it will now be pushing against more air than before, causing even more heat and thus more energy release.
This may cause these pieces to break up even more, increasing the total surface area and so on, which ends up in an accelerating runaway chain reaction where the entire meteor is pulverized into smithereens in a small fraction of a second.
In other words, all the kinetic energy of the falling meteor (which even for a relatively small meteor is absolutely enormous) gets converted into heat in a small fraction of a second, which effectively causes an airburst that depending on the mass and velocity of the meteor may reach even the megaton range.
It could also be due to the presence of ice in the meteor.
If heated extremely fast, ice will quickly sublimate into steam, and the resulting steam explosion is strong enough to destroy it.
An example of this was the explosion from the accident at Chernobyl, reactor fuel cannot explode like a nuclear weapon does, because its uranium is not enriched enough. However, it can quickly boil the water coolant off and cause a steam explosion. In Chernobyl's case, it was strong enough to destroy the containment building and release radioactive materials in the air.
I have hard time believing that you'll get a megaton-range explosion by sublimating ice.
It's the kinetic energy of the meteor (which is absolutely ginormous due to the speed it's traveling) that gets converted into heat due to colliding with air. It's why they are so bright in the first place. If they break up, it may cause a chain reaction where the fragments themselves will break up even more, and so on. When it breaks up, the total momentum remains the same, but the surface area (and thus the amount of air it compresses in front of it) increases.
I think you're misunderstanding his point Warp.
The explosion is caused by rapid heating of the air in your scenario.
In p4wn3r's scenario it's that and the sublimation of ice, both contribute to the effect.
Considering that at boiling temperature the expansion of ice into steam is roughly a factor of 1000, it's entirely plausible that it has a noticeable effect.
Remember that in your scenario the "airburst" is simply due to non-chemical heating and expansion of the air after being compressed by the meteor. This might result in a factor of at most 100x? (Though over a potentially larger volume of air to begin with.)
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Sorry for taking too long to answer, I could not check the forum for a while.
Warp wrote:
I have hard time believing that you'll get a megaton-range explosion by sublimating ice.
It's the kinetic energy of the meteor (which is absolutely ginormous due to the speed it's traveling) that gets converted into heat due to colliding with air.
I don't think we can rule out one scenario or the other just analyzing the kinetic energy. Sure, since the meteor slows down, its energy has to go somewhere. To understand where it goes, we have to model it somehow. If you think it's improbable that a good chunk of the kinetic energy can be transferred to steam, please share with us why. I am not a specialist in this topic and am just guessing, it would be great to hear.
OmnipotentEntity wrote:
I think you're misunderstanding his point Warp.
The explosion is caused by rapid heating of the air in your scenario.
In p4wn3r's scenario it's that and the sublimation of ice, both contribute to the effect.
My point is that, for a complicated system like a meteor, I find it unlikely that you can point out the explosion mechanism to a single cause, and it's worth to throw around ideas to brainstorm it.
Most problems in science today are not those that you can solve with absolute principles like "you cannot travel faster than the speed of light", or "the gravitational force falls with the inverse of the squared radius".
The systems of interest today are pretty complicated and you have to model them to understand the mechanism. It's not very difficult to come up with a model that favors your favorite explanation, if you are willing to do it. Popular science expositions usually give the impression that a phenomenon is very deterministic and has a unique cause, but usually things are more blurry.
No asteroid is the same as another one, so it's perfectly possible that the explosion in one is very different from the explosion from another one. In fact, if it's really true that every asteroid that crashes into the atmosphere explodes in the same way, then that should tell us a lot about the internal structure of asteroid, which would be a conclusion far more remarkable than the explosion mechanism itself!
If you think it's improbable that a good chunk of the kinetic energy can be transferred to steam, please share with us why. I am not a specialist in this topic and am just guessing, it would be great to hear.
I'm a complete layman myself.
I would guess that ice inside the meteor could explain one of the reasons why it suddenly breaks up into pieces in mid-air (although in many cases it's probably not the only reason). After all, the examples we know of have exploded at relatively low altitudes, meaning that they have already traveled a quite large distance in the Earth's atmosphere without breaking, and then suddenly it just explodes.
If the explosion were caused merely by ice sublimation, why would it take that long before it suddenly decides to sublimate? It has traveled through the atmosphere for a quite long distance and time, and at much higher speeds as that (as it's continually slowing down).
More likely, at some point during its descent so much physical stress builds up in the asteroid (due to heat changes, perhaps also due to ice inside it, if it has any) that it just breaks up into two or more pieces, and due to the sudden increase in surface area caused by this, it may cause an accelerating chain reaction of these pieces themselves breaking up into even smaller pieces and so on. The total surface area grows without limit, and thus proportionally more air gets compressed in front of it, causing even more kinetic energy to be converted to heat.
How much antimatter would you need to destroy the Earth?
What are we defining as destroy the Earth? Make it unlivable? Make it unable to pull itself back together under the force of its own gravity? No trace of matter whatsoever?
I'll assume the second, release enough energy such that the gravitational binding energy is overcome. This amount of energy is 2.487 x 10^32 J, which corresponds to 2.767 x 10^15 kg of antimatter.
The earth has a mass of 5.972 x 10^24 kg, so if only roughly 1 particle in 2 billion in Earth is replaced by an antiparticle the resulting explosion would be enough to overcome the gravitational binding energy and destroy the planet forever.
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In a conversation about physics and general relativity I said that in GR, essentially, an accelerometer is enough to tell if you are accelerating or not. If the accelerometer says zero acceleration, then you are not accelerating, no matter what. If it says non-zero acceleration, then you are accelerating, no matter what. (And this does not depend on anything else, and isn't relative to anything else.)
So, for example, a free-falling accelerometer will show zero acceleration, so it's not accelerating according to GR. An accelerometer resting on the ground will show a non-zero acceleration, so it is accelerating, according to GR.
Is this actually correct, or did I speak out of my posterior?
It is not. You seem have a fundamental misunderstanding about the relationship between gravity and acceleration as it pertains to general relativity.
The actual idea is that gravity and acceleration are indistinguishable within the context of general relativity (in general), Einstein called this idea the "principal of equivalence."
(In actual reality, the force you feel due to acceleration is parallel to the direction of acceleration, whereas the force due to a massive body is radial to the body, so you will experience tidal forces which can be detected (if the body is under you, then your feet experience slightly lower acceleration than your head, so you are stretched by this imbalance of forces, and the force on your left arm is down and to the right, whereas the force on your right arm is down and to the left, squeezing you slightly left to right.) However, if you were to construct an infinitely large flat massive surface then gravity and acceleration would be indistinguishable, even in principal.)
If the accelerometer says zero acceleration then you are in free fall and accelerating towards the nearest massive body at whatever amount the force divided by your mass says you should, because it is exerting a force on you that isn't being checked in any way.
That being said, in your example, the accelerometer is actually accelerating as it rotates with the surface of the Earth, but it is not accelerating in the motion that it will read, which is in the direction due to the force of gravity.
Accelerometer is a bit of a misnomer, because what is actually being measured is the force experienced by the thin silicon capacitive MEMS
This force can be from gravity, or it can be from the base of the chip acting upon the MEMS to accelerate it when their relative velocities are different.
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But I thought that according to GR there is no gravitational "force". An object in free-fall is in inertial (ie. non-accelerating) motion which looks non-linear because of the curvature of space-time. Conversely, an object resting on the ground is in constant acceleration, ie. non-inertial motion, in relation to this curved space-time, which is why it experiences acceleration (which can be measured).
Here's an example to see how acceleration due to gravity is different than acceleration due to everything else, if the Einstein equivalence principle holds.
If you have a point charge moving, and suddenly impart it with some acceleration, it will start radiating, in a phenomenon we call bremmstrahlung. This is measured everyday in particle accelerators. Now, if you are in a frame together with the electron, can you measure that it's accelerating? Well, yes. If you see radiation coming from it, the electron must be accelerating due to something , if there's no radiation, no acceleration.
Consider now doing the same thing with gravity. Should an electron orbiting a gravity well should also radiate? Well, according to Newton it should, because there isn't much difference between the electric and gravitational force.
However, if you assume the Einstein equivalence principle, you must conclude that it does not radiate. Because if it did, you would be able to measure gravitational acceleration. So, the gravitational force in GR must have a very special form so that electric charges subject to it do not radiate.
(Incidentally, that's because astronomical bodies do a much better job than artificial accelerators and fusion reactors. In human made accelerators, we use the electric force to accelerate particles, this process is inefficient because of the energy lost due to radiation, while black hole accretion disks can subject charged particles to huge velocities without causing them to radiate. Same thing with fusion reactors, because we use magnetic fields to confine the hot plasma, there's energy loss due to radiation. The sun uses gravity to confine the plasma, which is much more efficient).
So, as you can see, accelerating something with gravity is different from accelerating it with something else. When you read that, for someone standing on Earth, an accelerometer shows non-zero acceleration, you can think of it in two ways:
(1) Gravity is exerting a force and the Earth is also exerting a force on the other direction. That applies some stress in your body, and the accelerometer measures this stress.
(2) Gravity is not a force at all, and the only measurable acceleration you have is the one coming from the Earth. Since you are accelerating, the electrical properties in your body should change, and it's that change the accelerometer measures.
It turns out both of these explanations are correct, because in GR what's called "force" and what's called "inertia" is essentially a matter of convention. Explanation (2) is in a language more in line with the philosophy of GRm but (1) is correct, too.
(In actual reality, the force you feel due to acceleration is parallel to the direction of acceleration, whereas the force due to a massive body is radial to the body, so you will experience tidal forces which can be detected (if the body is under you, then your feet experience slightly lower acceleration than your head, so you are stretched by this imbalance of forces, and the force on your left arm is down and to the right, whereas the force on your right arm is down and to the left, squeezing you slightly left to right.) However, if you were to construct an infinitely large flat massive surface then gravity and acceleration would be indistinguishable, even in principal.)
If I'm not mistaken, Lorentz contraction means there's an acceleration gradient along the length of an accelerating object. (See this blurb on Rindler Observers.) That is, both gravitational and non-gravitational acceleration result in tidal forces, making them indistinguishable in this regard.
I must admit that rather than clarifying, this discussion only made me more confused about whether my original assertion is "correct" or not.
It was correct as far as General Relativity is concerned. Free-falling objects are not accelerating, they are following a geodesic in a curved spacetime. On the other hand, anything coupling with a Standard Model gauge field is accelerating. (That is, anything being acted upon by electromagnetism, the weak interaction, or the strong interaction.)
(In actual reality, the force you feel due to acceleration is parallel to the direction of acceleration, whereas the force due to a massive body is radial to the body, so you will experience tidal forces which can be detected (if the body is under you, then your feet experience slightly lower acceleration than your head, so you are stretched by this imbalance of forces, and the force on your left arm is down and to the right, whereas the force on your right arm is down and to the left, squeezing you slightly left to right.) However, if you were to construct an infinitely large flat massive surface then gravity and acceleration would be indistinguishable, even in principal.)
If I'm not mistaken, Lorentz contraction means there's an acceleration gradient along the length of an accelerating object. (See this blurb on Rindler Observers.) That is, both gravitational and non-gravitational acceleration result in tidal forces, making them indistinguishable in this regard.
It seems like that would work in reverse though. The Lorentz contraction squeezes you, while the tidal forces in GR stretch you.
Warp wrote:
I must admit that rather than clarifying, this discussion only made me more confused about whether my original assertion is "correct" or not.
According to pwn3r, It seems to depend on convention used. But at the end of the day, the accelerometer is measuring an EM restorative force, because it cannot in principal measure a gravitational one.
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Without doing any research, my off-the-cuff response would be somewhere between, "Water is naturally blue," and "The oceans are reflecting the sky." Even if you can't really "see" the atmosphere from space, you can still see blue on the planet's surface, and the blue would be reflected outward.
A hundred years from now, they will gaze upon my work and marvel at my skills but never know my name. And that will be good enough for me.
Without doing any research, my off-the-cuff response would be somewhere between, "Water is naturally blue," and "The oceans are reflecting the sky." Even if you can't really "see" the atmosphere from space, you can still see blue on the planet's surface, and the blue would be reflected outward.
Water is pretty much colorless, although I think that when light passes through enough water, it gets filtered so that it becomes slightly bluish. However, I'm not sure that can be an explanation, especially since the surface of water is very reflective (the amount of reflection depending on the angle of incidence) and, I think, the vast of the color you see is reflection. I could be wrong, of course.
If the deep blue color is caused by water reflecting the atmosphere, I don't really understand why the atmosphere would look deep blue when looked from below but not from above. If the atmosphere looked deep blue when looked at from orbit, surely eg. clouds would be heavily blue-tinted, yet they are quite white in all such photos.
Joined: 10/27/2004
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Because the atmosphere doesn't absorb that much light. The only reason the sky appears blue when viewed from the surface is because its set against the lightless background of space. You can still see bright objects through it though. Look at the daytime moon. The only parts that have a blue tint to them are the less well lit portions.
So the sky is blue when viewed from the surface because of the darkness of space. When viewed from space, all you can see is the brightly lit earth shining though the atmosphere. But the water is blue because it's reflecting the blue sky.
I'm thinking something similar to seeing a reflection of a teleprompter. If I'm in the audience, I can't see what's on the teleprompter unless you place a mirror in front of it.
A hundred years from now, they will gaze upon my work and marvel at my skills but never know my name. And that will be good enough for me.
