What caused the massive explosions in Russia?

[russ_watters]

First of all, Jimmy I never know when you are being serious. I'll be more serious now in case you really didn't understand this about ballistic trajectories: they are symmetrical. Absent atmospheric resistance, if you fire something up in the air, it hits the ground at exactly the same speed you fired it at. So if you fire an object up at just a little bit less than escape velocity, it hits the ground later at just a little bit less than escape velocity.

So that means that if a random object in space is dropped from stationary far above earth, it hits the ground at close to escape velocity. But there are no objects just sitting there stationary, held up by unseen forces. Everything is already in motion, so any object that approaches us would have to hit at about escape velocity + initial approach velocity.

Since you're talking relative velocity (the Earth is traveling around the Sun at nearly 30 km/sec), I guess you could conceivably come up with some other trajectories that just happen to finally synch up with the Earth's motion for the first time ever. It's just that the probability of those trajectories are going to be incredibly low.

For practical purposes, russ's statement is correct.

I don't think that's true. If an asteroid is on an orbit that is just barely overtaking ours, eventually our gravity takes hold and pulls it in and the speed ends up above escape velocity. It has to because we are starting with a non-zero relative velocity towards each other.

I'd like a confirmation from berke or DH or one of our other aero/astro guys though to make sure I'm not missing something...

 

[BobG]

Are we talking ever? Or are we talking now?

The gaps in the rings of Saturn are the perfect example. A moon has swept out virtually all of the objects in a similar orbit, creating a gap in the rings.

The same is true of each of the planets orbiting the Sun, even if the Sun's debris disk isn't as spectacular as Saturn's.

Virtually all of the objects that could intersect the Earth at less than escape velocity have already been captured (aside from a few exceptions, such as Cruithne's orbit).

Virtually all objects that might intersect the Earth now or in the future have probably escaped Earth's gravity in the past unless this is the very first time the object has approached the Earth. And the fact that the object has never approached the Earth in the past actually reduces the chances that the velocity of the object would be anywhere close to the Earth's velocity.

 

[AlephZero]

There is no minimum speed for a meteor colliding with the Earth (ignoring air resistance) because the meteor could have been going around the sun in the same orbit as the Earth before the collision.

Ignoring air resistance, the trajectory of the meteorite is reversible. So try to figure out a way to throw a rock into space, starting from a very slow speed on the surface.

[Ducks behind wall to avoid being hit by a failed experiment.]

 

[Jimmy Snyder]

There is no mechanism that prevents an asteroid from injecting into a solar orbit similar to but not exactly the same as the Earth's.

Are there no asteroids in the same orbit as the Earth such as the trojans in the orbit of Jupiter? This site indicates that there might be.

Another important group is called Trojans; they are in the orbit of Jupiter, on two Lagrangian points. Similar sets of asteriods appear to lie in the trojan points in almost all planetary orbits.

http://www.redorbit.com/education/reference_library/space_1/universe/2574624/asteroid/

If the Earth is included in 'almost all', then in order to prevent such Trojans from colliding with the earth, the center of the Trojan would have to be exactly the same distance from the sun as the Earth's center, and unlikely situation.

 

[russ_watters]

Are we talking ever? Or are we talking now?

The gaps in the rings of Saturn are the perfect example. A moon has swept out virtually all of the objects in a similar orbit, creating a gap in the rings.

The same is true of each of the planets orbiting the Sun, even if the Sun's debris disk isn't as spectacular as Saturn's.

Virtually all of the objects that could intersect the Earth at less than escape velocity have already been captured (aside from a few exceptions, such as Cruithne's orbit).

I'm talking ever. I think all of those examples involve collisions above their respective escape velocities. Indeed, the examples you gave would indicate to me that over time the chances of a minimum speed (escape velocity) impact go down and the average impact speed rises.

 

[russ_watters]

There is no mechanism that prevents an asteroid from injecting into a solar orbit similar to but not exactly the same as the Earth's.

It is of course possible. But that doesn't change the issue. An object that was just barely overtaking Earth (or vice versa) would still accelerate to (just barely above) escape velocity at impact.

 

[russ_watters]

By the way, the link I provided earlier to the impact calculator doesn't explain, but says this:

The minimum impact velocity on Earth is 11 km/s. Typical impact velocities are 17 km/s for asteroids and 51 km/s for comets. The maximum Earth impact velocity for objects orbiting the sun is 72 km/s. [emphasis added]

[edit] Ok, I found a paper: http://www.arm.ac.uk/~ambn/356.pdf

Page 2 shows (in graph form), impact velocities and probabilities for known near Earth objects. The top left graph is asteroids, which have the lowest impact speed due to their relatively low orbit eccentricity compared to comets. There is a sharp cutoff at the 11 km/sec minimum.

 

[aquitaine]

You have to ask yourself just how much of their income people would be prepared to spend on this. The money wouldn't just turn up by magic. 10% Asteroid tax??

Well if you scare people enough about something you'll get them to shovel as much as you could possibly need. In reality it wouldn't take *that* much, the costs of launching things into space is going down pretty significantly, and will continue to do so. In addition to that there has been some interest in surveying asteroids from private companies, particularly planetary resources which also adds our detection capability at no cost to the taxpayer.

 

[sophiecentaur]

To expand: 11 km/s is the minimum possible speed of an approaching meteor because that's escape velocity. Most objects in the solar system orbit in the same direction, but if one is on an opposite course or is a sun-diving comet, it could be as high as 72 km/sec. http://impact.ese.ic.ac.uk/ImpactEffects/

I don't understand what you are saying here. Why would there be any 'minimum speed'? There are some 'very unlikely speeds', true, and we would have already hit any object which had been in a stable orbit 'near' us, but an object could find itself approaching Earth at a very low speed if it had been affected, 'recently' by another planet. It could have been nudged into an orbit with almost the same speed, position and direction as Earth at a given time. There are many choices of elliptical orbit with a range of energies to achieve this 'first-time possible' event. Clearly, that situation has not occurred very frequently in Earth's orbital position but there will the other places in the Solar System where it could happen more often (where there a many more asteroid bodies and a nearby massive planet.

Or did I not get your drift? (All too common these days )

 

[Jimmy Snyder]

Sorry, I see it now. At any event, it will have at a minimum, the potential energy indistinguishable from an object at infinity and in addition, at least some component of velocity toward the earth.

 

[sophiecentaur]

Well if you scare people enough about something you'll get them to shovel as much as you could possibly need. In reality it wouldn't take *that* much, the costs of launching things into space is going down pretty significantly, and will continue to do so. In addition to that there has been some interest in surveying asteroids from private companies, particularly planetary resources which also adds our detection capability at no cost to the taxpayer.

Is there ever anything that will cost me nothing? Somehow, the cost will always get back to the individual (me) and, with such a massive project, how could this not affect my disposable income? If it's that important then whoever does it will be charging for it, surely. I am a big believer in considering the 'total costing' when someone says "it'll be free". I question your statement about the costs of launching - I mean the real costs.

PS People don't scare that easily. So many of them are still smoking themselves to death and the risks are clear.

 

[BobG]

It is of course possible. But that doesn't change the issue. An object that was just barely overtaking Earth (or vice versa) would still accelerate to (just barely above) escape velocity at impact.

So let's say the Earth is approaching perigee. It's speed with no orbital perturbations would be:

v=\sqrt{(\mu_h (\frac{2}{147.1x10^6 km} - \frac{1}{149.6x10^6 km})}=30.285 km/sec

heliocentric gravitational constant is 1.327x10^11 km^3/sec^2
semi-major axis of Earth's orbit is 149.6 million kilometers
perigee is 147.1 million kilometers

You have an asteroid with a semi-major axis of 145 million kilometers and its apogee is 147.2 million kilometers, meaning its speed is:
v=\sqrt{(\mu_h (\frac{2}{147.2x10^6 km} - \frac{1}{145x10^6 km})}=29.8 km/sec

The asteroid goes slightly further out from the Sun than the Earth and the Earth is overtaking it. The relative velocity between the two is 485 meters/sec (0.485 km/sec)

The asteroid's gravity adds a bit of energy to the Earth's orbit, while the Earth subtracts quite a bit of energy from the asteroid's orbit.

You're going to get into issues as to the directions of the velocity vectors, making this a tough calculation, however, it can be made easier by the calculating the specific energy due to gravitational attraction.

\epsilon=\frac{v^2}{2}-\frac{\mu_g}{d}

with the geocentric gravitational constant being 3.986x10^6 km^3/sec^2

When the specific energy is 0, the object has achieved escape velocity for that current position (11 km/sec is escape velocity at the surface of the Earth, which is actually a really bizarre place to calculate it given the problems of traveling 11 km/sec through the Earth's atmosphere).

If the Earth and the asteroid are within 3.4 million km when the asteroid is at apogee and the Earth is at perigee, then the asteroid will not achieve escape trajectory relative to the Earth. If the Earth and the asteroid are at least 3.4 million km apart, then the asteroid will achieve escape velocity relative to the Earth, but could still impact the Earth just because of the direction of its trajectory. (3.4 million sounds big, but that's actually about 1.3 degrees of the Earth's orbit.)

 

[russ_watters]

11 km/sec is escape velocity at the surface of the Earth, which is actually a really bizarre place to calculate it given the problems of traveling 11 km/sec through the Earth's atmosphere.

11.2 actually, but 10.9 at the altitude of low Earth orbit, where the atmosphere is negligible: http://en.wikipedia.org/wiki/Escape_velocity

I don't get the point of any of the rest of what you did in that post. Yes, orbital dynamics is very complicated and yes a lot of it is over my head, but none of that has any impact on the issue we are discussing. The dynamics of how they come to be approaching each other does not change the fact that the approach speed (by definition) starts at a value greater than zero.

 

[russ_watters]

I don't understand what you are saying here. Why would there be any 'minimum speed'? There are some 'very unlikely speeds', true, and we would have already hit any object which had been in a stable orbit 'near' us, but an object could find itself approaching Earth at a very low speed if it had been affected, 'recently' by another planet...

Or did I not get your drift? (All too common these days )

An object "approaching Earth at a very low" speed doesn't stay "at a very low speed". It gets accelerated by the Earth's gravity.

 

[sophiecentaur]

An object "approaching Earth at a very low" speed doesn't stay "at a very low speed". It gets accelerated by the Earth's gravity.

Right - I get what you mean. The actual impact speed will have to be at least something like escape velocity, even if you just released the object from a 'stationary position' in the Earth's frame but a few tens of Mm away.

 

[BobG]

It means that, physics wise, you can have objects impact the Earth at less than escape velocities (in fact, decayed satellites do that all the time).

The reason the probability of an asteroid impacting us at less than escape velocity is virtually nil is that all of those objects had orbits so similar to ours that they've already impacted us.

And as for a stationary object starting far away from the Earth in a two-body scenario, it would be impossible for it to achieve escape velocity before impacting the Earth unless its initial distance was literally infinite. You'd need at least a little bit of tangential velocity to push it's energy level over the edge.

 

[sophiecentaur]

It means that, physics wise, you can have objects impact the Earth at less than escape velocities (in fact, decayed satellites do that all the time).

The reason the probability of an asteroid impacting us at less than escape velocity is virtually nil is that all of those objects had orbits so similar to ours that they've already impacted us.

And as for a stationary object starting far away from the Earth in a two-body scenario, it would be impossible for it to achieve escape velocity before impacting the Earth unless its initial distance was literally infinite. You'd need at least a little bit of tangential velocity to push it's energy level over the edge.

Not necessarily, surely. Could they not find themselves in that orbit for the first time ever, due to interaction with another large body (Slingshot)? Unlikely, of course.

 

[russ_watters]

It means that, physics wise, you can have objects impact the Earth at less than escape velocities (in fact, decayed satellites do that all the time).

Decayed satellites are "dropped" from low Earth orbit. Their GPE is relatively low and the trajectories fairly flat.

What it looked to me like you calculated is that for your hypothetical object, it would start its approach at 0.485 km/sec, which would result in an impact velocity of 11.685 km/sec.

And as for a stationary object starting far away from the Earth in a two-body scenario, it would be impossible for it to achieve escape velocity before impacting the Earth unless its initial distance was literally infinite.

Understood, but our number of significant digits here is pretty small, so "infinite" is not a very large number. Throwing an escape velocity equation into Excel, I find that at 750,000 km, escape velocity is 1 km/sec so an object "dropped" from that distance would still hit the Earth at more than 10 km/sec. That's close enough for our purposes.

And you're talking about probabilities here -- did you look at the scholarly paper I linked? Probability = 0.

 

[russ_watters]

Additional sources:

ESCAPE VELOCITY - the velocity required to escape entirely from the gravitational field of an orbit; also the minimum impact velocity for anybody arriving from a very great distance.

http://www.namnmeteors.org/appendixE.html

. The minimum impact
velocity for collisions with Earth is 11.2 km/s; this is, by
definition, equal to the escape velocity for an object launched
into space from Earth’s surface

http://www.lpi.usra.edu/publications/books/CB-954/chapter2.pdf

The minimum velocity of an asteroid impact is 11 km/sec. This is speed acquired simply from the Earth's gravitation.

http://www.ips.gov.au/Educational/4/3/1

The minimum impact speed is the planet’s escape velocity...

https://www.google.com/url?sa=t&rct...=r3o7W010wa7kbFtypTigOQ&bvm=bv.42553238,d.dmQ

 

[Astronuc]

This meteor was unusual because its material was so hard — it may have been made of iron, the statement said — which allowed some small fragments, or meteorites, perhaps 5 percent of the meteor’s mass, to reach the Earth’s surface. Nothing similar has been recorded in Russian territory since 2002, the statement said.

. . . .

So there was a similar event in 2002.

http://www.nytimes.com/2013/02/16/w...agments-are-said-to-rain-down-on-siberia.html

Size estimates cover a broad range - from "10-ton meteor around 10 feet in diameter" to "it was closer to 50 feet in diameter and probably weighed around 7,000 tons". But a 50 ft diameter sphere has 125 x volume of 10 ft diameter, and so assuming 10 ton for 10 ft diameter, it could be more like 1250 ton, which is still less than 7 kt. So the estimates are assuming different densities, with one assuming something closer to iron and another more like a lighter mineral.

 

[Jimmy Snyder]

So, I've gathered from this that we never saw this coming. I wonder if this is going to add impetus to develop a planetary defense system against this sort of thing...

Yes.
The Aquitaine bill.

The dramatic meteor explosion over Russia Friday (Feb. 15) highlights the need for more attention to be paid to the threat of near-Earth asteroids, an influential American congressman says

 

[BobG]

Not necessarily, surely. Could they not find themselves in that orbit for the first time ever, due to interaction with another large body (Slingshot)? Unlikely, of course.

Yes, just as in post #52. It's just that "unlikely" is a gross understatement. You'd be more likely to be struck by lightning while carrying a winning Powerball ticket at just the precise instant this falling asteroid struck you. (Okay, that's technically a mathematical impossibility for the existence of this asteroid to be less than the chances of it striking you, but whatever.)

I kind of feel like it's splitting hairs since the result is the same regardless of the reason, but the references stating that the minimum impact velocity equals the escape velocity don't explain why that's the case.

We're not talking about asteroids/comets that are orbiting the Earth. All of those asteroids/comets are either in stable orbits around the Earth, were in orbits where perigee happened to be below the Earth's surface, or in an orbit that already decayed due to orbital perturbations. Who knows how many of those type objects once existed, but they're gone regardless of how many there may have once been.

We're only talking about asteroids/comets that are not orbiting the Earth and the relative velocity of all of those objects is at least escape velocity.

 

[russ_watters]

I kind of feel like it's splitting hairs since the result is the same regardless of the reason, but the references stating that the minimum impact velocity equals the escape velocity don't explain why that's the case.

Most of them do explain it, it's just that the explanation is short and simple: when an object approaches the earth, it is already moving toward the Earth and then the Earth provides additional acceleration. The minimum therefore has to be when "already moving toward earth" is a very small number, equivalent to releasing the object from a stationary position above earth, very far away.

I also think the difference between "very unlikely" and "impossible" is significant enough to matter. It is very unlikely that I'll win the Powerball, but people still do win.

We're not talking about asteroids/comets that are orbiting the Earth.

We're only talking about asteroids/comets that are not orbiting the Earth and the relative velocity of all of those objects is at least escape velocity.

You meant to say orbiting the sun, not earth, right? There is only one celestial body orbiting Earth and there has never been more than a couple (a few years back we captured an asteroid for a few orbits, then lost it again).

The upper-left graph in the scholarly paper I linked was for near-earth objects, which are the type of object you are hypothesizing about. They are on low-eccentricity orbits of similar distance from the sun as Earth (that's the definition of a NEO). There aren't many left, but there are enough to care. http://en.wikipedia.org/wiki/Near-Earth_object

2012DA14, which passed us yesterday, is such an object and has such an orbit (0.8-1.0AU): http://en.wikipedia.org/wiki/2012_DA14

Since it is only moving a little bit faster than Earth in its orbit (since the orbit is usually a bit closer to the sun), if it impacted (wiki says "atmospheric entry velocity"), it would only be going a little bit faster than escape velocity: 12.7 km/sec.

 

[BobG]

You meant to say orbiting the sun, not earth, right? There is only one celestial body orbiting Earth and there has never been more than a couple (a few years back we captured an asteroid for a few orbits, then lost it again).

The upper-left graph in the scholarly paper I linked was for near-earth objects, which are the type of object you are hypothesizing about. They are on low-eccentricity orbits of similar distance from the sun as Earth (that's the definition of a NEO). There aren't many left, but there are enough to care. http://en.wikipedia.org/wiki/Near-Earth_object

2012DA14, which passed us yesterday, is such an object and has such an orbit (0.8-1.0AU): http://en.wikipedia.org/wiki/2012_DA14

Since it is only moving a little bit faster than Earth in its orbit (since the orbit is usually a bit closer to the sun), if it impacted (wiki says "atmospheric entry velocity"), it would only be going a little bit faster than escape velocity: 12.7 km/sec.

No, I meant that none of the asteroids/comets we're talking about orbit the Earth, so they must be traveling faster than escape trajectory (or else their speed was radically changed very recently to make the relative velocity less than escape velocity).

And while 2012DA14 has a similar size orbit, it's also inclined 11.6 degrees relative to the Earth's orbit. While it's speed was only around 1.5 km/sec less than the Earth's speed, the angle between the two orbits gave a relative velocity of over 6 km/sec (Law of Cosines). At the distance of closest approach (34,050 km from the center of the Earth), escape velocity is 4.84 km/sec.

A different angle and you could have a drastically different result. Even so, the close approach reduced the orbital period of the asteroid from 368 days to 317 days, which is a pretty drastic change in itself.

With the angle between the orbits, it's hard to get the relative velocity below escape velocity, but it's conceivable that a different asteroid (such as Apophis with an inclination of only 3.3 degrees) could be changed enough to reduce the relative velocity below escape velocity. If 2012DA14 had only a 3.3 degree inclination, the relative velocity would have only been 2.26 km/sec, which would have been below escape velocity.

So, I concede the possibility of an impact below escape velocity is probably a lot higher than just looking at current orbits. But, given all the possible changes that could occur to the orbit as a result of a close approach, the chances the change results in a collision below escape velocity is still very small. Plus, the chance of collision between coplanar objects (lower velocity collisions) is going to be a lot higher than for objects in a significantly different orbit plane, and I think most of those are self-cleaning, if you will.

We only discovered Aphophis in 2004. It would be interesting to know the history of its orbit, since surely it couldn't have been in its current orbit for very long, astronomically speaking. It's orbit is due for another large change at the next close approach.

 

[Astronuc]

Russian Meteor Blast Bigger Than Thought, NASA Says
http://news.yahoo.com/russian-meteor-blast-bigger-thought-nasa-says-234920189.html

. . . late Friday, NASA revised its estimates on the size and power of the devastating meteor explosion. The meteor's size is now thought to be slightly larger — about 55 feet (17 m) wide — with the power of the blast estimate of about 500 kilotons, 30 kilotons higher than before, NASA officials said in a statement.

. . . Scientists at NASA's Jet Propulsion Laboratory in Pasadena, Calif., now say the meteor weighed about 10,000 tons and was traveling 40,000 mph (64,373 km/h) when it exploded.

. . .

Meteor That Hit Russia Presents Rare Opportunity For Scientists
http://news.yahoo.com/video/meteor-hit-russia-presents-rare-234000073.html

Now that's the proper perspective.

 

[aquitaine]

Is there ever anything that will cost me nothing? Somehow, the cost will always get back to the individual (me) and, with such a massive project, how could this not affect my disposable income?

The magic of privately funded enterprises. It won't affect your disposable income if you don't buy their products. Their efforts with surveying asteroids are privately funded.

If it's that important then whoever does it will be charging for it, surely. I am a big believer in considering the 'total costing' when someone says "it'll be free". I question your statement about the costs of launching - I mean the real costs.

I never said it would be free. Their survey satellites will be launched per a contract they signed with SpaceX, another privately funded venture. The money they are spending is from their investors. Launch costs with SpaceX are quite a lot lower than with other rockets.

PS People don't scare that easily. So many of them are still smoking themselves to death and the risks are clear.

Here's some proof to the contrary:

1.) Lots of people were scared that Y2K would cause the end of the world as we know it.

2.) Lots more people were terrified by the color coded terror alerts of about a decade ago. In one particular case there was a vague terror alert about an imminent terrorist attack with chemical weapons. That one caused a tremendous run on plastic sheeting and duct tape, across the country for days you couldn't buy that stuff anywhere.

3.) More than a few people bought into the whole 2012 Maya doomsday thing.

4.) There are lots of people who think climate change will cause billions of people around the world to die and cause the end of the world as we know it. A few years ago an ABC "documentary" called Earth 2100 was all about this.

So yes, people do scare easily.

 

[sophiecentaur]

The magic of privately funded enterprises. It won't affect your disposable income if you don't buy their products. Their efforts with surveying asteroids are privately funded.

I never said it would be free. Their survey satellites will be launched per a contract they signed with SpaceX, another privately funded venture. The money they are spending is from their investors. Launch costs with SpaceX are quite a lot lower than with other rockets.
Here's some proof to the contrary:

1.) Lots of people were scared that Y2K would cause the end of the world as we know it.

2.) Lots more people were terrified by the color coded terror alerts of about a decade ago. In one particular case there was a vague terror alert about an imminent terrorist attack with chemical weapons. That one caused a tremendous run on plastic sheeting and duct tape, across the country for days you couldn't buy that stuff anywhere.

3.) More than a few people bought into the whole 2012 Maya doomsday thing.

4.) There are lots of people who think climate change will cause billions of people around the world to die and cause the end of the world as we know it. A few years ago an ABC "documentary" called Earth 2100 was all about this.

So yes, people do scare easily.

Being "scared" by a brief flurry in the media is very different from pouring your hard earned cash into a tenuous form of insurance, which is what the anti-asteroid projects would be. A tremendous run on plastic sheeting and duck tape was the only example of substance that you quoted - how much did that cost the few people who bought it? What were the real figures? My point is that this would require a significant lifestyle change for the wealth nations, whatever you may say about it being 'free' because private companies are paying for it.
You forget that these so called good will projects are significantly funded through the tax breaks that the companies are allowed on the strength of them. Successful capitalists do nothing (altruistic) that doesn't make financial sense to them. Has Warren Buffett put money into it? I know he's given away a vast amount for charity so perhaps he's not a good example. Perhaps I should ask if he would have done something like that forty years ago.

The global warming thing is more in favour of my argument, I would say. It's only been a few governments that have actually encouraged action in that direction and the 'deniers' are the majority in big business, except where there's a profit to he had. There is no identifiable profit in perhaps pushing and, as yet unidentified, asteroid out of the way in twenty year's time - which is on a timescale that few company accountants work.

Don't misunderstand me. I think it would be a good idea - but no better than feeding the World and avoiding the Ice Caps melting. Perhaps I'm just old and cynical.

 

[Color_of_Cyan]

Kinetic energy is 1/2 mv^2

The velocity of objects in space tend to be very high - with the relative velocity even higher if the two objects are traveling towards each other.

With a speed of 18km/sec, the kinetic energy of a train locomotive would be equivalent to a kiloton of TNT.

Hah, thanks. Looks like that would still make it the equivalent of a small nuke then. Well, for sure it still would be devastating to the immediate impact area and probably the surrounding area (my apologies for insensitively looking over this issue). I was originally talking something more on the scale of horribly physically affecting the entire Earth / ecology in some way though (dinosaur extinction, etc.). It just seems that obvious to tell certain things like that too.

 

[mheslep]

I can see several reasons why a planetary defense system would not be feasible against meteors.

I came across the website of the American Meteor Society and noticed that the number of reports of 'fireballs' increased from zero in 2004 - 2006 to 2219 in 2012..

Here is the full result

https://dl.dropbox.com/u/22026080/meteor-rep.jpg

Now which of the following is true?:

A. it's unreliable/fake;
B. armageddon 12-21-12-hype;
C. it merely reflects the profileration of the site;
D. Earth is actually entering a dirty piece of the cosmos
E. a bit of all of the above?

My guess(es):
i) the recent availability of cheap and always on the person cameras in personal phones and the like, the theory being that a sighting with imagery to back it up is much more likely to be reported;
ii) increasing confidence in the Chicxulub meteor dinosaur extinction theory, with media coverage following the increasing scientific confidence to a point recently of near certainty;
iii) increasingly accurate account of near Earth objects made possible by ever improving observations, again with corresponding media coverage which also prompts reports.

 

[Redbelly98]

.
.
.
And while 2012DA14 has a similar size orbit, it's also inclined 11.6 degrees relative to the Earth's orbit. While it's speed was only around 1.5 km/sec less than the Earth's speed, the angle between the two orbits gave a relative velocity of over 6 km/sec (Law of Cosines). At the distance of closest approach (34,050 km from the center of the Earth), escape velocity is 4.84 km/sec.

A different angle and you could have a drastically different result. Even so, the close approach reduced the orbital period of the asteroid from 368 days to 317 days, which is a pretty drastic change in itself.

With the angle between the orbits, it's hard to get the relative velocity below escape velocity, but it's conceivable that a different asteroid (such as Apophis with an inclination of only 3.3 degrees) could be changed enough to reduce the relative velocity below escape velocity. If 2012DA14 had only a 3.3 degree inclination, the relative velocity would have only been 2.26 km/sec, which would have been below escape velocity.
.
.
.

You seem to be talking about the relative velocity when the meteor is still many Earth radii away from Earth -- that is, the relative velocity as given by its normal orbit around the sun, neglecting the effect of Earth's gravity on the meteor. I think we all agree that that speed can be well below escape velocity.

However, Earth's gravity will increase the meteor's speed as it approaches Earth. It looks like you are ignoring this.

 

[BobG]

You seem to be talking about the relative velocity when the meteor is still many Earth radii away from Earth -- that is, the relative velocity as given by its normal orbit around the sun, neglecting the effect of Earth's gravity on the meteor. I think we all agree that that speed can be well below escape velocity.

However, Earth's gravity will increase the meteor's speed as it approaches Earth. It looks like you are ignoring this.

No, I'm not.

If you know how fast the Earth's gravity will accelerate an object (which we do), then no matter how far away or how close the object starts out, I know how fast it will be going when it hits the surface of the Earth (or at least the denser part of the atmosphere). The value of escape velocity may be low (if you're far away from Earth) or it may be high (if you're close to Earth).

But you're either always above escape velocity or you're always below escape velocity.

You can't start out below escape velocity and then exceed escape velocity unless something besides the Earth accelerates you because the Earth's gravitational acceleration is already taken into account. Likewise you can't start out above escape velocity, but drop below escape velocity as the Earth's gravity slows you down.

This phenomenon is more commonly known as Conservation of Energy.

Of course, both the asteroid and the Earth are actually orbiting the Sun, which makes it a three-body problem instead of just a two-body problem. To collide at less than escape velocity, both the asteroid and the Earth have to have very similar orbits. And the 'trailing' object has to start out just a little lower than the 'leading' object, since the 'leading' object accelerates the 'trailing' object, increasing the size of its orbit, resulting in a longer orbital period and the 'trailing' object slowing down relative to the 'leading' object.

The problem with the three-body scenario is that the two objects won't stay in a very similar orbit for very long, at least on astronomical time scales. The two objects will have close approaches repeatedly until the small object is diverted into a non-similar orbit, finds a semi-stable balance with the larger object (Cruithne, for example), the small object is captured and orbits the Earth, or the small object collides with the Earth. And the chances of finding a stable balance with the Earth that will last for eons is very, very, very small. Virtually all of those objects are gone, one way or the other.

 

[D H]

But you're either always above escape velocity or you're always below escape velocity.

In the two body problem, yes. In the N-body problem, not necessarily.

There are a few ways that a meteor could hit the upper atmosphere with less than escape velocity. They all involve weak stability boundaries or ballistic capture trajectories. Suppose an object enters the vicinity of the Earth near the Sun-Earth L1 or L2 point. If the velocity is right, this object will be on a ballistic capture trajectory (it will lie inside a weak stability boundary). Some of these weak stability boundaries come fairly close to the Earth, meaning that the object can impact the Earth with less than escape velocity.

This in general doesn't work with something that enters near the Earth-Moon L2 point. The WSBs of the Earth-Moon system don't come close to the Earth -- unless the Earth-Moon L2 point is close to the Sun-Earth L1 or L2 point. Now we're in the domain of the restricted four body problem, something that makes the restricted three body problem look like child's play.

 

[Redbelly98]

BobG, I'm reading back more carefully on earlier posts, it looks like we were in agreement after all:

We're only talking about asteroids/comets that are not orbiting the Earth and the relative velocity of all of those objects is at least escape velocity.

Sorry about the misunderstanding.

 

[BobG]

In the two body problem, yes. In the N-body problem, not necessarily.

Yes, that's the point. It's physcially possible to have impacts at less than escape velocity. It's just very rare because an asteroid can't survive very long in an orbit that would result in an impact at less than escape velocity. It's going to be kicked out, collide, etc.

In fact, that refers directly to one of the IAU definitions of a planet:

(1) A "planet"1 is a celestial body that: (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighbourhood around its orbit.

(bolding mine)

The only asteroids that can collide at less than escape velocity would be asteroids that have had their orbits changed very recently (astronomically speaking), since those asteroids probably won't survive in that orbit for more than a few million years. It's a low probability to be changed into a similar orbit and it's a low probability to survive very long if it is changed into a similar orbit.

 

[Astronuc]

The Rush is on!
http://news.yahoo.com/meteorite-rush-begins-russian-scientists-fragments-111415119.html

. . . .
Scientists at the Urals Federal University were the first to announce a significant find - 53 small, stony, black objects around Lake Chebarkul, near Chelyabinsk, which tests confirmed were small meteorites.
. . . .

More video - http://news.yahoo.com/video/local-expert-russia-meteor-strike-155657134.html


Watch out for 'infrasound':

The waves can bounce off buildings and be stronger in some places than others; they can also resonate with glass, explaining why bottles and dishes might have shattered inside undamaged kitchens, as if crushed by the airy hand of the meteor itself.
. . . .

http://www.nytimes.com/2013/02/18/w...-ruined-and-spared-by-meteor-share-space.html

 

[D H]

In fact, that refers directly to one of the IAU definitions of a planet:

(1) A "planet" is a celestial body that: (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighbourhood around its orbit.

(bolding mine)

You are misinterpreting. That "has cleared the neighborhood around its orbit" clause doesn't mean that every last bit of stuff has either been swept up, ejected, or captured as a moon. It means almost everything. IIRC, a planet-like body is deemed a planet if the mass of that planet-like body is 100 times more than the mass of all the other stuff that orbits in the same orbital zone as the body in question.

There are plenty of small solar system bodies that orbit in the same orbital zone about the Sun as does the Earth. The total mass of all of those bodies doesn't come anywhere close to the mass of the Earth.

 

[Oldfart]

Almost free, relative to development of an effective early warning system that can detect incoming meteors, would be an advertising effort that simply explains that it's necessary to seek cover away from windows in the event of a brilliant flash of light.

I suspect that many of the injuries were caused by people going TO windows after the flash to see what was going on...

 

[Jimmy Snyder]

There are plenty of small solar system bodies that orbit in the same orbital zone about the Sun as does the Earth. The total mass of all of those bodies doesn't come anywhere close to the mass of the Earth.

Does this help?
2010 TK7

2010 TK7 has a diameter of about 300 meters (1,000 ft). Its path oscillates about the Sun–Earth L4 Lagrangian point (60 degrees ahead of Earth), shuttling between its closest approach to Earth and its closest approach to the L3 point (180 degrees from Earth) about every 400 years.

 

[russ_watters]

No, I meant that none of the asteroids/comets we're talking about orbit the Earth, so they must be traveling faster than escape trajectory (or else their speed was radically changed very recently to make the relative velocity less than escape velocity).

Bob, I don't know if you've changed your position or if I misunderstood earlier, but your examples of the Earth sweeping out its orbit and Saturn's rings lead me to think that you were under the impression that all near-earth asteroids would necessarily hit earth/earth's atmosphere significantly below escape velocity. Edit: note, you continue to use wording that implies you think all NEOs would impact at a speed below escape velocity:

It's just very rare because an asteroid can't survive very long in an orbit that would result in an impact at less than escape velocity. [emphasis added]

Do you really mean 'could result in an impact at less than escape velocity if properly perturbed just prior to impact'?

If all you meant was that if some event like a close encounter with the moon perturbs its trajectory just before it hits Earth (or bouncing off the atmosphere or getting hit by a nuclear bomb), an asteroid could hit the Earth a little below escape velocity, then we're all good. The paper I linked mentions the effect of the moon. Heck, the moon has its own mass and escape velocity and will often act to increase the impact velocity on earth!

 

[russ_watters]

Does this help?
2010 TK7

Very cool. Something else I learned:

Earth Usually Has More than One Moon, Study Suggests

The team concluded that at least one asteroid with a diameter of 3 feet (1 meter) or more is likely orbiting our planet at anyone time. There may be many smaller objects circling Earth, too, but the study didn't address them; it was tough enough to model the motions of the bigger space rocks.

http://www.space.com/15151-earth-multiple-moons-asteroids.html

Now we'll have to quibble over the definitions of "moon" and "asteroid" as it pertains to object size.

 

[Jimmy Snyder]

Here is a contrived, but possible situation. An asteroid hits the Moon a glancing blow and is sent from there to a point just past the Earth-Moon L1 Lagrange point with a velocity nearly zero w.r.t. the Earth. At what speed will this asteroid hit the Earth? Neglect air resistance.

 

[D H]

Now we'll have to quibble over the definitions of "moon" and "asteroid" as it pertains to object size.

And longevity. Those chaotic orbits aren't very stable. Moons are things that are more or less permanently resident. (Some of the moons of Jupiter are dubious as "moons".) Those objects drift into the vicinity of the Earth inside what's called a weak stability boundary. They come for a visit, but they don't stick around for long.

A couple of examples of such temporary moons: J002E3, which turned out to be the upper stage of the Apollo 12 spacecraft , and 2006 RH₁₂₀, which is a natural satellite.

NASA recently used weak stability boundary transfer concepts to get the GRAIL satellites to the Moon. Instead of going directly to the Moon, the satellites went out almost to the Sun-Earth L1 point and then fell back toward the Moon on a ballistic capture trajectory. The 3 to 3.5 day journey to the Moon used by the Apollo program became a two month long slow drift, but saved a whole lot of fuel. (The so-called Interplanetary Highway System would be more aptly named as The Interplanetary Conestoga Wagon Trail. It's never fast to use those weak stability boundary transfers.)

 

[aquitaine]

Being "scared" by a brief flurry in the media is very different from pouring your hard earned cash into a tenuous form of insurance, which is what the anti-asteroid projects would be. A tremendous run on plastic sheeting and duck tape was the only example of substance that you quoted - how much did that cost the few people who bought it? What were the real figures? My point is that this would require a significant lifestyle change for the wealth nations, whatever you may say about it being 'free' because private companies are paying for it.
You forget that these so called good will projects are significantly funded through the tax breaks that the companies are allowed on the strength of them. Successful capitalists do nothing (altruistic) that doesn't make financial sense to them. Has Warren Buffett put money into it? I know he's given away a vast amount for charity so perhaps he's not a good example. Perhaps I should ask if he would have done something like that forty years ago.

Ok, what tax breaks do Planetary Resources get? They do have significant private investment from such people as Larry Page, Erich Schmidt, James Cameron and some other highly successful people. Show me where there is significant government intervention specifically for them.

The global warming thing is more in favour of my argument, I would say. It's only been a few governments that have actually encouraged action in that direction and the 'deniers' are the majority in big business, except where there's a profit to he had.

And not one of those governments that is "encouraging" action actually has a realistic plan to do it. Denmark has been spending huge amounts of tax money on wind farms. And 20 years later the percentage of electricity generated from coal is still 80%, higher than China's. There's a very basic reason for this, fear of nuclear power. This actually goes towards my point because it's a long running irrational hysteria. Germany in the past ten years has spent 100 billion Euros of tax money on solar alone plus a rather substantial amount of tax money on wind farms. So when it shutdown all of it's nuclear power plants (because of that fear factor I mentioned) despite the truly stunning amounts of money spent on the green saviors they ended up with major shortfalls in electricity production, an unstable grid, and skyrocketing electricity costs. So what are they going to do about? Why go back to COAL and NATURAL GAS of course. In other words, more fossil fuels. All because of fear. You can make people afraid of almost anything for a surprisingly long period of time as long as you control the narrative in a way that preys on their ignorance.

The reason the other governments aren't so into it is because most of them are poor. They want to develop their economies and that's what their constituents also want. The difference here is the narrative and in developing countries they don't have the same levels of fear mongering about this, so that's not high on their list of priorities. Interestingly enough one of the effects of this is to render all of our CO2 control efforts, ineffectual as they often are, a complete waste of time. Even if our carbon emissions went to zero it wouldn't matter because the growth of the third world.

There is no identifiable profit in perhaps pushing and, as yet unidentified, asteroid out of the way in twenty year's time - which is on a timescale that few company accountants work.

That wasn't my point. My point was that the means are private now which has reduced the costs of launching a probably government paid for asteroid pusher thing into space pretty significantly, which does matter a lot.

 

[BobG]

Bob, I don't know if you've changed your position or if I misunderstood earlier, but your examples of the Earth sweeping out its orbit and Saturn's rings lead me to think that you were under the impression that all near-earth asteroids would necessarily hit earth/earth's atmosphere significantly below escape velocity. Edit: note, you continue to use wording that implies you think all NEOs would impact at a speed below escape velocity: Do you really mean 'could result in an impact at less than escape velocity if properly perturbed just prior to impact'?

If all you meant was that if some event like a close encounter with the moon perturbs its trajectory just before it hits Earth (or bouncing off the atmosphere or getting hit by a nuclear bomb), an asteroid could hit the Earth a little below escape velocity, then we're all good. The paper I linked mentions the effect of the moon. Heck, the moon has its own mass and escape velocity and will often act to increase the impact velocity on earth!

Perhaps you have misunderstood my position, since this started with a post where I agreed you were essentially correct, but only because the probability of an impact at less than escape velocity was so incredibly low - not because they were impossible.

Which eventually prompted your reply...

I also think the difference between "very unlikely" and "impossible" is significant enough to matter.

But it isn't impossible and the perturbation doesn't have to occur just before impact (at least not if you mean the type of duration described by being perturbed by the Moon just before impact). It's original orbit has to be altered so that it's new orbit is almost the same size as the Earth's orbit, it's orbital plane has to be very close to the Earth's orbital plane, the trailing object has to be slightly lower than the leading object's position as they approach towards the collision - and the collision practically has to happen on the first close approach of the two objects, since the orbit of the asteroid is going to be drastically changed by the close approach. (Or perhaps an asteroid starts out not meeting those criteria, but a close approach changes the orbit to meet those criteria.)

It has to be an asteroid that has moved into the Earth region recently, since the Earth tends to clean out debris too close to its own orbit. While that happens continuously (or else we wouldn't have as many near Earth asteroids as we do and also means "clearing the neighbourhood" is an unending task, as DH pointed out), the probability of altering it to meet the criteria for a low velocity collision makes "very unlikely" an understatement.

Actually, I think I did say, or at least implied, that there was a time in the past (early in the solar system) that low velocity impacts were common (even if a very low percentage). They aren't common now.

 

[OmCheeto]

I can see several reasons why a planetary defense system would not be feasible against meteors.

I came across the website of the American Meteor Society and noticed that the number of reports of 'fireballs' increased from zero in 2004 - 2006 to 2219 in 2012..

Here is the full result

https://dl.dropbox.com/u/22026080/meteor-rep.jpg

Now which of the following is true?:

A. it's unreliable/fake;
B. armageddon 12-21-12-hype;
C. it merely reflects the profileration of the site;
D. Earth is actually entering a dirty piece of the cosmos
E. a bit of all of the above?

"D" sounds plausible, based on the numbers.
With an orbital period of 240,000,000 years for the sun to go around the galactic center, we should look for clues around that time period in the past.

It looks like we transitioned from the Paleozoic to the Mesozoic eras around 250,000,000 years ago. Did anything special happen back then? I'm not much of a historian. Lot's-o-space rocks maybe? This might be fun. I've never seen a big meteorite before.

hmmm...

The Permian–Triassic (P–Tr) extinction event, informally known as the Great Dying, was an extinction event that occurred 252.28 Ma (million years) ago, forming the boundary between the Permian and Triassic geologic periods, as well as the Paleozoic and Mesozoic eras. It is the Earth's most severe known extinction event, with up to 96% of all marine species and 70% of terrestrial vertebrate species becoming extinct. It is the only known mass extinction of insects. Some 57% of all families and 83% of all genera became extinct.

Oh my. I think I'll stock up on canned beans and toilet paper.

 

[russ_watters]

But it isn't impossible and the perturbation doesn't have to occur just before impact...

I'm still unclear. It still sounds like you are saying that an object can approach from a long distance (say, 10 million km since its last major interaction), not interact with the moon on its way in, and hit Earth significantly below escape velocity and that a significant class of NEOs fit that description, regardless of if we've cleared most of them out (note: according to the paper I linked, these are still the most likely objects to hit us).

Or put another way, it sounds like you think an unperturbed trajectory (again, of at least the last 10 million km) exists that can cause a below escape velocity impact and that most or all NEOs that hit us have such such a trajectory by definition of being NEOs. It doesn't make sense to me that you used the Earth sweeping out its NEOs as an example unless you think a significant fraction of them (all of them?) Impacted at below escape velocity.

Could you please try to answer more succinctly because all of the qualifiers you are putting on this don't add clarity and seem to contradict your examples.

 

[D H]

I'm still unclear. It still sounds like you are saying that an object can approach from a long distance (say, 10 million km since its last major interaction), not interact with the moon on its way in, and hit Earth significantly below escape velocity

Yes, that is possible Russ. Significantly below escape velocity? No, but below is possible. Likely? No. It's rather unlikely. It is not, however impossible. It is impossible in the context of the two body problem (the Earth, the asteroid, and effectively nothing else). Add a big third body, i.e. the Sun, and things get weird.

and that a significant class of NEOs fit that description, regardless of if we've cleared most of them out (note: according to the paper I linked, these are still the most likely objects to hit us).

It's a small fraction of NEOs that fit this description. The vast majority that impact the Earth will do so with a velocity greater than escape velocity. Saying that all of them will isn't quite true, but it's pretty close to being true. It's close enough to being true that a lay article can legitimately say that it is true.

Regarding the paper you linked, the authors didn't write clearly, which in turn led you to misread/misinterpret what they wrote. This is, I think, the bit from that article that you are interpreting incorrectly:

Most asteroids snagged by Earth's gravity don't zoom around our planet in neat circles, according to the simulation. Instead, they follow complicated, twisting paths, tugged this way and that by the gravitational pulls of Earth, the moon and the sun.​

That "snagged by Earth's gravity" was not alluding to the asteroids that impact the Earth. It was alluding to the very, very few asteroids that, at least temporarily, orbit the Earth. Most (almost all) asteroids that impact the Earth aren't "snagged by Earth's gravity" (i.e., orbiting). They came into the vicinity of the Earth on a hyperbolic trajectory and they would have immediately have left on a hyperbolic trajectory had the Earth not have been in the way.

What that part of the article was alluding to is that it is unlikely to capture an asteroid and have it end up in a circular orbit. Very, very unlikely. For example, the "captured asteroid" explanation for the moons of Mars has come under increased scrutiny because this explanation doesn't make sense from a dynamical point of view.

 

[g.lemaitre]

If the Russian meteorite released 20 Hiroshimas of energy, then how come only two people were injured? I'm guessing they're measuring energy from the time it entered the Earth's atmosphere until it hit the ground, whereas the Hiroshima Bomb released all of its energy right at one time, the meteorite released its energy over a long period of time. Still, that doesn't sound like a good explanation to me.

 

[Borek]

If the Russian meteorite released 20 Hiroshimas of energy, then how come only two people were injured? I'm guessing they're measuring energy from the time it entered the Earth's atmosphere until it hit the ground, whereas the Hiroshima Bomb released all of its energy right at one time, the meteorite released its energy over a long period of time. Still, that doesn't sound like a good explanation to me.

Not necessarily - it is a matter of distance from the explosion.

 

[Borg]

If the Russian meteorite released 20 Hiroshimas of energy, then how come only two people were injured? I'm guessing they're measuring energy from the time it entered the Earth's atmosphere until it hit the ground, whereas the Hiroshima Bomb released all of its energy right at one time, the meteorite released its energy over a long period of time. Still, that doesn't sound like a good explanation to me.

As Borek stated, it's the distance. And there were 1200 people injured - mostly from flying glass. The main shock wave was strong enough to blow out windows all over the city but only one building's roof partially collapsed. If it was a little bigger, this event could have been a lot worse. Also, it's been reported that there were three separate shock waves. The first one, along with the initial flash got everyones attention. Then, when people went to look out the window, the second shockwave hit strong enough to blow the windows in their faces. Nature can be unforgiving sometimes.