What caused the massive explosions in Russia?

[Andre]

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?

 

[Evo]

I read this over a week ago.

At the current rate that near-Earth asteroids are being detected, it will take astronomers 15 years to identify every one of significant size

Scientists have estimated that 20,000 asteroids lurk in the solar system, of which only 6,000 have been identified, Beeson said.

Beeson and her colleagues looked at the historical rate of asteroid discovery and found that, at the current pace, it will take about 15 years to identify all the asteroids in the solar system that are wider than 100 meters (328 feet).

Most of the missing asteroids are traveling by during the daytime or traveling through a patch of the sky not watched by existing surveys, she found.

To speed discovery, the team should expand the patch of sky observed by two programs, the Mount Lemmon and Catalina sky surveys, she said. To find asteroids that are crossing by Earth only during the day, scientists should prioritize the B612 Sentinel mission, which aims to send a telescope into a Venus-like orbit around the sun, Beeson added.

http://news.yahoo.com/search-near-earth-asteroids-needs-speed-boost-114855823.html?_sr=1

 

[sophiecentaur]

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...

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??

 

[phion]

Hundreds reportedly injured!
http://www.cnn.com/2013/02/15/world/europe/russia-meteor-shower/index.html?hpt=hp_t1

Those number have risen to more than 1200.

 

[Color_of_Cyan]

This is crazy... same day the asteroid passes by too. However I fail to understand how any sort of rock barely half the size of a football field could possibly do any major, apocalyptic-scale harm to earth. What if it just landed in the ocean or something?

 

[BobG]

This is crazy... same day the asteroid passes by too.


However I fail to understand how any sort of rock barely half the size of a football field could possibly do any major, apocalyptic-scale harm to earth. What if it just landed in the ocean or something?

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.

 

[russ_watters]

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/

 

[Jimmy Snyder]

To expand: 11 km/s is the minimum possible speed of an approaching meteor because that's escape velocity.

Wouldn't that make it the minimum speed of an escaping meteor?

 

[russ_watters]

Wouldn't that make it the minimum speed of an escaping meteor?

Or of a meter that almost escaped, then fell back down.

 

[Jimmy Snyder]

But if I merely toss an object up, it comes back down without ever going 11 km/s

 

[russ_watters]

But if I merely toss an object up, it comes back down without ever going 11 km/s

Keep lifting those weights and you'll get there eventually.

 

[Jimmy Snyder]

Actually, 11 km/s is the maximum speed of a meteor that almost escaped, then fell back down.

 

[BobG]

To expand: 11 km/s is the minimum possible speed of an approaching meteor because that's escape velocity.

Wouldn't that make it the minimum speed of an escaping meteor?

True.

However, for the speed to be less than 11 km/sec for a close approaching object, something had to change the speed of the object very recently or it would already be orbiting the Earth instead of just having a trajectory that intersects the Earth's orbit.

Both the Earth and the asteroid/comet/etc have to have the same specific potential energy per unit of mass (relative to the Sun) since they're intersecting. For the relative velocity to be small, both the Earth and the asteroid have to have a total specific energy per unit of mass that's almost equal. That means the orbit of both has to be close to the same size, meaning the two should come near each other repeatedly over eons of time.

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.

 

[Jimmy Snyder]

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. Indeed, it is possible that the Earth was made of such meteors and if so, there was negligible air resistance when it happened.

 

[Redbelly98]

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. Indeed, it is possible that the Earth was made of such meteors and if so, there was negligible air resistance when it happened.

But ... if the meteor is going roughly the same speed as Earth when far away, it will speed way up (relative to us) as it gets closer. Gravitational attraction to Earth will make it speed up. The same escape speed you calculate from conservation of energy principles does give the minimum speed of a meteor strike.

 

[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.