Relativistic impact effects

[Grashtel]

Myself and a few other people are arguing about the effects of a relativistic impact (from a 150 metric ton object moving at anything between 0.1c and 0.95c) on a planet on a science fiction message board. I was wondering if anyone here could help bring some more real science into the discussion by pointing me towards any relevant information, I've tried a quick Googling but can't find anything particularly relevant.

Thank you for any assistance you might be able to provide.

[Robert Andersson]

You can start by using the relativistic version of calculating the Kinetic Energy.

Or, consider this quote from Sam's How to destroy Earth:

Obviously a smaller rock would do the job, you just need to fire it faster. Taking mass dilation into account, a 5,000,000,000,000-tonne asteroid at 90% of light speed would do [destroy Earth] just as well.

[Grashtel]

You can start by using the relativistic version of calculating the Kinetic Energy.

Or, consider this quote from Sam's How to destroy Earth:

Thank you for your reply, I should have mentioned that I have calculated the relativistic KE of the missiles[1], the debate is about just what effect it will have on the planet, I am most of the other people think that it will produce major destruction, the person we are debating claims that the effects will be minor, no more than a fairly light EMP.

[1] From 6.8*10^19 J at 0.1c to 2.9*10^22 J at 0.95c if I've not screwed up, please feel free to check my numbers.

[Robert Andersson]

[1] From 6.8*10^19 J at 0.1c to 2.9*10^22 J at 0.95c if I've not screwed up, please feel free to check my numbers.

Yes, I didn't see your calculation first, so I did it and came up with 3*10^22 J.

If we trust the number given in a linked article in my link above, and energy of 2.24*10^32 would completely destroy Earth. Meaning enough energy to accellerate all particles to escape velocity. Our object is going to give less than a billionth of that effect.

It is a tough call to try to imagine the effect though. Could it penetrate to earth to the core? The heat released must be enough to boil the oceans. I don't know, but I doubt Earth would be a pleasant place to live on.

EDIT: About boiling the oceans, it might not be correct. I skimmed through our Bad Astronomer's review of The Core, where he says that 10^35 ergs would be enough to vaporize the oceans ten times over. If he's right, that would mean our energy is about 10,000 times short of that effect.

[Robert Andersson]

I keep thinking about the dynamics involved. Consider that the object has a speed that would pass earth in the order of 1/100 s. I tend to think that the Earth would not be able to stop it, thus not all the kinetic energy would be transfered to the Earth. Not sure, collision of complex bodies at relativistic velocities is nasty business to figure out.

[Grashtel]

Yes, I didn't see your calculation first, so I did it and came up with 3*10^22 J.

Thanks, at least I now know I haven't got horribly wrong somewhere.

If we trust the number given in a linked article in my link above, and energy of 2.24*10^32 would completely destroy Earth. Meaning enough energy to accellerate all particles to escape velocity. Our object is going to give less than a billionth of that effect.

It is a tough call to try to imagine the effect though. Could it penetrate to earth to the core? The heat released must be enough to boil the oceans. I don't know, but I doubt Earth would be a pleasant place to live on.

EDIT: About boiling the oceans, it might not be correct. I skimmed through our Bad Astronomer's review of The Core, where he says that 10^35 ergs would be enough to vaporize the oceans ten times over. If he's right, that would mean our energy is about 10,000 times short of that effect.

The KE even at 0.95c is only about 7% that of the Chicxulub impactor so its pretty safe to say that it won't be boiling the oceans or anything worse, the question is just how much damage it will do, is it a mass extinction event or just a pretty light show or somewhere in between (I'm pretty certain that its closed to a mas extinction than a light show but don't have any proof), and what happens at lower velocities.

[Grashtel]

I keep thinking about the dynamics involved. Consider that the object has a speed that would pass earth in the order of 1/100 s. I tend to think that the Earth would not be able to stop it, thus not all the kinetic energy would be transfered to the Earth. Not sure, collision of complex bodies at relativistic velocities is nasty business to figure out.

I think that passing right through the planet is unlikely, considering the amount of mass in front of the object I would think that it would stop somewhere in the planet (this is nothing more than a semi-educated guess though). The question is is it in the atmosphere, crust, mantle, or core, and what effect it has there and in the process of getting there.

[Robert Andersson]

The KE even at 0.95c is only about 4% that of the Chicxulub impactor so its pretty safe to say that it won't be boiling the oceans or anything worse, the question is just how much damage it will do, is it a mass extinction event or just a pretty light show or somewhere in between (I'm pretty certain that its closed to a mas extinction than a light show but don't have any proof), and what happens at lower velocities.

Assuming all energy is transfered, it will likely affect the whole planet. Beside just the energy and dust that will spread around the globe, it will likely also produce secondary effects, like earthquakes. Earth will continue to happily orbit the sun, and most life will likely survive, but it will be a different world to live in for a good while.

For lower velocities, eg 0.1c, 10^19 J is still a lot of energy. However, comparing that value (about a gigaton) makes me think it wouldn't be that devastating. Locally it would be, but I think globally, although there would probably be some effect, it wouldn't change much.

[Grey]

I'd suggest that you go here or here for some rough estimates. Neither allows relativistic impact velocities, but you could choose a larger impactor moving at a lower velocity that gives the same total energy you've worked out for your high-speed projectile. It won't be perfect, but it should give a good idea.

[eburacum45]

One possibility that I just thought of is that the initial impact might compress the missile so much it becomes degenerate- that it it turns into neutronium.

This might not last very long, but it might last long enogh for a lot of the momentum to be carried underground- in which case the effects mught be relatively minor.

[gopher65]

Really hard to say. I was watching stargate (I know, not the best source hehe) and they claimed on there that a detenation of 2 gigatons would be sufficent to alter the enviroment enough to cause a significant extinction event.

When I think about what even a dinky impact like the impact in Russia in 1908 did (about the same as a 15 megaton warhead) I have to agree that something on the order of 2 gigatons would through up a huge amount of dust and do some serious damage to the biosphere (note: IF it exploded at the maximum damage point, which isn't a given).

If I am doing this correctly, then 150 tonnes at 0.9c = about 4.1 teratons (after conversion). LOL that is huge. Again, that would assume a perfect transfer of energy into a single location. Not at all likely.

EDIT: I can't find where I figured out how much energy it would take in megatons to vaporize earth, but it was a lot. I guess I could just convert from the above figures *points up a few posts*, but I'm coming very close to being late for work. If I remember I'll come back to this topic after work.

[eburacum45]

You might want to look here;
http://www.stardestroyer.net/Empire/...alculator.html

That gives a lower figure of 2.24e32 Joules, or 5.35e15 megatonnes to destroy the Earth completely..
I think...

[Avatar28]

Actually, I think you were off by a factor of 10. According to onlineconversion.com (killer tool, btw) that stardestroyer.net figure works out to 53,537,284,894,837,472 megatons. 53 zettatons if I'm not mistaken. Now for some fun facts, it would take a mass of TNT approximately 8 times greater than the mass of the earth to blow it up or about half the mass of Neptune. The sun's energy output is approximately 3.9e26 joulse/second. So you would need the entire power output of the sun for around 574,000 seconds (a bit over 6 1/2 days) to destroy the earth completely.

[eburacum45]

Sorry about that- posted in a bit of a hurry.
A mass of TNT 8 times the mass of the Earth to blow it up eh?

In other words, a mass of TNT the size of the Earth could not explode with enough force to put all it's mass into orbit.
That is interesting when you consider Van Flandern's 'theory' that there used to be a planet orbiting between Jupiter and Mars, which exploded to form the asteroids...

one of the methods he suggested for supplying the energy for this destruction was 'phase change energy' - that is the latent heat of melting (or freezing) of the core of that world. This energy would obviously be woefully inadequate to destroy a world.
See here-(a disclaimer; this theory is nonsense)
http://www.metaresearch.org/solar%20...ph/eph2000.asp
scroll down to the section 'Planetary Explosion Mechanisms'

[snarkophilus]

What if the object was really squishy and porous, like a gigantic marshmallow? It might undergo considerable vaporization when it entered the atmosphere, raising surface temperatures to ludicrous heights in mere moments, raining fire down upon us. Also, when it hit ground, a lot of the impact force would be redirected laterally, too -- even worse for anything on the surface!

To put it in perspective, the Krakatoa explosion was about 100-200 megatons TNT. The shock wave circled the Earth seven times, there were 40 m tsunamis, and you could hear the thing 5000 km away. It pumped 25 cubic km of stuff into the air.

You want to hit the planet with four teratons (gopher65's number), 20000-40000 times that? I'd say you're looking at some pretty widespread damage, even if it doesn't burn up at all (and I think that any burning would be pretty bad).

Possibly even more dangerous is if it broke up into a few pieces and acted a little like a cluster bomb. Imagine forty thousand Krakatoas scattered all around the world. That would be the end of everyone, almost guaranteed.

So what if the thing totally vaporizes in the atmosphere? Roughly how much heat is it adding? The atmosphere is 5 * 10^18 kg. We'll call the specific heat capacity 1000 J kg-1 K-1. So the atmosphere warms up a degree for every 5*10^21 J you put in. 3*10^22 J of added energy means you're only warming the whole planet about 2.5 K. Of course, you're doing it in a hundredth of a second.... Then you have a pressure wave, and the reflection (like when a nuclear weapon is detonated above ground to take advantage of reflections), and a portion of the atmosphere blowing off entirely....

I say it would suck.

[gopher65]

Hmmmm. I just remembered this topic, and I was thinking, since this object is travelling at ~0.9c, you might be correct that it would vaporize upon hitting the atmophere. But I don't think this would diminish its destructive effect. This just means that the entire energy of the object (which is considerable) would be tranferred into the atmophere instead of the ground. So there wouldn't be much of a crater, and there wouldn't be much in the way of a dust cloud (or at least not as much of one), but you would have a truely gigantic shockwave travelling around the earth.

I have no idea how to calculate the damage that such a shockwave would do. Anyone care to take a shot at it?

[snarkophilus]

Hmmmm. I just remembered this topic, and I was thinking, since this object is travelling at ~0.9c, you might be correct that it would vaporize upon hitting the atmophere. But I don't think this would diminish its destructive effect. This just means that the entire energy of the object (which is considerable) would be tranferred into the atmophere instead of the ground. So there wouldn't be much of a crater, and there wouldn't be much in the way of a dust cloud (or at least not as much of one), but you would have a truely gigantic shockwave travelling around the earth.

I have no idea how to calculate the damage that such a shockwave would do. Anyone care to take a shot at it?

I'm not sure it would vaporize. It is moving so quickly that it might not have time to heat up much as it entered. In order to vaporize, I think it would need a large surface area (ie be composed of a porous material), or it would need to slow a great deal as it entered the atmosphere.

Actually, this brings up an interesting question. How does time dilation enter into the picture? Does the object, because it is moving so quickly, heat up at a different rate than classical thermo would indicate? I'd like to say yes, but I'm still undecided as to what I think would happen.

Anyway, maybe I'll give the shockwave model a shot, assuming that the thing vaporizes entirely. I know how to model pressure waves in open space, but the existence of ground and the fact that the world is a closed surface make it a little more challenging (accursed co-ordinate conversions! ) We'll see if the long weekend gives me time to try it out...

[gopher65]

Time dialation wouldn't have any effect from our perspective (and the equation I used already takes mass changes into account). From our inertia frame it would simply appear as if a very fast thingy-ma-bobber hit the atmosphere and exploded (assuming it vaporized entirely). From the interia from of the *mass* it would probably appear that everything was happening a tad fast, but that is its problem for not accounting for its mass and length changes now isn't it .