[Scenario] We have 4 years.

[sndrtj]

No, no, no.

Tsar bomba was a test to prove a theory. Theory proved to be valid: the yield can be scaled up without any practical limits - just add canisters of deuterium/tritium (whatever they used there). You can make 100 Mt, 200 Mt, even 1000 Mt or more. Yes, it could stretch our capabilities of obtaining so much thermonuclear fusion material but it's not impossible.

And besides, I'm not talking about destroying the thing, I'm talking about redirecting it. I'm too tired now to do the math, but I doubt the figures would look all that impossible.

I've done some math. Lets assume we need to change Pallas' velocity by about 100 m/s. That's a wild assumption, but one has to assume something.

The kinetic energy required would thus be, following E(k) = 0.5m*v^2 = 0.5*2.1E20 * 100^2 = 1.05E24 J

Tsar bomba had an estimated yield of 240 PJ, i.e. 1.05E17 J. So that's almost exactly 7 orders of magninute too small. You'd need 10 million Tsar Bomba's to yield that energy, and assume all of its energy would be directed as pure kinetic energy (which really won't happen). More likely you need something like 100 million Tsar Bomba's.

To calculate the amount of nuclear material needed: 1 kT is roughly 4.18 TJ. You need about 6kg of fissile material/kT. You need at least 2.5E11 kT (= 250 gigatons of TNT), so roughly 1.6 billion tons of fissile material. Good luck with that.

[-Velocity-]

You'd be much better off using all the fissile material to build giant Orion vessels to evacuate as much life- and even more important- industrial equipment and supplies- from Earth as possible. You've got to get your @$$ to Mars with enough supplies and backups to give you hope that you can figure out how to live sustainably there before the supplies run out and everything dies... because we don't know how to do that right now.

At least you wouldn't have to worry about the radioactive fallout from launching Orion ships from Earth's surface, because no one would give a crap anymore.

[cicatrix]

I've done some math. Lets assume we need to change Pallas' velocity by about 100 m/s. That's a wild assumption, but one has to assume something.

A fraction of a degree deviation would be enough provided we blew it far enough from Earth.

Ok. We need to change the course of a 2.06E20 kg asteroid.

Its size 532 km, so we need it to miss, say, at least 1000 km (to be on a safe side).

if we have 6 month, then, at the speed of 20 km/s the distance would be 20 * 3600 * 24 * 180 ~ 311 milliion km

1000:311000000 ~ 3.21 mm

We need to move it by only 3.21 mm

The kinetic energy required would thus be, following E(k) = 0.5m*v^2 = 0.5*2.1E20 * 100^2 = 1.05E24 J

Tsar bomba had an estimated yield of 240 PJ, i.e. 1.05E17 J. So that's almost exactly 7 orders of magninute too small. You'd need 10 million Tsar Bomba's to yield that energy, and assume all of its energy would be directed as pure kinetic energy (which really won't happen). More likely you need something like 100 million Tsar Bomba's.

To calculate the amount of nuclear material needed: 1 kT is roughly 4.18 TJ. You need about 6kg of fissile material/kT. You need at least 2.5E11 kT (= 250 gigatons of TNT), so roughly 1.6 billion tons of fissile material. Good luck with that.

1 MT ~ 4.2 PJ (4.2E15)

Tsar Bomba at max power (it was reduced) yielded 100 Mt (4.2E17) MT _AND_ you don't need fissile material, you need deuterium/tritium in much less quantities.

0.5 * 2.06E20 * 0.00321^2 = 1,0613223e+15 J

This means, that 100 MT yield will be more than enough.

P.S. If we make it faster than 3.5 years we would need even less powerful blast.

P.S.S. Besides, the blast will evaporate/scatter a part of its mass.

So the key is time - the faster we could deliver the charges to Pallas - the better our chances are.

Edited December 11, 2014 by cicatrix

[sndrtj]

I've got the faint idea that that straight line is not really how it works, but I could be mistaken. In any case, 1000km still seems very close; I haven't done the math, but that's probably well within its roche limit. Make it something like 50k km, that sounds safer.

Anyhow... all current "solutions" on this thread imply we either have to flee or act on Pallas directly. In stead of trying to push Pallas, which is going to be difficult, why not redirect something far smaller, but with enough impact to do some decent damage.

E.g. comet 67P has a weight of of approximately 1E13 kg, which makes it 7 orders of magnitude easier to push than Pallas. Decent nuke can most certainly do that. If we manage to intersect a similar object like that with Pallas' orbit, assuming the relative velocity is 10km/s, the energy released in that collision would be 5E20 J. That's enough to change Pallas velocity by sqrt(5E20/(0.5*2.1E20)) = 2.18 m/s. Not exactly hundreds of m/s dV, but it's getting somewhere.

[EzinX]

Anyhow... all current "solutions" on this thread imply we either have to flee or act on Pallas directly. In stead of trying to push Pallas, which is going to be difficult, why not redirect something far smaller, but with enough impact to do some decent damage.

So you want to shove something far enough from it's current trajectory to intersect Pallas within a couple years. Also, you don't want to launch a 100 megaton warhead, which is fairly small, but a spacecraft carrying hundreds of warheads so you can fine tune the new trajectory of the object you are shoving.

It's probably possible but only if the "pool table" of stellar objects is set up just right for it to work. I suspect out of all possible configurations of the solar system, the proportion where such a "pool shot" maneuver is possible is a small fraction of the possibilities.

[frizzank]

If we are talking an extinction level event then everything gets put on the table, and I mean Everything!!. That means all those nasty nuke powered rockets are not so dangerous now that our existence is on the line. Your not going to give 2 cents about hurting the environment or even half the life on the planet if it gives the other half a small chance chance to live.

Money and cost also have no value at this point , cant spend it if the earth is dead.

That means anything that was too expensive or cost prohibitive is now possible, like antimatter and gigaton nukes.

When talking about human extinction anything you do to ensure the survival of the human race all the sudden becomes not only rational but justified....

A ship powered by nukes or antimatter that irradiates its occupants and a quarter of the planet? Who cares as long as they live long enough to get the job done and save the planet.

Would you kill or work to death most of the population of the planet if it ensured the survival of even a few humans and the human race?

Edited December 12, 2014 by frizzank

[cicatrix]

I've got the faint idea that that straight line is not really how it works, but I could be mistaken.

This doesn't matter straight line or not, deviation IS deviation. You can experiment in KSP

In any case, 1000km still seems very close; I haven't done the math, but that's probably well within its roche limit. Make it something like 50k km, that sounds safer.

Roche limit only means that IF Pallas will be close enough it will be torn apart by tidal forces which would also mean the accomplishment of our goal. Besides, that would be a sight to see.

Still, since 100 Mt is more than enough for it to miss (even if we disregard the evaporation of mass from the blast) we can reverse the equation and see the final speed after three 100Mt blasts:

3 (three bombs) * 4.2e+17 (Joules each)

v = SQRT( (3 bombs * 4.2e+17) * 2 / 2.06e+20) ) = 0,063856 m/s

0.063856 * 321000000 = 20498 km

Anyhow... all current "solutions" on this thread imply we either have to flee or act on Pallas directly. In stead of trying to push Pallas, which is going to be difficult, why not redirect something far smaller, but with enough impact to do some decent damage.

The problem is accuracy. As you saw - even a tiniest deviation off course results in big errors in the end. You're proposing to shoot a bullet at an incoming bullet and while this is theoretically possible, the practics is more grim. Anyway - your proposal could be Plan D

Edited December 12, 2014 by cicatrix

[sndrtj]

The problem is accuracy. As you saw - even a tiniest deviation off course results in big errors in the end. You're proposing to shoot a bullet at an incoming bullet and while this is theoretically possible, the practics is more grim. Anyway - your proposal could be Plan D

We've made a flyby to comet Halley at an astonishing relatively velocity of 60km/s (the griotto probe), send an impactor to a comet when the mother ship was moving away at several km/s (deep impact), and even rendezvouzed with a comet (Rosetta/Philae).

I'd say this just reduces the problem to an engineering one rather than a physical limit. And humanity has shown it becomes absolutely great at engineering when faced with its own imminent destruction (e.g. we probably wouldn't have had all this rocketry business if it weren't for WWII)

[cicatrix]

We've made a flyby to comet Halley at an astonishing relatively velocity of 60km/s (the griotto probe), send an impactor to a comet when the mother ship was moving away at several km/s (deep impact), and even rendezvouzed with a comet (Rosetta/Philae).

I'd say this just reduces the problem to an engineering one rather than a physical limit. And humanity has shown it becomes absolutely great at engineering when faced with its own imminent destruction (e.g. we probably wouldn't have had all this rocketry business if it weren't for WWII)

You'll need more than that.

You have to rendezvous with a comet, calculate its new collision course with Pallas (which should happen at distances of million km magnitude), actually change the course according to your calculations then wait and see if you done it right and the comet indeed is going to collide with Pallas in the end.

Or you can fly along with the comet and correct its course along the way right till it hits the target. I think, an attempt to redirect Pallas itself is more promising.

[kerbiloid]

We would launch a big charge to a tiny asteroid and throw it off course.

The tiny asteroid hits a small asteroid, and throws it from its course.

In turn, the small asteroid hits a medium asteroid.

The medium asteroid hits a large asteroid...

Wait.. The large asteroid WAS that Pallas!

[wasmic]

According to the Wikipedia, we need around 1e-2 m/s of delta-v a few years before an asteroid impact to avoid the impact. The mass of Pallas is around 2e20 kg. Assuming that we can make something hit the asteroid at 1000 km/s, we need around 2e12 kg of it for the task. In order to avoid the impact, everyone on Earth just has to launch a 300 kg impactor at 1000 km/s at the asteroid (or 30 tonnes at 10 km/s). Sounds easy enough.

Could we hypothetically launch a (bunch off) nuke(s) up there, have it drill into the asteroid, and then detonate? This could sling a lot of the asteroid away, and thus we'd be using the asteroid itself as reaction mass instead of having to bring it from the Earth. A nuclear warhead also has a much higher energy/mass ratio than we can hope to get from rockets.

[Jouni]

Could we hypothetically launch a (bunch off) nuke(s) up there, have it drill into the asteroid, and then detonate? This could sling a lot of the asteroid away, and thus we'd be using the asteroid itself as reaction mass instead of having to bring it from the Earth. A nuclear warhead also has a much higher energy/mass ratio than we can hope to get from rockets.

That could be quite efficient, at least on qualitative level, but I don't know enough physics to say how efficient it would be. The more reaction mass you have, the more delta-v you get for the same amount of energy. On the other hand, the bigger chunk you break off from the asteroid, the more energy is lost in breaking the asteroid and in deformation.

[J.Random]

What do you think could be done?

Lots of stuff. Orgies and mass drug addiction are first to come to mind. Also, pillaging, suicides, homicides, genocides, a couple (of dozens) of revolutions. Anarchy sounds like fun. Oh, cults! Religious fanaticism! Have I missed something? Edited December 12, 2014 by J.Random

[Starman4308]

Lots of stuff. Orgies and mass drug addiction are first to come to mind. Also, pillaging, suicides, homicides, genocides, a couple (of dozens) of revolutions. Anarchy sounds like fun. Oh, cults! Religious fanaticism! Have I missed something?

Silly, uninformed opinions on how we could move Pallas.

Don't forget a whole bunch of people sitting under the impact site, because if they're going to die, they might as well go out with a bang. I know I'd be tempted.

[ZetaX]

Don't forget a whole bunch of people sitting under the impact site, because if they're going to die, they might as well go out with a bang. I know I'd be tempted.

Better being there and dying instantly than painfully dying over the next few minutes/hours/days (depending on where exactly you are).

[cicatrix]

Could we hypothetically launch a (bunch off) nuke(s) up there, have it drill into the asteroid, and then detonate? This could sling a lot of the asteroid away, and thus we'd be using the asteroid itself as reaction mass instead of having to bring it from the Earth. A nuclear warhead also has a much higher energy/mass ratio than we can hope to get from rockets.

It won't work without Bruce Willis.

[Pixel of Life]

Could we hypothetically launch a (bunch off) nuke(s) up there, have it drill into the asteroid, and then detonate? This could sling a lot of the asteroid away, and thus we'd be using the asteroid itself as reaction mass instead of having to bring it from the Earth. A nuclear warhead also has a much higher energy/mass ratio than we can hope to get from rockets.

Hypothetically, yes, but lots of small rocks could be much more destructive than a single large one. Since most people live in a city, that large asteroid impacting the east coast would actually cause relatively little damage. Several densely populated cities such as New York, Washington DC and Montreal would be destroyed. There would be hundreds of millions of casualties.

However, when you consider the asteroid's capability to wipe whole countries off the map, it doesn't sound so bad anymore. Why? Because if you were to blow it up, many of the resulting pieces - potentially dozens or even hundreds of them - would still be big enough to demolish a large city. Tokyo? Gone. London? Gone. LA? Gone. You get the idea. The death toll could rise up to several billion. You might get lucky and all the big ones would crash into an ocean or some other rural area. The question is, would you be willing to take the risk?

I think the best idea would be to use a powerful orbital laser to change the asteroid's trajectory or turn most of it into dust before it reaches Earth. Connect all the power plants to a network of microwave transmitters and beam the power up to the laser.

[ZetaX]

Hypothetically, yes, but lots of small rocks could be much more destructive than a single large one. Since most people live in a city, that large asteroid impacting the east coast would actually cause relatively little damage. Several densely populated cities such as New York, Washington DC and Montreal would be destroyed. There would be hundreds of millions of casualties.

If that asteroid impacts the east coast, there will be no west coast left; it will be burried under hundreds of meters of stone, flooded with lava or wiped away by flood- and shockwaves. Such a large impact also ejects lots of material which will then fall down on the whole world. And all that is before we even consider climatic or political effects.

At that size, there is no effective difference between small rocks or a big rock. If it hits, it's the end.

I think the best idea would be to use a powerful orbital laser to change the asteroid's trajectory or turn most of it into dust before it reaches Earth. Connect all the power plants to a network of microwave transmitters and beam the power up to the laser.

You have a weird idea of lasers. They defocus long before reaching the asteroid (unless you are planning on waiting untill it looks a hundred times the size of the moon in the sky) and their energy output is ridiculous in comparision to even a smaller asteroid, and definitely a much worse choice if the alternative is nukes.

[YNM]

http://what-if.xkcd.com/13/

Let's do this. "Consuming Earth oil resources in two minutes".

[ZetaX]

http://what-if.xkcd.com/13/

Let's do this. "Consuming Earth oil resources in two minutes".

It would at least give Pallas a nice bright glow to watch while we wait for the impact^^

[Starman4308]

Well, as long as we're coming up with silly ways to move Pallas:

A mere 53,000 Harrington-verse missiles should do the trick. The Lorentz factor for 0.8c is 1.67, so the inertia of a single 100-ton missile is 4*10^13 kg*m/s. We need to shift Pallas by about 0.01 m/s, so we need 2.11*10^18 kg*m/s of inertia, which comes out to about 53,000 missiles. I think I remember missile swarms of about that size in major fleet engagements, so that's reasonable. One might be able to get away with even fewer if the missiles have a top speed faster than the 0.8c limit of the ships, and in a pinch, a suicidal superdreadnought should do the trick.

It says something about the Harrington universe, that moving Pallas is feasible for them.

[cicatrix]

However, when you consider the asteroid's capability to wipe whole countries off the map, it doesn't sound so bad anymore. Why? Because if you were to blow it up, many of the resulting pieces - potentially dozens or even hundreds of them - would still be big enough to demolish a large city. Tokyo? Gone. London? Gone. LA? Gone. You get the idea. The death toll could rise up to several billion. You might get lucky and all the big ones would crash into an ocean or some other rural area. The question is, would you be willing to take the risk?

Smaller pieces will burn in the atmosphere and since only part of them will be hitting anyway it's much better than a single big rock.

I think the best idea would be to use a powerful orbital laser to change the asteroid's trajectory or turn most of it into dust before it reaches Earth. Connect all the power plants to a network of microwave transmitters and beam the power up to the laser.

I thought we were speaking about doable things, not 'big lazerz'.

[jwenting]

A, that technology is very implausible. We aren't even close to von Neumann machines, there's no reason to try "3D printer" when all you would need is a coat, and it'd probably be more practical to have a factory converting regolith to reflective material (then spread by robots) anyways.

B, Pallas is simply not large enough to be its own solar sail by at least an order of magnitude. The square cube law works against you for trying to move large objects: you would need absolutely colossal solar sails to move Pallas, much larger in area than Pallas itself.

EDIT: This raises interesting questions on how one would support such a solar sail. You might need something which looks more like a space elevator than a tower.

and even if we had von Neumann machines, I'd not use them to turn the surface into a mirror in the hope it'd deflect the thing (which wouldn't work).

I'd set those things into turning the entire asteroid into a cloud of loose atoms or small molecules, which would be at least in part deflected or dispersed by the atmosphere and solar wind.

You'd still blast every satellite and other space based resource out of existence as you now have a massive shotgun blast of small particles impacting instead of a single big thing, but at least there's a chance there won't be an ELE when it all hits. It'll probably trigger an ice age because of the amount of dust it puts into the upper atmosphere, but that could be lived through.

[Laie]

From the calculated results, pp.1-3 of this thread:

By the time the shock wave reaches the far side of the world, it will still travel at twice the speed of sound; peak overpressure 150psi. Repeat, that's at 20,000km distance.

IIRC, nuclear airbursts over cities were to be optimized for like ~10psi to cause maximum destruction.

[about that very subject]That sounds decidedly not fun.

lots of small rocks could be much more destructive than a single large one.

For that kind of single large one, I doubt it.