Why is comet deflection so hard (and how does a fusion rocket help)?

Question

I just read an article arguing that we need very fast rockets for the deflection of comets, since we will probably detect them just several months before impact. So we need to hurry in order to pick them up as far away as possible. It explicitly motivates fusion rockets, since comets might be detected only 6 to 18months prior to impact.

That got me thinking. For the sake of argument, assume we have several ICBMs in orbit (political likelihood left out of this question). Assume they are armed with 500kt warheads. Furthermore, assume they are able to meet the comet 1 month away from earth and we want it to be deflected by 5 times the diameter of earth (60 000 km). So by my rough calculation we want to achieve a 23m/s acceleration.

The scary nuclear weapons calculator gives a vaporization of 140mm of (carbon) surface material for a detonation as close as 250m. That value more than doubles (330mm) in case of water ice. That seems to be quite a lot. That means the payload of a single Trident II missile could vaporize between 1.7m and 4.5m of surface material from a given comet. So for a water ice surface of roughly 4km x 4km that gives us a "propellant" of 72 000 000t of fuel. For your typical $10^{13}$ kg comet that should be 0.5/1000 of your mass (give or take). Assuming that our vaporization is at least as effective as a rocket engine (ISP 500 seconds) and crunching the numbers using a delta-v calculator that gives 2.5m/s delta-v.

So according to my rough calculations, there is no extreme advantage of a faster rocket here. How would a fusion rocket change the above principles? Why can't we simply put some 20+ Trident II like missiles somewhere in orbit (as I said, politics aside) and wait for a target to pop up? Where is my error? And if my calculations are totally wrong (which might well be), what makes it better to have a very fast rocket and get things done 6 months away from earth (couldn't we as well send 6 times the number of nuclear warheads with conventional slow rockets)?

Answer 1

Assuming that our vaporization is at least as effective as a rocket engine (ISP 500) that gives 2.5m/s delta v

Unlikely - the rocket engine uses a shaped engine bell tuned to give the best thrust (put simply) over a several minute burn. Whereas vaporised material from the comet itself would consist mainly of low energy expanding gas and its "exhaust angle" (don't know if there is a proper term) would be spread out over 180 degrees.

In short I think the question overestimates the available thrust from vaporising cometary ice. There would be some, but I suspect it would be far, far less than is needed.

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Another point:

The question's calculation is based on vaporising a given depth of material from a range of 250 meters, but assuming this depth is taken over an area of 4x4 kilometres. That looks like another overestimate.

You could perhaps take the depth equation over the 4x4 kilometre area, work out the ranges and depths for each point and integrate to get the volume vaporised. This still wouldn't give a reliable exhaust velocity for the material though.

Answer 2

The simple fact is that we don't know what the effects of a nuclear blast on a comet would be as it's never been done, and each comet is different. You're thinking of a nuclear explosion next to a comet in terms of a hammer, but it's more like a gentle nudge at best. Whatever thrust ratio you get is likely to be very low, what if only .1% of the energy gets translated into movement? If all you get is a .05 m/s change then that adds up to 4 km per day - good enough if it's done soon enough as that change will add up quite a lot over time. Close to the earth it's not likely to help.

You assume that a nuke is going to just move the comet, but there's other things that might happen. The comet may break into chunks, and those pieces each would need to be dealt with separately.

If you let the comet get into earth orbit then you have to fight the earth's gravity as well. This gets exponentially greater the closer the comet gets to the earth. If you let the comet get into a low earth orbit you will have to impart it with around 9m/s acceleration just to counteract gravity, meaning more nukes are needed.

Getting nuclear weapons into space and be able to maneuver them to where they need to go will require powerful rockets - it's not just the nuclear charge that needs to be lifted, it needs to be on a rocket of its own - and these are expensive. It won't cost that much more to make a rocket that can reach a comet millions of miles away than one that can get to geosynchronous orbit. If you wait until it's close you will need many of these and that adds huge cost. It's much cheaper to hit the comet farther away using fewer charges.

Would you want to take the risk of waiting until you see the whites of its craters anyway? Hitting a comet far away gives you options, if you wait until it's close and it doesn't work you are totally screwed. Hitting it far away gives you time to evaluate changes in its orbit, and take other steps. You can nudge it again - I wouldn't send just one nuke!

EDIT: A fusion rocket helps because it gets your nukes to the comet sooner, so you will have less time between detection and intercept.

I think you have the right idea that you want this already in orbit, I wouldn't want the delays in prepping a rocket on short notice, even if there's one available. As for problems with nukes in orbit the best way to appease people would be to design the charges so they would not be able to survive re-entry.

Answer 3

I don't have an exact answer but some relevant bits of information:

You're looking at how much material is vaporized. That's irrelevant, vaporizing material gets you nothing. To move the comet you need to expel material from the surface. Your thrust is based on mass * final velocity (after climbing the comet's admittedly minuscule gravity well), whether it's solid, liquid or gas gains you nothing. While vaporization is pretty much necessary to expel it it's actually lost energy when it comes to pushing the comet.

Instead of trying to figure the amount vaporized we should look for data we already have: We are describing an Orion drive. A NASA page I found some time back gave efficiencies of 10-50% for Orion--since we don't get to carefully build our engine I would take the lowest of their numbers as the best we could hope for.

Expecting a result similar to rocket ISP is completely unjustified. Much of the energy is wasted in material being blown sideways as you have no bell on your engine to direct the force in the direction you want.

Despite all this my attempts to work out the math show practical nuclear weapons can deliver quite a shove. However, that's not the whole picture.

First, what is local escape velocity on the comet? If you administer a shove that exceeds this you're just asking to break the comet and now you have two (or more) parts to deal with, unless you have plenty more boom to use you're worse off than if you didn't shoot in the first place.

Second, you're proposing an intercept one month out. Lets consider the recent near miss--Siding Spring. It flew past Mars at 56 km/sec. I'm not finding the delta-V of a Titan missile but it's probably in the ballpark of 10 km/sec. Supposing it's in low Earth orbit--it's going to use nearly half of that to escape Earth, it's going to be heading out at about 6 km/sec. Thus to get that intercept one month out you need to fire almost 10 months out.

In practice it's going to be worse because you won't have precise targeting that far out, you'll need a maneuvering engine. You'll also need a separate probe to refine the targeting as you need to place the warhead very accurately (against a target like Siding Spring a miss by a single kilometer renders it entirely useless and if the threat is from ahead or behind you'll have to shoot in passing and your accuracy will have to be in the tens of meters.) All that takes mass that will reduce your delta-V and require a launch even farther out. (If all the extras weigh as much as the warhead you have no way to get your one month intercept against Siding Spring.)

Meanwhile, lifting a single Titan missile into orbit will take multiple launches of the heaviest rockets we have. (Yes, we can do it with multiple launches as most of that weight is fuel.)

Answer 4

Another way of estimating the energy transferred to the target?

10E+13 kg of comet v.s. 500 kT Nuke: where 1kg TNT=4.2 MJoule. This looks like a 20 km (13 miles) diameter comet. Looks like 10 times the mass of the K-T event (Dino killer).

The energy from the bomb will spread in a sphere and less than half will go towards the comet. Lets try 1/3 or 33%. From the energy hitting the comet some will be reflected back into space - the value here is a guess - lets try 1/3 reflected back. 67% effective. Now to the final step - the energy will heat an area on the comet to different temperatures. Extreme near the blast and less so further away from the blast. Lets look at the energy available: 500.000.000 (kg) * 0.33*0.67*4.200.000=4.6E+14 Joules.

When trying to calculate the impulse we have two factors: Mass and temperature.

What happens to 4x4 km and a depth of 0.2m? Density 1.5g/cm3? 4000*4000*0.2*1.5=4.8E+6 kg. Temperature (half water half rock 2600J/K) We get 35000K temperature - everything is a gas at this temperature - since the speed of sound in a gas is proportional to the square root of the temperature - speed of sound = max possible exhaust speed - aproximately 11 times that of air or 3.7 km/s. This is spread in a half sphere (not directed as from a rocket engine): 50% useful.

So the Impulse contribution comes out as: 3700*0.5*4.8E6/10E13=8.8E-4 m/s = 1mm/s. What about the efficiency? (3700*0.5*4.8E6)/4.6E14=0.02%

It does not look like this is effective enough to make a difference to the path of the comet.

On the other hand if the comet is 2 km instead of 20 we get about 1 m/s or 2600 km deflection in one month. This is 26.000 km in one year = 2 earth diameters.

Per