RKV Prevention Rough Time frame.

[Exileman]

In another topic, RKV's are brought up and a discussion involving prevention becomes a sort of subtopic. Surlathe lists the formula for determining the time till impact as d(1/v - 1) where v is equal to the fraction of the speed of light the object is traveling and d the distance. Now, assuming v is .99, and starting from now, what is a rough estimate of what d needs to be for our chances to go beyond "totally boned" if an RKV was headed towards earth right now. Now, to clarify, I am asking how long as a civilization you can roughly state, based upon current trends in technological advancement and what not, will we have even an abysmally small chance of intentionally stopping it.

[Ender]

In another topic, RKV's are brought up and a discussion involving prevention becomes a sort of subtopic. Surlathe lists the formula for determining the time till impact as d(1/v - 1) where v is equal to the fraction of the speed of light the object is traveling and d the distance. Now, assuming v is .99, and starting from now, what is a rough estimate of what d needs to be for our chances to go beyond "totally boned" if an RKV was headed towards earth right now. Now, to clarify, I am asking how long as a civilization you can roughly state, based upon current trends in technological advancement and what not, will we have even an abysmally small chance of intentionally stopping it.

Recommend this thread be merged back in.

And it depends on its power and acceleration.

[Exileman]

Actually, I had intended the missile already having achieved its "top speed" of .99c. As for power, that I should have specified. Lets assume, for the purposes of a baseline, that the output would be enough to fragment the earth to asteroids. Asteroids roughly the size of.... i'm going with australia in diameter.

[Ariphaos]

In another topic, RKV's are brought up and a discussion involving prevention becomes a sort of subtopic. Surlathe lists the formula for determining the time till impact as d(1/v - 1) where v is equal to the fraction of the speed of light the object is traveling and d the distance. Now, assuming v is .99, and starting from now, what is a rough estimate of what d needs to be for our chances to go beyond "totally boned" if an RKV was headed towards earth right now. Now, to clarify, I am asking how long as a civilization you can roughly state, based upon current trends in technological advancement and what not, will we have even an abysmally small chance of intentionally stopping it.

In an argument I had in another thread, I pointed out that a tiny fraction of Solar output would be enough to vaporize a tungsten rod a hundred meters thick and over a thousand kilometers long in several days.

In order to get a civilization with an RKV you pretty much have to be right on top of them. For a .99c RKV your coilgun would be longer than the distance from home star to target star for said definition of 'right on top'.

[Junghalli]

To destroy an RKKV is easy. The same thing that makes it dangerous (its KE) also makes it incredibly vulnerable to kinetic impactors. Toss a nickel in its path and it's shrapnel. Though shrapnel going at .99 c is still dangerous, so you'll want to destroy it well away from you, and hope the inverse square law saves you from being hit by anything in the expanding cone of debris, or at least that what does get through doesn't do too much damage.

The biggest problem with RKKVs is at the detection end. At .99 c this thing is chasing the coat-tails of its own image; say you can detect it at 100 light minutes out, you only get 1 minute warning. If it has to do terminal burns it can probably be detected and destroyed rather easily at a distance, if not it's going to be coming in dark and cool, which will make it harder to detect.

So, I'd say bare minimum you need the ability to launch a rocket out to a distance of some significant fraction of an AU on very short notice.

[starslayer]

It very much depends, as has been said, on how far out we detect it, and what we have around to throw at it. Today, we'd probably be blindsided, and rather dead. I'd estimate that it will be several hundred years before we can even begin to think about stopping one, physically easy as it may be. Junghalli mentioned just throwing a nickel at it; true, this would destroy it, but we have to get the nickel there in the first place. New Horizons is the fastest thing we've ever launched, and it will still take another decade, IIRC, to reach Pluto. Sure, a laser would work, but then there are the issues of beam spread and power. Building a Dyson swarm, a la Xeriar's plan, is thousands of years in the future at the least, simply because of the industrial capacity required.

So, I think the laser is obviously the best plan for now. Aiming should be trivial, but getting the collimation necessary, and the power (radiation pressure and heating are small for metals in most frequency ranges), is the tricky part. The advances necessary for getting this thing ready on short notice (say, a few years) are several hundred years in the future, methinks.

If it has to do terminal burns it can probably be detected and destroyed rather easily at a distance, if not it's going to be coming in dark and cool, which will make it harder to detect.

Even if it isn't doing terminal burns, it'll be easy to detect, assuming we have something that is covering the entire sky to very faint signatures. Why? Friction. Surlethe showed in the other thread that even discounting dark matter, we are dealing with an ISM that is considerably more dense than it looks at first glance. And all the energy that got pumped into this thing is bound to leave plenty of inefficiency room for heating the RKV as it is accelerated and then coasts. I haven't run any hard numbers (I'll run those later today and post them), but it should be well above background temperature, and that will make it stand out, assuming we disregard all known sources like stars and planets.

[Covenant]

Even without the limitations of acceleration via magnetic means or others, anyone who is throwing around RKVs is going to be more than competant at spaceflight. If you assume that a civilization has a sizable detection net of no-greater-than lightspeed warning capability in a general radius of a single lightyear (not even to our next closest neighbor) then a cold RKV travelling at .99c should still trip the nets and get warning to Earth four days ahead of impact.

Four days is not a long time to do much to avoid a relativistic projectile like that, but it's sure easy to throw something in it's way. If you assume that Earth would have some manner of space force or orbit guard military presence then you could try to do something like drag an asteroid into it's way or--if you have anywhere the same level of technology--fire something else back along an intercept course.

These are really, really deadly weapons, but if you assume that a nation capable of accelerating a projectile to .99c can also set up multi-year tours of duty to patrol a certain sphere of influence, it's hardly the game-ender that it first appears. At the distance of a light year, even going .99 percent of lightspeed--which is a really ABSURDLY fast speed even for an RKV--isn't good enough to catch people totally off-guard. RKVs are essentially higher-tech than a Death Star, but could be stopped by Battlestar Galactica level defenders.

[Sea Skimmer]

To destroy an RKKV is easy. The same thing that makes it dangerous (its KE) also makes it incredibly vulnerable to kinetic impactors. Toss a nickel in its path and it's shrapnel. Though shrapnel going at .99 c is still dangerous, so you'll want to destroy it well away from you, and hope the inverse square law saves you from being hit by anything in the expanding cone of debris, or at least that what does get through doesn't do too much damage.

Put a decent mass in its path and it wont be shrapnel, it will be very explosively converted into heat and vapor which is much less of a threat.

[Surlethe]

Put a decent mass in its path and it wont be shrapnel, it will be very explosively converted into heat and vapor which is much less of a threat.

That depends on how much time the vapor has to expand before it hits you. If you get hit by the RKV's vaporized mass traveling at 0.9c, you're just as dead as if you get hit by the solid RKV traveling at 0.9c.

[Junghalli]

And all the energy that got pumped into this thing is bound to leave plenty of inefficiency room for heating the RKV as it is accelerated and then coasts.

The thing will have had years to centuries to cool down (I think - what is the time dilation factor at .99 c?). And it'll probably have been externally powered (i.e. a laser/particle beam/sail beam rider) anyway to go at the speed it does - I don't think a .99 c rocket is practical.

These are really, really deadly weapons, but if you assume that a nation capable of accelerating a projectile to .99c can also set up multi-year tours of duty to patrol a certain sphere of influence, it's hardly the game-ender that it first appears. At the distance of a light year, even going .99 percent of lightspeed--which is a really ABSURDLY fast speed even for an RKV--isn't good enough to catch people totally off-guard.

I don't know if stringing observation platforms around a light year perimeter is going to be practical. Remember, a light year is an absurdly huge volume. Even if the platforms were seperated by planetary distances you'd need a ridiculously huge number. You'd probably be a lot better off with one or a handful of big telescopes, something like a thin-film paralens hundreds of km across (the kind you'd use as the focusing mirror for a laser lightsail).

[Ariphaos]

The thing will have had years to centuries to cool down (I think - what is the time dilation factor at .99 c?). And it'll probably have been externally powered (i.e. a laser/particle beam/sail beam rider) anyway to go at the speed it does - I don't think a .99 c rocket is practical.

About 7.

At .99 of c it will be remaining pretty warm, as the ISM is hitting it pretty hard (~2e11 particles/second hitting it at .99 of c per square cm).

No matter how you reach that speed.

I don't know if stringing observation platforms around a light year perimeter is going to be practical. Remember, a light year is an absurdly huge volume. Even if the platforms were seperated by planetary distances you'd need a ridiculously huge number. You'd probably be a lot better off with one or a handful of big telescopes, something like a thin-film paralens hundreds of km across (the kind you'd use as the focusing mirror for a laser lightsail).

It's pretty feasible to assume that the region around every remotely nearby star is kept pretty solid track of, as close as one could possibly get and with as much parallax as you can possibly get. A one-light-year radius for these purposes is insanely conservative. Ten light-years or higher is far more likely.

[starslayer]

Here are my numbers:

Assume that our hypothetical attackers have assembled a one kilometer long, ten meter thick cylinder of tungsten to use as their RKV. They have not polished it (this is in fact important), seeing as it will simply be destroyed on impact, and they have sent it on its merry way at .9c. Thus, it has a mass of ρV = (19250 kg/m^3) (π * (5 m)^2 * 1000 m) = 1.5E9 kg. This gives it a kinetic energy of E_k = mc^2(γ-1) = (1.5E9 kg)(3E8 m/s)^2 (1/sqrt(1-(.9c)^2/c^2) - 1) = 1.8E26 J, or about 42 petatons. Goodbye us.

Anyways, how hot would it be? I'm not sure how to model ISM friction effects, so I'll assume for the moment that space is a perfect vacuum. How hot it is is thus entirely dependent on inefficiencies due to firing. Assuming, say, a 50% efficiency in the launcher, this leaves 42 petatons of energy unaccounted for. Most of it went into the launcher itself (the RKV is still very small compared to it), so maybe .1% went into the RKV, tops. This comes out to be 42 teratons, more than enough to completely vaporize the RKV. Whoops. Of course, this energy didn't go into the vehicle all at once; let's say that we managed to get down to the point where we escaped with a bar of 2000 K tungsten (I'm not sure how reasonable this assumption is).

Now, how long would it take to cool down? Using the Stefan-Boltzmann equation, ΔQ/Δt = εσAT^4. The rod's emissivity is about .2 (unpolished tungsten), σ is the Stefan-Boltzmann constant, A is the RKV's surface area, and T is its temperature. So, right after it starts to coast, it loses heat at a rate of 5.7 GJ/s. But our rod has a total thermal energy of C*T*m = 130 J/(kg*K) * 2000 K * 1.5E9 kg = 3.9E14, five orders of magnitude more than our current rate of heat loss, which is decreasing all the time. As a (physically impossible) lower limit, then, it'll take about 19 hours for it to cool down to near absolute zero.

But wait! With a little substitution and manipulation, we can get a cooling time far closer to reality. ΔQ = mCΔT, since we have had no state changes. If we presume to start at t = 0, then Δt just equals t. Thus, t = (mCΔT)/(εσAT^4). ΔT = T_i - T_f, in this case. Let's say we can detect the projectile when it has a temperature in excess of 150 K. Thus, T_i is 2000K, and T_f is 150 K. This gives us a cooling time of about 18 hours, not much different than the "impossible lower limit." Well, the numbers don't lie. Unless ISM friction makes up the difference, Junghalli's right: if the RKV isn't doing terminal burns, it won't be picked up by EM sensors, unless we have extremely good radar (it will have a relatively strong radar return).

[starslayer]

Ghetto edit: it just occurred to me that we still must account for conduction between the interior of the rod and its surface; still, that shouldn't increase the cooling time more than an order of magnitude, while we need several orders of magnitude at the least to detect this thing from its radiation.

Oh, Junghalli, you're thinking about time dilation the wrong way; the rod will see less time pass by a factor of seven, not an increase. According to it, it will have much less time to radiate away its heat before it hits its target.

[Admiral Valdemar]

I recall one line of discussion talking about the possibility of multiple launches of rods that produce emissions only in the range of some of the fainter stars in the Milky Way i.e. the attacker spoofs the enemy countermeasures by having dummy RKVs that are a fraction of the length, but have the same cross-section, much like ICBM spoofs.

I'm going by memory, but the problem was moving dedicated counter-measures quick enough and to the right approach vector without having pitifully short reaction times (this was using a several AU radius interferometer array, IIRC).

There comes a point anyway where the defender civilisation is more than capable of detecting and protecting beyond the heliosphere, in which case strategic RKVs become somewhat useless as a one-shot-one-kill weapon.

[Wyrm]

Yeah, starslayer, I have a real problem with your figures and derivations, owing to the fact that blackbody radiation intensity is to the forth power of temperature, which case the radiated heat is going to fall really rapidly with temperature. When you solve the ordinary differential equation: dQ = mCdT & dQ/dt = -εσAT^4, you get the solution Δt = (mC/4εσA) (T_f^{-3} - T_i^{-3}), which when you plug in all the requisite figures, gets you 4.03235e7 seconds, or 1.27777 years, not 18 hours. (Space is a really good insulator.) During this time, the energy shed is 3.6075e14 J, or 86.2 kt.

In view of this and our efficiency (99.9%), we can give the RKV a kick of 86.2 Mt every 1.27777 years (anything more would involve the RKV melting, and certainly passing the metal's curie point). It would take at least 637.5 billion years to get this thing to the required speed (neglecting the inevidible relativistic effects). The sun would be long-dead and the Earth long sizzled by then.

Let's take a different approach: make the input of energy continuous, so that the heat input matches the heat output. At 2000 K the projectile radiates 5.72901 GW, so the input power can be 5.72901 TW (99.9% efficiency). This takes 3.14190e13 seconds to put in 42 petatons of energy, or 995.6 thousand years (again, neglecting relativistic effects). Errors in your determination of the target planet's orbit, as well as additional nudges from other planets, are going to add up to a missed Earth.

Also, you made a small error in emissivity. If you want to have a low emissivity, you'd better make the RKV shiny. A good absorber makes a good blackbody emitter. If you want the emissivity low, you need the reflectivity or transmissivity high (and you're not going to get a high transmissivity in tungsten).

[Wyrm]

Ghetto Edit: Gah! I hate integrating negative exponents! The solution is actually Δt = (mC/3εσA) (T_f^{-3} - T_i^{-3}), but this quite frankly makes the problem worse, and my figure is within an order of magnitude anyway.

[Junghalli]

Unless ISM friction makes up the difference, Junghalli's right: if the RKV isn't doing terminal burns, it won't be picked up by EM sensors, unless we have extremely good radar (it will have a relatively strong radar return).

You'd probably pick up a cold RKKV by the way it eclipses stars as it passes in front of them. Or by reflected light (that could probably be helped by painting it black). Though you might be able to give one an active camouflage system that projects the image of the stars it eclipses on its hull, as long as it doesn't generate too much heat (the thing has to retain all the heat it generates, at least during the terminal approach).

Oh, Junghalli, you're thinking about time dilation the wrong way; the rod will see less time pass by a factor of seven, not an increase.

That's what I meant. This thing will have been drifting for at least years, probably decades or centuries - unless the time-dilation factor is great enough that comparitively little time has passed ship-time.

[starslayer]

Ah, ok. I thought something was off there.

Also, you made a small error in emissivity. If you want to have a low emissivity, you'd better make the RKV shiny. A good absorber makes a good blackbody emitter. If you want the emissivity low, you need the reflectivity or transmissivity high (and you're not going to get a high transmissivity in tungsten).

I looked up the emissivity of tungsten before using .2; that is a median value for unpolished tungsten at 300 K. Polished tungsten has an emissivity in the neighborhood of .03, IIRC. I never supposed that they specifically wanted a low emissivity, just that they picked a dense, tough material and they didn't bother polishing it because it would be destroyed on impact. If they wanted to be really complete, yeah, they'd polish it. This polish would be quickly destroyed by slamming through the ISM, I'd think. If they really wanted low emissivity, they'd go with silver, but that just makes the acceleration problems worse. Oh, and to the transmittance of tungsten being rather low, well duh .

[Wyrm]

I looked up the emissivity of tungsten before using .2; that is a median value for unpolished tungsten at 300 K. Polished tungsten has an emissivity in the neighborhood of .03, IIRC. I never supposed that they specifically wanted a low emissivity, just that they picked a dense, tough material and they didn't bother polishing it because it would be destroyed on impact. If they wanted to be really complete, yeah, they'd polish it. This polish would be quickly destroyed by slamming through the ISM, I'd think. If they really wanted low emissivity, they'd go with silver, but that just makes the acceleration problems worse. Oh, and to the transmittance of tungsten being rather low, well duh .

Okay, so the emissivity of unpolished tungsten is higher than polished tungsten. Sorry for that.

A higher emissivity means that our hell-bent civilization can pump in energy faster without melting the projectile; if anything, they should be roughening the surface to increase emissivity and therefore be able to pump power in faster. Of course, there is a limit to how fast they can do this, as emissivity cannot exceed 1, so our ~1 million year figure is correct within an order of magnitude.

One million years is, of course, a lot of time for chaos to make hash of your predictions. There is going to be error in determining the solar velocity, on the order of several km/s (which over a million years would add up to tens of light years), there is error in the mass of the galaxy, which is going to affect the solar wobble through the plane of the galaxy. And so on. So there are going to be many, many course corrections, and lots and lots of opportunities to be spotted.

[Ariphaos]

I made a javascript calculator for determining the length, time, and energy input for a projectile with various parameters. I'll put it up when I move my site to a vps (hopefully soon) but my general impression is that RKVs are simply not a remotely feasible weapon, in any sense of the word.