RKV's and Defence

[lucretiabrutus]

Hi, I was having a discussion with one of my friends, and we figured you would be the perfect people to bring the discussion to. So without further ado (after adding I hope I'm posting this in the right place) I shall get onto the main topic.
tl;dr version is available at end. And sorry for the typos!

Our scenario involves two planets twenty LY apart, called 'ours' and 'theirs'.
To simplify things, we're going to assume that both these planets are Earth, and have our solar system, and that both are in the same inertial frame. They each have the same tchnology, and both just finished with their crowning accomplishments - Von Neumann factories were sent to Mercury in each solar system, and have just finished a complete solar panel field across the entire planet.
We are taking all the energy produced here to be the total expendible energy for extrasolar affairs in each system (so don't worry about civilian uses for it). For the sake of ease, let's assume these solar panels are 100% efficient (we're worrying about orders of magnitudes anyway).

I'm still setting up the problem, so please bear with me. To give us some numbers to work with, the sun's lumosity is 3,8 E26 Wats, so Mercury at roughly 5,8 E10 metres with a radius of 2,5E6 metres gives us 1,8 E17 Watts to play with. Let us assume this can be transformed to kinetic energy with 100% efficiency in terms of transportation, perhaps converted to matter/antimatter pairs in Mercury, but that's neither here nor there. Now to the scenario!

Their planet decides to launch RKVs at us (we estimate a tonne per piece). We decided that we can ignore those with γ < 2, since we would have at least two years to build and intercept them, and the energy cost required to intercept is negligible compared to the cost to launch. We decided after some calculations that we could detect any launch 'they' make in the γ > 2 range unless they wish to spend the next century accelerating (it's possible to detect them, just not very plausible).

At any rate, sending an RKV of γ = 4 requires roughly 3 E22 joules, meaning they can make roughly two hundred per year (so roughly four per week). This is where we decided to come to you. A defence was proposed of basically deconstructing a large number of asteroids, charging them, and placing them in a dense orbit ... very expensive, but certainly possible with the energy available and the fact our entire species hangs in line. Presuming these are ten grammes each, that means they have E7 Ns of momentum relative to the RKV, or 3 E15 J of kinetic energy - that's about a million times the energy required to vapourise the RKV if it's made out of steel. Presuming the RKV has a thousand times the specific heat, heat of fusion and heat of vapourisation of steel, only 0.1% of the KE of the rock needs to be transferred to heat to vapourise the entire thing.. But even if it's not vapourised, it will be deflected massively (our goal). So call it two rocks to underestimate the defences to stop a single RKV.

With these numbers in mind, we'd propose a defence 'field' consisting of a rectangular prism of these stones at Mars' orbital radius (2,3E 11 metres), with a width and height of of twenty thousand kilometres - we want to defend the Earth, so double its radius should stop most tricks. We chose a rectangular prism because it has a constant depth, unlike a torus which thins out at the top and bottom. The RKV's would enter this region (which would be aligned with Earth's orbital plane) and hopefully smash into the rocks. For now, we're going to assume that their solar system lies along the plane of the ecliptic, and will address the problems of it doesn't later.

Now, we'll want to know the mean pathlength of an RKV, assuming a surface area of a square metre. To be safe, we'll want our wall of rocks to be roughly ten thousand times thicker than the mean pathlength, to stop anything getting through. We have 2 E7 metres thickness, so with a surface area of one metre we have an intersection volume of 2 E7 cubic metres. This means we'll want a rock roughly every thousand cubic metres. Now, the volume of our field is 6 E26 cubic metres, giving us 6 E 19 rocks, which is 6 E17 kg. We can easily get this much mass - Ceres is E21, and the energy required souldn't be any problem.
So we have demonstrated using ten gramme rocks would work on the ecliptic., and even if we need to replace them every decade we've got enough for a hundred thousand years. Obviously, it would be good to shoot back at them, but if they try to pull the same trick we do it'd be a stalemate, so we may as well use our energy more constructively.
I could dump all this in one formula, differentiate and find the optimal speed for an attacking RKV based on kinetic energy and rock size, but it would be the optimal speed based on a series of rather questionable assumptions, and we built in six orders of magnitude safety margin (if you're planet can be destroyed, you'd want as big a safety margin as you can).

However the next point is where we are having problems: what if they are not in the ecliptic? This seems a vastly more likely proposition. The logical conclusion seems to be a spherical shell, which would have a volume of roughly E25 cubic metres, so E22 rocks equalling E20 kg. This seems like a large amount (a tenth the mass of Ceres), but we did build in a factor of a million on our RKV-killing rocks' mass, perhaps it would be best to decrease their mass by a factor of a thousand, and increase their density by a factor of ten, meaning that we have E18 kg, which should be fine - I was initially very surprised that we've only used a thousandth of the asteroid belt's (aka Ceres') mass to construct this.

And here our puzzle for you kicks in - can such a sphere be constructed with any kind of stability? Obviously, friction and the gravity of the planets prevent most natural orbits, but could the rocks be held by static (or dynamic) electric or magnetic fields being created by satellites with thrusters? This way, we'd have a series of 'points' that are moving the rocks, which if equipped with thrusters should be quite capable of moving the rocks and readjusting their orbits. Charging the rocks should be quite easy with the ludicrous amount of energy - two months gives us enough energy production to counter the gravitational binding energy of the part of Ceres we want to chip off, and worse comes to worst we could just throw them through Jupiter's field of radioactive death to charge them.
But still ... would it be possible? I understand it would be ludicrously difficult, but that's a small price to pay to save your planet's surface from doubling in temperature.

tl;dr version: We have a planet, the have a planet 20 LY away, they fire RKV's at us. Would building a shell of pebbles work?

[Steel]

Another problem with RKVs is inefficiency in accelerating them. Consider how long it would take to put your 10^22J into your 1t projectile at 99.9% efficiency, given that that means the projectile is being heated by the remaining 0.1% and melts at a finite temperature.

If you dump it all in at once, and the projectile is made of tungsten (specific heat capacity 0.13 kJ/(kg K)), then your projectile suddenly increases in temperature by about 7.710^13 K, which is certainly going to melt it, turn it to plasma and then scatter it across the sky.

So if we were to consider your projectile being kept just below its melting point (3700K for tungsten) and see how fast you can put energy into it at that efficiency in order to get it up to 10^22J of kinetic energy...

Assuming our projectile can have a surface area of about 1 m^2, and will radiate energy as a black body where energy/unit area J goes as sigma*T^4,

T temperature and Boltzmann constant sigma = 5.67×10−8 W m−2 K−4

We get that the projectile will radiate at 1m^2 * sigma * (3700K)^4 = 10.6 MW

So that means we can only put in energy at a rate 10^3 times that, ie 10^10 W, without melting our projectile.

So to get our 10^22J that means it takes 10^12s or 32000 years, even at 99.9% efficiency.

So you can basically guarantee your civilisation will not be attacked within 32 millennia of your first detection, even if your neighbours are right next door and total bastards who fire on anyone who figures out the radio.

Also note that if you make the projectile bigger then you'll increase the mass much faster than the surface area and so it will take even longer to accelerate the projectile as it radiates less heat per unit mass, and so to the same velocity will take longer. The time will increase as mass^(2/3)

[IvanTih]

This may sound dumb,but what RKV stands for?

[Crazedwraith]

Here We go

[IvanTih]

Here We go

Googled after I posted.

[dworkin]

This may sound dumb,but what RKV stands for?

Reykjavik Airport. While indeed it would be dangerous to fling it at something it seems rather impractical and the people in Iceland may be upset.

[lucretiabrutus]

RKVs are fucking retarded. Ignore them and odds are it will be deflected by natural winds or just miss due to imperfect targetting anyway.

If you are really concerned, point some sunlight at it, or better yet, a laser.

edit: Though if you just want to know: will pebbles kill it? Yeah, probably. Keeping a sphere of them around the sun is a no, a ring ready to go on demand prolly would.

We assumed an RKV could have thrusters to alter their trajectory a tiny amount to account for that kind of thing ... you don't want to just fire it off and hope for the best.

As for a ring on demand, we considered that, but the problem is as gamma increases, you have incredibly little warning, less than a few months, and if it changes its velocity slightly in the last year your ring (which, if outside the ecliptic, will likely only protect the planet for a few seconds due to the orbit) could just be avoided entirely. If a sphere won't work, then the entire defence is probably useless. As for pointing a laser at them, well, if they change their speed even slightly (burning random amounts of re-mass for the last six months to a year) the laser would miss every single time.

[On heat capacity]

A good point, one which I hadn't considered. A question, though - what if one were to construct a launcher in their own solar system? Does the waste heat go to the launcher, leaving the RKV intact?
Otherwise I suppose one could posit the same scenario with planets on the opposite side of the galaxy, but by the time the RKV arrives it would be largely pointless since the civilisation you fired it at either disappeared millenia ago, or have spread to the stars.

Thanks to both of you for your help thusfar ^.^

[Terralthra]

An RKV's relativistic mass makes altering its trajectory even a small amount require stupendous amounts of energy.

[Simon_Jester]

If both cultures have the technology to boost objects to high-relativistic speeds over distances this short (and over timescales of "a few months,") they can put clouds of shrapnel out into the path of the missile more or less at will; they're not limited to mere chemical rocketry or the like.

A shrapnel-based defense is really your best bet, I think, because the resulting collision will turn the missile into a gas cloud- at which point thermal diffusion in vacuum will reduce its density to something that no longer qualifies as an extinction-level event, if you intercepted it far enough out. Sure, the RKV's center of mass is still pointed at your planet, but if the mass itself is effectively a spray of cosmic rays a few million kilometers across, it's a problem for radiation shielding, not "oh my god evacuate the planet!"

...I think.

In any case, your interception problem is going to be made a lot easier by the fact that your countermissiles don't need to be moving at 0.9c. So you can make course changes much more easily than the RKV, and because you can launch many of them for the same energy investment as one RKV.

[Steel]

[On heat capacity]

A good point, one which I hadn't considered. A question, though - what if one were to construct a launcher in their own solar system? Does the waste heat go to the launcher, leaving the RKV intact?

Who knows what is happening to the launcher while the acceleration is going on. What I was modelling there is the fact that you are dumping lots of energy into the projectile, and no matter the mechanism used* that is going to be inefficient to some degree, which is going to result in some heating of the projectile.

I don't think theres any cooling system which wont result in horrendous amount of drag making it impossible to get the projectile up to speed in the first place.


*e.g. if you are magnetically accelerating it then there will be eddy currents in the material which will cause heating, using a rocket will obviously cause heating, a solar sail is going to absorb some photons no matter how reflective it is etc.

[lucretiabrutus]

An RKV's relativistic mass makes altering its trajectory even a small amount require stupendous amounts of energy.

Really? I had thought that because it was in its own inertial frame it would see itself with rest mass, and if worse comes to worst, at γ = 4, it's only four times as massive (I think) ... I would have thought the largest obstacle would be its relativistic speed, making aiming and changes by anything more than tiny fractions of radians impossible.

If both cultures have the technology to boost objects to high-relativistic speeds over distances this short (and over timescales of "a few months,") they can put clouds of shrapnel out into the path of the missile more or less at will; they're not limited to mere chemical rocketry or the like.

I was thinking a year or two acceleration, which if γ = 4 gives them something less than eight years to accelerate in their own reference frame. The 'few months' comment was based on the fact that it takes a finite time for the light to reach you ... I don't have the GR knowledge to calculate the time spent accelerating, so I just took it as taking the entire journey at maximum speed.

[On shrapnel based defence]

I suppose that's a fair point. With that much technology, you can probably shield a few hundred thousand square kilometres without too much trouble at will. My only issue was that the RKV could accelerate slightly over time, to attack the planet in the unshielded section of its orbit, but I suppose if you can make it explode fast enough. Still, you probably want it to spray across the entire face of your planet at narrowest, so you're going to want it to explode very quickly (or have some way to protect a few million square kilometres at Saturn's orbit on demand).
Given the technology that I assumed both sides had, I think your suggestion is probably right with the counters.

[On inefficiencies]

You're probably right. The only thing I can actually think of is a Gauss gun with a superconductor, and I have absolutely no idea how well that would work. I had presumed ideal, but didn't realise if I had merely presumed exceptionally high the technology still wouldn't work.

Thank you all for your criticisms ^.^ It's really appreciated.

P.S. I hope I'm not offending someone by abridging their posts! They're rather large, and anyone reading this thread will have already read them once

[Junghalli]

A more modest RKKV wouldn't require as long an acceleration time. This Forward lightsail proposal calls for reaching .5 c in 1.6 years of acceleration. With a total mass of 80,000 tons it should make a pretty respectable bang when it plows into a planet at .5 c (I'm too lazy to do the proper relativistic KE equation at the moment but the easier conventional KE equation says 225 teratons). Even the fully internally powered Daedalus proposal had an acceleration time of about 4 years to ~.1 c, for which I calculate a yield still in the gigatons for a projectile massing 1000 tons.

Of course you lose the effect of the ship being right behind its own light.

[adam_grif]

You could always try some insane combo-rocket thing (lightsail propelled by stupidly high-power laser(s), whose payload is an antimatter catylized fusion rocket or something) but no-matter which way you spin it, it's an unfathomable energy requirement. Of course, the downside is that it means that interstellar travel won't even hit the light speed limit, which makes or slow-going. Time dilation doesn't become meaningful until you get to high fractions of C as well, so...

[Simon_Jester]

An RKV's relativistic mass makes altering its trajectory even a small amount require stupendous amounts of energy.

Really? I had thought that because it was in its own inertial frame it would see itself with rest mass, and if worse comes to worst, at γ = 4, it's only four times as massive (I think) ... I would have thought the largest obstacle would be its relativistic speed, making aiming and changes by anything more than tiny fractions of radians impossible.

One problem is that while it can make course changes... from its point of view the stuff it's aimed at is approaching fast, with enormous distortions due to time dilation and length contraction. It has very little time to make course corrections, thus requiring extremely high lateral thrust if it is to hit its target. And changing its speed along the line of flight is practically impossible.

If both cultures have the technology to boost objects to high-relativistic speeds over distances this short (and over timescales of "a few months,") they can put clouds of shrapnel out into the path of the missile more or less at will; they're not limited to mere chemical rocketry or the like.

I was thinking a year or two acceleration, which if γ = 4 gives them something less than eight years to accelerate in their own reference frame. The 'few months' comment was based on the fact that it takes a finite time for the light to reach you ... I don't have the GR knowledge to calculate the time spent accelerating, so I just took it as taking the entire journey at maximum speed.

Thing is, those "few months" add to the advance warning you get that the projectile is inbound: you see a very high energy event in a nearby star system, headed straight for you, and you know something big and nasty is coming in hard on its heels. Also, if you have equivalent drive technology, it is trivial for you to get interceptor weapons out by the orbit of Pluto or so long before the incoming RKV reaches your star system, assuming you launch your defensive interceptors during the enemy RKV's boost phase.

[On shrapnel based defence]

I suppose that's a fair point. With that much technology, you can probably shield a few hundred thousand square kilometres without too much trouble at will. My only issue was that the RKV could accelerate slightly over time, to attack the planet in the unshielded section of its orbit, but I suppose if you can make it explode fast enough. Still, you probably want it to spray across the entire face of your planet at narrowest, so you're going to want it to explode very quickly (or have some way to protect a few million square kilometres at Saturn's orbit on demand).
Given the technology that I assumed both sides had, I think your suggestion is probably right with the counters.

The trick is that my shrapnel defense is guided: I am firing a guided missile with a bursting charge designed to fill the volume in front of the RKV with shrapnel. Since I know its line of flight and can easily track where it was, I can saturate the cone of space it might occupy (given its maneuver envelope).

[Junghalli]

You could always try some insane combo-rocket thing (lightsail propelled by stupidly high-power laser(s), whose payload is an antimatter catylized fusion rocket or something)

It would probably be more efficient just to keep the giant laser focused on the ship for a little bit longer. A laser lightsail has theoretically arbitrary delta V - it's all a question of how long you keep the huge laser pointing at the ship.

Of course if you had a proper giant lightsail pusher laser you already have a huge laser with light year ranges, so it might be a better idea to just hit the target world with the laser directly. It'd be much more energy efficient and since the laser moves at c the target could get no warning whatsoever.

[adam_grif]

It would probably be more efficient just to keep the giant laser focused on the ship for a little bit longer. A laser lightsail has theoretically arbitrary delta V - it's all a question of how long you keep the huge laser pointing at the ship.

Maybe. It would depend on how the numbers come out, I suppose. High delta-v on-board is good for course correction, of course.

Of course if you had a proper giant lightsail pusher laser you already have a huge laser with light year ranges, so it might be a better idea to just hit the target world with the laser directly. It'd be much more energy efficient and since the laser moves at c the target could get no warning whatsoever.

That's not necessarily so. You might be using a "railroad" of connected satellites going out several AU, powered by pixie dust or something. You also might be firing at things arbitrarily large distances away (i.e. 200 ly), or be wanting to use it for non-destructive purposes.

[Norade]

It seems like it would be easier to just send a drone swarm to land on another planet, natural satellite, or asteroid belt in system and use the resources gained there to attack with. If a swarm of small objects landed in the Asteroid belt with our current technology we wouldn't know even if we were already mining the field. The only issue is that this has a rather long lead time or you'll see the drones from ages out as they decelerate from some fraction of c.

It is nice to know that RKV's aren't the killers many sources make them out to be though. That is unless we armed them with point defense lasers or simply had them fire a counter shrapnel barrage to knock your debris cloud out of the way, but those seem to be more like drones than RKV's at that point.

[lucretiabrutus]

Thank you all for your help, we're now convinced that the RKV assault is implausible unless it were launched from halfway across the galaxy. Our other main idea for planetary bombardment was just mass drivers at 30% c, so we don't need to worry about relativity, only the ridiculous kinetic energies (a gigatonne TNT equivalent per tonne).

However, can someone say why the spherical idea wouldn't work? I can understand it suffering high rates of attrition, but if everything is kept in magnetic traps, you really only need a rock per cubic kilometre, so why couldn't you have the satellites ferrying the rocks on a whole bunch of circular orbits across every plane?

[Norade]

Thank you all for your help, we're now convinced that the RKV assault is implausible unless it were launched from halfway across the galaxy. Our other main idea for planetary bombardment was just mass drivers at 30% c, so we don't need to worry about relativity, only the ridiculous kinetic energies (a gigatonne TNT equivalent per tonne).

However, can someone say why the spherical idea wouldn't work? I can understand it suffering high rates of attrition, but if everything is kept in magnetic traps, you really only need a rock per cubic kilometre, so why couldn't you have the satellites ferrying the rocks on a whole bunch of circular orbits across every plane?

I think the real question is why bother. You can build intercept stations armed with either missiles or laser at key points for cheaper than orbiting a ton of rocks everywhere.

[lucretiabrutus]

As near I can tell, we'd have thirty-six thousand orbital planes intersecting at two spots (opposite the sun), with each rock having a mean free path of ten thousand kilometres ... since the intersection is much larger than that, we'd expect massive attrition, but my friend is insisting it is a plausible defence unless it's impossible, and as such we need information as to whether it is possible or not, or quantitatively how difficult it would be if it is possible.

As far as 'why bother' goes, we wish to know if this solution would work at all, rather than the optimum way to stop an RKV.

[Junghalli]

That's not necessarily so.

Indeed, if you're using your normal starship launching infrastructure it may well be based on sailbeams.

You might be using a "railroad" of connected satellites going out several AU, powered by pixie dust or something.

I calculate several million tons of deuterium burned to fire a 40,000 TW laser for 1 year, and there would probably be plenty of deuterium available in the Kuiper Belt and Oort Cloud, so powering such arrays by fusion may not be entirely unfeasible. It would be an enormous duplication of effort though, compared to the original proposal, which calls for one huge solar powered laser array and an enormous focusing lens.

[Simon_Jester]

It is nice to know that RKV's aren't the killers many sources make them out to be though. That is unless we armed them with point defense lasers or simply had them fire a counter shrapnel barrage to knock your debris cloud out of the way, but those seem to be more like drones than RKV's at that point.

Sensors and weapons mounted on the nose of an RKV are unlikely to survive being flayed at by the interstellar medium, and you can't counter a shrapnel cloud with another shrapnel cloud.

Shrapnel clouds are dangerous because hitting a gram-mass fragment at these insane speeds is like taking a kiloton-range nuke on the chin, enough to vaporize your projectile. Throwing more shrapnel ahead of your ship doesn't help much. They're dangerous to you because you're a huge target; if the fragments are spread finely enough you're sure to hit some. If you try to clear the area ahead by firing your own flak shells, the individual shrapnel fragments will just miss each other; you'd need a ludicrous amount of material to sweep the space in front of you finely enough to be sure that no little pebbles are still lurking out there in the space your nosecone is going to pass through.

[Junghalli]

Sensors and weapons mounted on the nose of an RKV are unlikely to survive being flayed at by the interstellar medium

They would logically be positioned behind some kind of shield, or spend most of the time retracted into the body of the spacecraft.

The interstellar medium plasma could probably be deflected with a magnetic shield.

[mdiinican]

Or the sensors could just face radially outward, fully protected by the frontal shield. They could check the position of the RKKV by observing the relative positions of the stars. It's not like planets are particularly small or nimble things.

[Atlan]

Or the sensors could just face radially outward, fully protected by the frontal shield. They could check the position of the RKKV by observing the relative positions of the stars. It's not like planets are particularly small or nimble things.

Over interstellar distances planets are actually ridiculously small. If your initial targetting vector has even the most minute error in it your RKV can very easily miss a planet.