Relatavistic Projectiles

[xammer99]

Good afternoon,

I have a couple of questions for the more scientifically inclined around here.

In a story I read by Ian Douglas (yeah yeah, not the highest of sci-fi, but I'm curious if it'd actually work), the protagonists run a ship up to .99c or so, dump out a cargo load of sand directed at a planet. In the resulting hilarity, the planet's atmosphere is burned off and a bunch of ships/stations in orbit are destroyed as well.

So a few questions, assuming it is possible and using a ship with the capacity of a modern super tanker (500,000 dwt cargo capacity)

1. Would it be better just to ram the ship into the planet at .99c to kill it?

2. Could that volume of sand pull it off and burn off the atmosphere? Or at least render the planet uninhabitable.

3. If 500,000 tons of sand could do it, is that over kill? And if so, how much would actually be needed?

Thanks!

[Serafina]

Well, i am not sure what that amount of sand would do, but i can say one thing about question 1:
It's entirely dependable whether you want to sacrifice your ship or not. In the case of a manned spacecraft, dumping your cargo on the planet is definately the preferable option.
And you can repeat a cargo dump over and over again.

[Samuel]

1. Would it be better just to ram the ship into the planet at .99c to kill it?

Yes. More mass is always better.

KE=.5mv^2 so given 453,592,370 kg and a velocity of 296794533.42 m/s...

20 × 〖10〗^24 power joules.

2. Could that volume of sand pull it off and burn off the atmosphere? Or at least render the planet uninhabitable.

I don't know about the first part, but the second? Definately.

[Starglider]

KE=.5mv^2

That is not correct, or rather, it's a classical approximation that does not work at relativistic speeds. The appropriate equation is in fact KE = m*c^2*((1/sqr(1-(v^2/c^2)))-1). The actual KE for this case is 2.7e26 J. That's about 64 billion megatons, more than enough to vaporise the entire biosphere.

You may find the relativistic KE calculator handy for estimating the effects of various relativistic impactor scenarios. Note however that to accelerate to that speed the ship's engine has to generate substantially more energy and channel it through the drive, which is a bit of a plausibility problem.

[Samuel]

Opps- forgot relativistic works differently than normally calcualtating KE. Get 25×〖10〗^19 instead.

[Darth Wong]

I don't know why sci-fi authors always have to engage in ridiculous overkill, like accelerating objects to 0.99c. That takes enormous amounts of energy, and you could easily sterilize a planet by hitting it with a large object at 0.01c, with FAR fewer engineering difficulties.

[tim31]

I expect the reason they indulge as such is halfway between a real-world answer of keeping it with an acceptable timeframe, and space-wank.

[Starglider]

I don't know why sci-fi authors always have to engage in ridiculous overkill, like accelerating objects to 0.99c.

In a hard sci-fi setting, the scariness of relativistic projectiles comes from the near impossibility of detecting them in time to perform any kind of interception. Tossing an asteroid at 0.01c gives the target a chance (not necessarily a good chance - it depends on how prepared their defences are) to detect, intercept and deflect the projectile.

[Nyrath]

I found a value for the energy required to blow off Earth's atmosphere. It was an utterly outrageous 77 petatons (about 3.2 x 10^25 joules). This is a lot.

The equation for relativistic damage is here: http://www.projectrho.com/rocket/rocket3x.html#rbomb

The back of my envelope tells me that if you start with 500,000 tons of sand (5 x 10^8 kilograms), it will have to be moving at 0.99999999999999999999999999999999 c
Or if it is moving at 0.99 c, you'll need 6 x 10^23 kilograms, which is roughly the mass of the planet Mars.
(check my math, I sometimes make foolish mistakes)

To merely destroy all life on Earth takes a lot less energy, of course. I'm not sure just how much though.
Check the Boom Table and decide yourself.
http://www.projectrho.com/rocket/rocket3x.html#boom

[Samuel]

To merely destroy all life on Earth takes a lot less energy, of course. I'm not sure just how much though.

Well, if you get the atmosphere hot enough, you boil the water on the planet and all above ground life dies. However, life at black smoker vents and in the crust is harder to kill, although honestly no would be space-terrorist would care. Just killing large scale life and plants is enough for almost anyone. To do that you probably just need something with the energy of the dinokiller. Or just drop something into each ocean really hard so that most of the land floods.

If you are going for sterilization you need to melt the crust- otherwise there are multiple ways to kill to everything important.

[Ford Prefect]

I don't know why sci-fi authors always have to engage in ridiculous overkill, like accelerating objects to 0.99c.

It's like a disease. You put pen to paper and suddenly your spaceships are pulling five hundred gees, have a twenty terawatt laser and every piece of associated handwaving to make it happen. Characters start casually mentioning dismantling planets, you start using scientific notation and it becomes seemingly impossible to describe velocities which are below tenths of the speed of light. The only way to counteract this tendancy is meditative readings of 2OOI: A Space Odyssey.

Anyway, while killing an entire planet with a boatload of sand has its own kind of preposterous assholery to it, though not as bad as nuking people with empty bean cans or a bag of kitty litter, it sounds like way more trouble than its worth (setting aside the difficulties in accelerating to just below the speed of light). Five hundred thousand tons of sand isn't exactly like tossing a brick out the proverbial window.

[Batman]

I don't see how accelerating something to .99c is really overkill in SciFi terms. There's franchises where you LITERALLY can go to to the edge of the universe to pick up a pack of smokes on your way home from work (at least where stardrive speeds are concerned) and teleporting an entire galaxy from one universe to another is entirely possible.
And 2001: A Space Odyssey is boring as hell.

[Samuel]

I don't see how accelerating something to .99c is really overkill in SciFi terms. There's franchises where you LITERALLY can go to to the edge of the universe to pick up a pack of smokes on your way home from work (at least where stardrive speeds are concerned) and teleporting an entire galaxy from one universe to another is entirely possible.
And 2001: A Space Odyssey is boring as hell.

Because the amount of energy required. To get something going that fast you need hypermatter, engines that shit on the laws of physics, or ships that are all fuel supply.

Most FTLs do not require you to put in the same amount of energy as needed to that speed under Newtonian physics, which makes quite a bit of difference.

The book was okay, although the sequels sucked.

Anyway, while killing an entire planet with a boatload of sand has its own kind of preposterous assholery to it, though not as bad as nuking people with empty bean cans or a bag of kitty litter, it sounds like way more trouble than its worth (setting aside the difficulties in accelerating to just below the speed of light).

It gets you a kill on sight label.

[Batman]

Um-any kind of FTL ALREADY requires you shit on the laws of physics. And the sequels were tons better than 2001.

[Junghalli]

Because the amount of energy required. To get something going that fast you need hypermatter, engines that shit on the laws of physics, or ships that are all fuel supply.

Theoretically, you could do it with reasonably hard SF tech with a Bussard ramjet.

[Jonen C]

Because the amount of energy required. To get something going that fast you need hypermatter, engines that shit on the laws of physics, or ships that are all fuel supply.

Theoretically, you could do it with reasonably hard SF tech with a Bussard ramjet.

Except a Bussard ramjet has a terminal velocity equal to the velocity of its exhaust.

[Samuel]

Um-any kind of FTL ALREADY requires you shit on the laws of physics. And the sequels were tons better than 2001.

It is called limiting the damage. Just because we add FTL doesn't mean we toss out all the laws of physics.

[TheLostVikings]

Because the amount of energy required. To get something going that fast you need hypermatter, engines that shit on the laws of physics, or ships that are all fuel supply.

Theoretically, you could do it with reasonably hard SF tech with a Bussard ramjet.

Except a Bussard ramjet is actually a brake that slows you down. You can never reach those speeds with one. (turns out that in order to have time for fusion to occur before the hydrogen zooms out the back of your spaceship you need to slow the interstellar medium down while collecting it, generating more negative thrust than you actually get from the fusion drive)

[Starglider]

Except a Bussard ramjet is actually a brake that slows you down. You can never reach those speeds with one.

Ah, well this is why you need a Bussard scramjet.

[Count Chocula]

Silly question time: would 500,000 tons' worth of sand have the effect predicted? I'm assuming that it would not hit the atmosphere all at once, but would inevitably disperse from being dumped out a freighter or two or three, and from hitting interstellar or near-planet dust and orbital objects on the way in. In addition, the individual grains of sand are unlikely to actually survive to hit the ground, instead burning up in the atmosphere like far larger meteors do today on Earth.

Now if it were a 500,000 ton nickel-iron asteroid moving at .99c, then turn off the lights...it's over. I think a cloud of sand, however, would have a harder time imparting that immense energy in as useful a fashion.

[Samuel]

Silly question time: would 500,000 tons' worth of sand have the effect predicted? I'm assuming that it would not hit the atmosphere all at once, but would inevitably disperse from being dumped out a freighter or two or three, and from hitting interstellar or near-planet dust and orbital objects on the way in. In addition, the individual grains of sand are unlikely to actually survive to hit the ground, instead burning up in the atmosphere like far larger meteors do today on Earth.

I don't see how it would take out the ships in orbit, but killing life on the planet? Yes.

I don't see how the sand would disperse fast enough- of course, it depends on the range.

Now if it were a 500,000 ton nickel-iron asteroid moving at .99c, then turn off the lights...it's over. I think a cloud of sand, however, would have a harder time imparting that immense energy in as useful a fashion

You fail physics forever. What do you think happens when the sand vaporizes in the atmosphere? It transfers its kenetic energy into heat energy.

80% of our atmosphere is Nitrogen and it has a specific heat of 1.04J/gK. Atmosphere weighs 5.3 E18 kg, We have 25×〖10〗^19 J

About a 45 K increase in temperature. 81 F. Of course, if it hits a localized area, it will get much hotter their and then spread out over the entire planet. How much spread did the cloud have?

[Darth Wong]

Um-any kind of FTL ALREADY requires you shit on the laws of physics. And the sequels were tons better than 2001.

That's one of the worst attitudes in sci-fi fandom: once you have FTL, you might as well just throw out all science and logic, right?

[starslayer]

Samuel, your energy value is wrong. Relativistic kinetic energy is always higher than that obtained using the classical approximation. 500,000 metric tons of sand moving at .99c has a kinetic energy of ~4E26 J, or about 20 times that needed to blow off the atmosphere.

[Samuel]

Samuel, your energy value is wrong. Relativistic kinetic energy is always higher than that obtained using the classical approximation. 500,000 metric tons of sand moving at .99c has a kinetic energy of ~4E26 J, or about 20 times that needed to blow off the atmosphere.

Shit. Thanks. I need to take a college physics class- we didn't cover that in AP Physics.

Okay, that changes the change in temperature to... 4,500,000 K. Water boils at 373 K. This is just for the atmosphere though, but all life on the surface dies.

[Junghalli]

Except a Bussard ramjet has a terminal velocity equal to the velocity of its exhaust.

Except a Bussard ramjet is actually a brake that slows you down.

I'm aware of the drag problem. It only applies if you slow down the fuel. Get the fuel to fuse without slowing it down and you can make a Bussard ramjet with theoretically infinite delta V.

Naturally this would be an absolute bastard from an engineering perspective (protium-protium is already a difficult reaction to begin with, and you've got to do it while the fuel shoots through your ship at significant fractions of c ... we need an eek icon like on SB.com), but compared to what regularly gets thrown around in sci fi it's relatively reasonable. At least it doesn't require basic physical laws being wrong.