Planet cracker
 

Been a while since I last posted, but I've got a new thought problem for you guys.

I'm transcribing a TL12^ race into GURPS, and I'm trying to figure out the damage that their main planet-destroying weapon does. It's a spinally mounted conversion beam (as per ultra-tech), and it takes 4 of them constantly firing for 15 minutes to detonate an earth-sized planet (the beams tunnel through the planet and detonate the core).

So what I'd like to know is:
-How many dice of damage per second does this beam produce?
-How much energy will this beam consume?

Explanations using math and/or physics is welcome.
Thanks in advance!

Re: Planet cracker
 

Have you seen this thread?

My main question though is why can't they just use kinetic kill?

Re: Planet cracker
 

This is going to sound an awful lot like useless trolling but this seems to merely an academic exercise.

It just seems at these levels you could simply say it costs a lot of TL12^ Energy (requiring a large shipboard power source and recharge in minutes) and being hit with it results in anything less than TL12^ shields and equipment being obliterated.

But then, most of my spaceships are powered by handwavium.

Re: Planet cracker
 

If you want the official take on it, there is a sidebar in GURPS Supers that goes over how much damage it would take to destroy the Earth that happens to be viewable on page 7 of the preview PDF.

The thread that was linked to might be more scientifically accurate, though. I'm not sure, since I didn't take too much time to look through it. But the section in Supers does seem to make sense.

Re: Planet cracker
 

Thank you for the link sir_pudding. I hadn't seen it.

I assume "kinetic kill" means smashing some other celestial object into it. The race has focused almost all of it's research efforts into energy manipulation, so they're not exactly inclined to chuck a moon at it if they already have beams at their disposal. Besides, the original targets for the weapons were actually hollowed-out planetships, which usually had enough firepower to take out objects like that.

As for Fwibos, I have considered handwavium, but I've worked on these guys for a long time before I came to GURPS, and I wanted to see what their abilities would translate as. Still, for actual play purposes (if that ever happens) handwavium will do nicely.

Re: Planet cracker
 

the energy to detonate an earth like planet so that it fly appart is usually estimated at 2E32 Joules, lower limit.

see http://www.stardestroyer.net/Empire/...DeathStar.html for the details.

(for reference, the sun output about 4E26 joules/secondes according to google.)

So you would need about a week of the sun power output.

Gurps super give 2.000.000.000 hp to Earth. Thats 12.000.000.000 damage for a sure kill.
So, 4 gun over 15 minutes would mean 1 000 000 D of damage per gun per secondes
But Earth have a Dr of 5000000.
So, each gun need to do about 2 500 000 dice of damage - per second.

Unless my math is wrong, wich would not surprise me.

Not that such numbers have any meaning anyway ...
It is ^superscience, so, your gun do as much damage as needed, by definition.

Celjabba

Re: Planet cracker
 

I was trying to come us with these numbers on my own and hit a problem. If a put "8*((cube root (weight of the earth)) in lb)" into Wolfram Alpha I get "1.88927x10^9 lb^(1/3) (cube root pounds)". What is a "cube root pound"? I get, like, no hits on Google!

Re: Planet cracker
 

Try GURPS Fantasy "Behind the Curtain: How Strong Is a Giant" p.51 it is basically a HP. (using the definition of pound being mass not force)

Re: Planet cracker
 

Its effectively the same as an HP. You're really meant to work out the weight in pounds then put that number into the equation without any qualifiers.

Re: Planet cracker
 

You may find the information on this website useful. There's actually some reasonably scientific discussion on the various difficulties involved in destroying the Earth, and how you might overcome them: http://qntm.org/geocide.

Re: Planet cracker
 

You don't need a moon. A old junked spacecraft will do.

Re: Planet cracker
 

To actually splatter the planet it needs to be a big spacecraft. On the order of miles of diameter even at .99C.

Now, if you only want to kill people it doesn't need to be nearly so big. It probably doesn't need to be going that close to C either.

Re: Planet cracker
 

In real life or in GURPS?

Re: Planet cracker
 

"Splatter" was used as shorthand for "make a new, long term asteroid belt". That's where the multiple miles in diameter at .99C comes from.

Doing enough HP to take the Earth down to automatic death is difficult to calculate. You don't know if the Earth has Unkillable I or Damage Reduction just for a start. It might have bought it out of it's experience pts after the Permian or KT boundary events.

If you wonder, yes, I am being sarcastic about giving inanimate objects HT scores and having them make death checks.

Re: Planet cracker
 

I should think that the most important elements in game terms would be how much space the weapon takes up, how much space is left in the platform for armor, secondary armament, etc. Because if a weapon is so big that it can destroy a planet, figuring out how much damage points it can cause is academic. Though it may be a fun exercise for those with a bent that way.

An exception might be if planet-crackers are fighting each other and each is well armored enough for calculations of damage to have an actual effect on game play.

Re: Planet cracker
 

The planet cracker was designed by the aliens to take out another race's battleship (which was made from a hollowed-out planet). Of course, the enemy planet-ship was also shielded, so I was wondering if I wanted to re-create that scenario for some players, what all would be involved for the ships (both firing and receiving).

And, yes, the planet-cracking ships are massive.

Celjabba, where did you find that number? I'd be interested in reading that article :)

Re: Planet cracker
 

You don't need to explode the planet to render it uninhabitable.

Re: Planet cracker
 

Mind if I slightly hijack this thread with a question about the equivalent toy from my own scifi setting:

The Excalibur Device projects a spherical field of hyperspatial energy. Any mass caught inside the field when it triggers (requires several hours to fully charge) is violently ripped into hyperspace. Because of the way hyperspace works in that setting, matter can't exist there for long and is ejected back...in highly destabilized form. It arrives as a mass of random particles, roughly half regular matter and half anti-matter.

So what takes place next is basically an anti-matter explosion with a size depending on the amount of mass converted.

This is where I get into some maths trouble.

I'm trying to come up with an approximate radius for the field that would make sense in that it'd reliably wipe out a planet (and subject the entire system to a lethal burst of radiation) but not significantly endanger systems over 5 LY away.

I've got as far as to dig up the volume-of-a-sphere formula (been a while), find the density of an earth-type planet's inner core (15g/cm³) and the energy density of an annihilation reaction (9e16 J/kg).

That's when the numbers involved got a little overwhelming :P.

Anybody here want to have some fun with that idea?

Re: Planet cracker
 

I get a sphere around 6.5 km in diameter at the core of the earth if transformed into antimatter would destroy the earth assuming your core density is correct (I know your antimatter reaction number is) and the death star guys in the post #6 link got their number right.

After a quick search, some estimates for core density are a little lower (12.6-13g/cm^3). So 6.5 km should be plenty.

Re: Planet cracker
 

Just for reference, in the thread that you link to the relativistic spacecraft would have a kinetic energy of 3.6E22 J (if I did the math right). From the ever useful Atomic Rocket boom table
http://www.projectrho.com/rocket/rocket3x1.html , about 1/6 of the way down the page
that's about an order of magnitude less energy than the Chicxulub event that ended the dinosaurs. It would cause a lot of consternation to the people living there, but would not really damage an earth-like planet.

With four orders of magnitude more energy, you could remove all of an earth-like planet's atmosphere. For five orders of magnitude more energy, you could turn all of earth's oceans into steam. Six orders of magnitude more energy allows you to melt the earth's crust, making the entire earth molten. It would take nine orders of magnitude more energy to blast the earth into gravitationally unbound rubble.

Luke

Re: Planet cracker
 

So as suspected the collision rules break down at relativistic velocities. I wonder where the breakpoint is?

Re: Planet cracker
 

Nice table. Thanks.

Re: Planet cracker
 

Hmm. Does your calculation use the whole mass, or just half of it? The way the planetkiller works in-universe is that it produces an even mix of matter and anti-matter from the converted mass...

Re: Planet cracker
 

Thanks for the link lwcamp! My only question is would these numbers be accurate for a continuous beam? For example: the table states that 2.9x10^31 Joules are needed to reduce Terra to gravel (the desired effect of the planet cracker). Is this energy delivered all at once? Or does the sum total of the energy imparted have to be equal to that?

Re: Planet cracker
 

That's the energy needed to overcome the gravitational binding energy of the planet. It does not matter how it is delivered, so long as there is not time for a significant amount to radiate away into space. Considering as it takes a full day or so for the sun to radiate away that much energy, and the sun has a much larger surface to radiate from than the earth (by four orders of magnitude), you should be fine if your planet killer takes less than a few decades to deliver its energy.

Luke

Re: Planet cracker
 

Yeah, that's for equal matter/anti-matter. I should have made that clearer. Actually, using the value for reducing the earth to an asteroid belt in Luke's handy-dandy table, and assuming a core density of 12.8g/cm^3, you need a sphere of 1/2 matter, 1/2 anti-matter around 3.65 km in diameter exploding at the core.

Re: Planet cracker
 

Why use gravitational binding energy as the threshold? A planet is "killed" for all strategic intents and purposes long before it is rubble. How much to just render the surface unusable for geologically meaningful timespans?

Re: Planet cracker
 

Why not just put the planet in an antigrav field? Without its self gravitation, Earth will blow up quite nicely.

Re: Planet cracker
 

That's a lower energy but more complex situation and quite a bit more difficult to calculate.

However, it you take that figure of the Earth having c.200,000,000 square miles of surface area and figure that about one megaton of nuclear explosion will totally sterilize one square mile of surface area then 200,000,000 megatons will scrub the Earth's surface.

This is a _very_ fuzzy estimate but the c. 10, kiloton blast at the Trinity test site has had relatively little long term effect. They give tours of the place. About the only thing they tell you not to do is pick up and carry away the few bits of radioactive glass still left. Partly this is because so much of it already has been carried off.

This is for direct effect of course. You might be able to get by with less energy if you're going to trigger a runaway greenhouse effect or something similar.

On the other hand, actually breaking up the entire crust of the Earth is going to take a good bit more energy.

Re: Planet cracker
 

Going from Atomic Rocket's boom table again
http://www.projectrho.com/rocket/rocket3x1.html#boom

3.2E26 J: Energy required blow off Earth's atmosphere
6.6E26 J: Energy required to heat all of Earth's oceans to boiling
4.5E27 J: Energy required to vaporize all of Earth's oceans
2.9E28 J: Energy required to melt Earth's crust
1.0E29 J: Energy required blow off Earth's oceans
1.5E30 J: Energy required blow off Earth's crust

Luke

Re: Planet cracker
 

I wonder where he got those numbers from.

Re: Planet cracker
 

He is an agent of The Shadows. Don't you know?

Re: Planet cracker
 

Why do you think they are called planetary nebulae?

Luke

Re: Planet cracker
 

Because they eventually coalesce into planets? I'm honestly not clear on the naming.

Re: Planet cracker
 

Ah, well in real life, a planetary nebula is a shell of gas spat off by a dying star. They were called that because old time astronomers (but not so old they didn't have telescopes) could see them as a faint disk. Since planets also had a visible disk, it reminded the astronomers of planets, hence the name.

As a joke, they are called planetary nebulae because Winch Chung (the Atomic Rockets guy) blew up planets into clouds of gas to experiment with how much energy it would take to cause various levels of disruption.

Luke

Re: Planet cracker
 

lol, okay I see. I suppose I can jus e-mail him and find out where the numbers came from.

Re: Planet cracker
 

Oh, you were being serious. In that case, the values for boiling or evaporating the oceans likely come from knowing the mass of the ocean and the specific heat and heat of vaporization of water. It takes 4180 J to raise the temperature of 1 kg of water by 1 degree C. So if the average temperature of the ocean is 10 C, for example, then for every kg of ocean water it takes (100 C - 10 C) * 4180 J to raise it to boiling. Once you have it at boiling temperature, it takes 2,257,000 J/kg to boil the water into steam. This is assuming the water is pure - salt and other stuff will affect these values a bit, but not by all that much.

The rest probably comes from knowing the mass of the atmosphere, oceans, and crust and figuring the work needed to take than mass from the planets surface to far enough away that it is no longer under the influence of the earth's gravity. Since the escape velocity on earth is 11.2 km/s, 1 kg of mass shot off the earth with enough speed to escape from the earth would have a kinetic energy of 63 MJ. This gives the energy per kilogram needed to gravitationally unbind something from our planet - assuming you are not lifting so much off the planet that the mass of the planet significantly changes. So multiply the mass of the oceans in kg by 63 MJ to get the energy to blast all the oceans on earth off the planet so hard they will not come back.

Luke

Re: Planet cracker
 

Handy little site... Bookmarked, and thanks for the link!