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[personal profile] james_davis_nicoll
Long

Destructive Potential of Lunar Rocks

If the catapults were able to fire stuff at velocities comparable
to Earth's escape velocity, the lag time issues would favour Terrestrial
catapults (mounted on moving vehicles, these might be called 'MBT cannons').
This means the energy content of the incoming rocks is something like
6x10^7 J/kg. For comparison, fission peace enhancement devices are good for
about 9x10^12 J/kg, ims, and fusion PED for 8x10^14 J/kg. It still compares
well to TNT's 4.6x10^6 J/kg but note we are not talking the five to seven
orders of magnitude between atomic and chemical but one order of magnitude.

If some arcane method could be found to focus the energy in a
chemical explosive into a smaller massed projectile, it seems possible
terrestrial chemically driven projectiles could compete with Lunar
ones in terms of EK/kg or alternatively one might use 15x as many
shots.

Cratering

Crater diameter scales roughly according to the cube root of
the delta energy. Barringer is ~1 km across and was formed by a 15 MT
(~6x10^16J) event. Diamter/depth ~6 is not a bad rule of thumb.

Say our lunar impactor is a 2 kt event. The crater would be
1 km x [8.4x10^12 J/6x10^16 J]^1/3 or ~50 m diamter x 8 m deep.

Cheyenne is destroyed in TMISHM by the impact of many rocks
from the Moon. Call it a cone of r = 1000 m and h = 1000 m, for a
Volume of about 10^9 m^3. Given the crater volumes (rouhly) 5300 m^3 it would
take very roughly 200,000 shots or at least 67+ days if they can fire
one shot every 30 seconds or so.

Note: a 2 kt device in this case is also a 140 tonne ingot,
because you are getting atomic weapon yields out of something with
an energy density only an order of magnitude better than chemical.
An iron package would be about 18 m^3 (a 3.2 m diameter sphere). An
osmium one would be but 6.2 m^3 (a 2.3 m diameter sphere).

NASA tracks orbital debris as small as 10 cm, and current
radar technology (which is to say, of an era earlier than the Lunar
Catapult) can track items as small as 3 mm, albeit below 600 km
altitude at present.

Incoming ingots are therefore likely to be noticed fairly early.

Wave formation:

Stolen without attribution from _Hazards Due to Comets & Asteroids_

Wave height, impact in shallow water:

h = 1450 m [d/r] [y/gigatons]^1/4

h = wave height
d = water depth
r = range to impact
y = yield

ditto, impact in deep water:

h = 6.5 m [y/gigaton]^0.54 [1000km/r]

Wave run in:

Xmax ~ 1.0 km [h/10 meters]^4/3

And this really is a *very* rough rule of thumb. Consider
what happens to a 10 meter wave hitting the cliffs of Dover vs
Bangladesh (with 17 million people roughly 1 meter above high
tide, IIRC).

RAH is unfortunately specific about the UK offshore impacts,
which is what led to the conclusion that the wave height at Margate
was 7 cm. Even more unfortunately, _The Effects of Nuclear Weapons_
would led one estimate this and it was available when TMIAHM was
written.

Small ingots make tiny waves. Large ingots are, well, large
and attract early detection and countermeasures.

Energy:

One of the attractive things about Lunar catapults is
that they led you leverage your input: most of the Ek comes
from falling 380,000 km rather than directly from the capapult
[After all, if the catapult could fire things at 11/km, you
could just put it on the Earth and lob objects at semiorbital
velocities around the planet]. You do have to get the objects
off the Moon, though.

Say this is an investment of 2.5 km/s. Each ingot masses
140,000 kg, so the Ek is 4x10^11 Joules. At ten gees, that's 25
seconds, or a power output of 16 gigawatts. This catapult needs
Pickering sized nuclear reactor or its equivelent to power it.

This raises more stealth issues. If 90% of the power goes into
Ek and 10% into heat, this is generating about 1.8 GW of heat for
half a minute. This is a serious problem because the heat flare lets
the targets know a shot has been fired. It also lets them know
where the radiators are, inviting attacks on them.

This is another reason why stealthy attacks are hard with the
catapult. The reason I mention stealth is because of

Time to Target:

A low energy orbit to Earth takes 3 - 5 days (Or even longer,
for other solutions). A Lunar Bombard begins by announcing each launch
with a flare of heat, then a large trackable object slowly orbits to
Earth, where it experiences a lithobraking phase at least 72 hours
later.

By comparison, a 1 km/s projectile fired from 100 km away
arrives in about 2 minutes (Hastily checks to make sure 100 km is
within the range of a 1 km/s ballistic object).

A Standard Wheelchair Bound Grandmother [SWBG] is assumed to
be able to procede over paved road at 2 km/hr and 100 m/hr on broken
ground. In 72 hours, assuming 8 hours of rest in every 24, a SWBG
can procede 96 km on paved road and 4.8 km in rough terrain. A SWBG
could therefore evade most of the effects of a 2 kt groundburst.

By comparison, a SWBG could only move 70 meters on paved ground
(the best case scenario), if the 2 kt event package was sent at 1 km/s
from a source 100 km away. 70 m is within the fireball of a 2 kt event.
Most SWBGs will not survive being in a fireball.

Lunar bombards are therefore only good against static targets.
And we already have weapons just as effective on static targets that
don't take half a week to arrive. Therefore Lunar bombards are not
competitive for targets on Earth with weapons we already have.

Date: 2012-07-11 02:12 pm (UTC)
From: [identity profile] carloshasanax.livejournal.com
BUT BUT BUT HEINLEIN INVENTED THE THINK TANK!

Date: 2012-07-11 02:16 pm (UTC)
From: [identity profile] james-nicoll.livejournal.com
I wonder if there's a specific moment we can point to when it became obvious Heinlein just couldn't bothered to do the math any more.

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Acceleration, distance, time

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when he gave up with the math

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Re:

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Date: 2012-07-11 02:15 pm (UTC)
From: [identity profile] martinl-00.livejournal.com
Your stealth argument peters out in the middle of

I would also like to add: No military I am aware of has seriously tried to make a lunar/gravitational bombardment thingy (hereafter referred to as lgbts), while lots and lots have tried to make nukes. Given the propensity of the military to love giant macho phallic projects, this argues strongly that any study of the relative effectiveness of nukes compared to lgbts gives a result so unambiguous that even a military procurement apparatus gives up on this approach.

Date: 2012-07-11 02:17 pm (UTC)
From: [identity profile] james-nicoll.livejournal.com
"of" leads to Time to Target or did you mean something else?

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Date: 2012-07-11 02:50 pm (UTC)
From: [identity profile] nathan helfinstine (from livejournal.com)
May as well use the lunar catapult to launch some nukes I guess. It'd be helpful if the nuclear reactor powering the whole shebang could be used to come up with weapons-grade isotopes.

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Date: 2012-07-11 02:16 pm (UTC)
seawasp: (Default)
From: [personal profile] seawasp
If you could throw 10-mile wide objects, then you're talking real damage. But of course, if you could do that, the power source you're using to THROW the 10-mile wide objects would probably be easier to weaponize in a compact form.

Date: 2012-07-11 03:31 pm (UTC)
From: [identity profile] keithmm.livejournal.com
Yep. That's my problem with most of these absurd concepts, like Project Thor. They're weapon systems in search of a use, when they don't bring anything better to the table than currently exists, and the technology they need to work as effectively as what currently exists would make what currently exists work even better.

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Date: 2012-07-11 02:30 pm (UTC)
From: [identity profile] nebogipfel.livejournal.com
Oh dear. And with what are the libertarians going to rule over us unwashed egalitarians now ?

Date: 2012-07-11 07:16 pm (UTC)
From: [identity profile] eyelessgame.livejournal.com
That's an easy one.

Date: 2012-07-11 03:34 pm (UTC)
From: [identity profile] jeffr23.livejournal.com
Can we make it up with volume? I mean, each side had a few thousand launch platforms for nukes, so why can't the Loonies use a similar saturation of catapults?

Date: 2012-07-11 04:40 pm (UTC)
From: [identity profile] http://users.livejournal.com/krin_o_o_/
I actually was able to follow most of that!

Thanks Mr Sharp* for giving me a decent foundation education in Physics!

- krin

* Yes, that's his real name! Best HS Physics Teacher ever!

Date: 2012-07-11 05:20 pm (UTC)
From: [identity profile] matt-ruff.livejournal.com
Why not just drop the whole Moon on the Earth and be done with it?

Date: 2012-07-11 05:28 pm (UTC)
From: [identity profile] neowolf2.livejournal.com
Where is Alexander Abian when we need him?!

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Date: 2012-07-11 05:58 pm (UTC)
From: [identity profile] http://users.livejournal.com/krin_o_o_/
Well, when the Primordial Ones tried to destroy their rebelling creations(the shoggoth) by smashing Theia into Earth about four and a half billion years ago, the result was that the Old Ones got pissed off and smashed their orbital fortresses between the resulting Moon and the freed moonlets of molten Earth mantle.

They should have stuck with Xeno's Plan "A" and just bombed the place.

Date: 2012-07-11 05:32 pm (UTC)
From: [identity profile] scentofviolets.livejournal.com
Sorry, James, but this is a rare instance in which I (mostly) take Heinlein's side, which can be summed up as "But the Moon has many rocks."

Iow, like a lot of things military, it all comes down to logistics and costs. Yes, incoming rocks are easily detected with plenty of advance warning. Given that, what countermeasures do you employ? Given that you're talking about big rocks, my first cut guess is that the only things that can take them out are (expensive) rocket-mounted (expensive) nukes.

Did I mention that the countermeasures would be expensive :-)

This was always the big argument against Ronnie Raygun's missile shield, btw. Not that it couldn't be made to work (it could, for various values of 'work'), but that differential the expenses of measure vs counter-measure would be a real killer.

Date: 2012-07-11 06:18 pm (UTC)
From: [identity profile] james-nicoll.livejournal.com
But only a finite number of launchers, each of which (if equal to the one in tMiaHM) will need a Pickering-sized power source. You do get more bang out than you put in but the ratio isn't that great, about 15:1 to 20:1 depending on assumptions and if I've done the math in my head correctly.

Date: 2012-07-11 06:27 pm (UTC)
From: [identity profile] tandw.livejournal.com
I think "be where it's not going to land" is a reasonable countermeasure, as per the note that it's only useful against static targets. A future Earth can reasonably be expected to have even better cislunar space surveillance capabilities than we, so they must have known what to expect from the impactor size and mass. Clearly, the authorities allowed the "congregate at the impact point" phenomenon to create a Lunar atrocity with which to rally the planet against the evil Moon people. (At least, that's what the Luna Truthers would have you believe....)

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Date: 2012-07-11 05:36 pm (UTC)
From: [identity profile] scentofviolets.livejournal.com
James, are you designing a new game? A couple of your recent posts suggest that this is the case.

Date: 2012-07-11 05:44 pm (UTC)
From: [identity profile] james-nicoll.livejournal.com
Yes but this has nothing to do with it. And what I am tossing around is pretty vague: interplanetary adventure in a setting where it is possible to imagine that at some point someone may have smiled.

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Date: 2012-07-11 06:31 pm (UTC)
From: [identity profile] neowolf2.livejournal.com
If the Loonies don't want to nuke Earth, could they still launch projectiles with nukes? Build large extremely sturdy metal projectiles and blown them off the moon with appropriate nuclear explosive devices. This would get around the problem of having to build large reusable power conversion machinery (Pickering in space).

If the projectiles were accelerated by nuclear-heated steam, you could classify this idea as Steampunk.

Date: 2012-07-25 12:54 am (UTC)
From: [identity profile] resonant.livejournal.com
Hmmm ... how about a Jules-Verne-style cannon? Drill a deep hole, similar to those used for underground nuclear testing. Carve out a large chamber at the bottom. Put multiple projectiles in the shaft (something like a very long MIRV bus) fill the chamber with cheap locally-available reaction mass (oxygen derived from regolith, perhaps), then detonate a nuclear weapon in the chamber. If you size the chamber and shaft diameters properly, you could keep the acceleration low enough for the projectiles to have guidance systems survive the launch.

Date: 2012-07-11 07:03 pm (UTC)
From: [identity profile] eyelessgame.livejournal.com
"fission peace enhancement devices" for the win.

Date: 2012-07-12 05:39 pm (UTC)
From: [identity profile] nelc.livejournal.com
Pre-internetz, a publication being available is not the same as knowing that it exists and that it contains information useful to you, let alone having it in your hands.

Altogether, it is not clear to me who this piece of criticism is aimed at: Heinlein, or Heinlein-worshipping libertarians of greatly lesser stature.

Date: 2012-07-14 02:41 am (UTC)
From: [identity profile] dbdatvic.livejournal.com
... I am really surprised that nobody has picked up on the fact that here we have a situation where stealth IS quite possible, versus Earth-based detection anyway. (And most geosynch detection as well.) Why? Well...

...put the catapult on the BACK SIDE of the Moon. Presto, a few thousand miles of shielding, plus a heat pulse radiating _away_ from the Earth. (Yeah, if there's stuff out in long-term orbits further than the Moon, it can see this. But we seem to be assuming here that most of the detection's groundbound?)

(Even for things sitting at L4/5, there's still about 1/6 of the Moon they collectively don't see, right?)

Dave, who knew Pink Floyd did space strategy?

Date: 2012-07-14 06:51 pm (UTC)
From: [identity profile] scott-sanford.livejournal.com
That was certainly my assumption.

Now, once a projectile is picked up on radar it's a certainly that someone will crank through the math to trace its orbit back and write up a memo explaining where this ballistic object's path intersects the lunar surface. So we can expect the general neighborhood of the catapult to hit the internet pretty quickly. Depending on the accuracy of that, the result may or may not be useful for targeting purposes; it will certainly highlight a region that will come under considerable scrutiny.

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Date: 2017-03-04 08:08 pm (UTC)
From: (Anonymous)
Heinlein did jigger the background to make his events plausible (though not necessarily mathematically accurate).

They will be useful!

Date: 2019-01-14 05:53 pm (UTC)
From: (Anonymous)
I actually don't think 16 gigawatts is that much for a future civilization. If they are using fission, fission fragment reactors promise efficiencies of 90% or higher. They may also be using aneutronic Helium 3 fusion reactors.

Here's the thing. Any space faring civilization will be building mass accelerators anyway. You need a cost effective solution for shuttling around cargo and people around the solar system, and rockets are not a practical solution in the long run. So mass accelerators will be built for this purpose, either coil guns, railguns, or laser/particle beam driven, they will be built. And any mass accelerator can easily be repurposed for military purposes. You will have battleships, and I think they have many advantages in space warfare, but it will occur to you that chucking rocks at the enemy is a lot cheaper and safe to do (why risk the ships?).

The catapults are not as vulnerable as you might think either, or at least not any more vulnerable than cities and infrastructure on Earth, which is far more vulnerable. Like someone else said, they will be on the far side of the moon, so the enemy doesn't have a line of sight to it anyway. The catapult can also defend itself. It can just hurl rock missiles at the enemy missiles. They are guided, and with some internal detonating charge, you can explode them beforehand and let the shrapnel rip into the enemy's missiles. The rock missiles are also dirt cheap compared to the enemy's missiles which are extremely expensive. Having ships to protect your catapult/infrastructure is definitely beneficial.

As for time to target, yes, it will take days for the rock missiles to hit Earth, but after the initial bombardment of static targets, you can alter the trajectory of your rock missiles and just put them in low Earth orbit. Basically you're parking thousands of rock missiles in orbit and then have some satellites, or ships, or even land ground units to observe what else needs killing, and then de-orbit your rock missiles as needed. You could just use ships for this purpose, but again, rock missiles are cheaper, so why not? You can use both. The rock missiles are expendable so it doesn't matter if the enemy shoots them down (they will need nuclear interceptors for that), and you have an ammo reserve in the thousands. In low Earth orbit, the orbital period is 1.5 hours. So with thousands in orbit, you have response time measured in minutes. Pretty good.

What it really comes down to is price and quantity. You have infinitely more rock missiles than the enemy has nuclear interceptors, and they are cheaper. The sheer volume, and difficulty in stopping it. The catapult won't. stop. shooting. And it has virtually unlimited ammo. Trying to kill the catapult requires your missiles to first, ignore all the city killing rocks heading towards your planet, and then somehow not get destroyed themselves in the long trek to the far side of the moon. More than likely, they will be destroyed long before they get close.

Not only is rock bombardment effective, it's over powered.

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