When the Moon hits your eye… (CC-BY State Farm)
Twitter likes to have its daily figures of mockery, and today that role fell to Brianna Wu – game developer, women’s rights activist and prospective politician. In response to Space X’s announcement that it was aiming to send people to the Moon (a pizza-pie in the sky idea, if you ask me) Wu tweeted “The Moon is probably the most tactically valuable military ground for earth. Rocks dropped from there have the power of 100s of nuclear bombs.” (The original tweet has been deleted, although she clarified that by “dropped” she meant “fired“, which seems fair enough).
She was mocked from both sides of the political spectrum, by people who often seemed to little understanding of the science involved themselves (for instance, people who believed that rocks would burn up in the atmosphere, and therefore be harmless – something very much untrue) but claimed to have the support of astrophysicist PhDs.
So, how plausible is the plan of attack that Wu outlines? Well, in a nutshell, the physics is correct, but the engineering is ridiculous.
Massive impact
In the Second World War, the US government made a discovery – they didn’t actually need to put explosives in their bombs. Drop a metal shell from an aeroplane – literally, just throw it out of the window – and it will hit the ground at nearly the speed of sound. Fill it with pellets, and they’ll be blasted out with explosive force. The Lazy Dog bomb, as they called it, was used through the Vietnam War as a cheap way to do horrible things to people on the ground.
More extreme – and thankfully not yet built – is Rods from God, an “orbital bombardment” platform consisting of a satellite and a set of tungsten rods each about the size of a telegraph pole and weighing in at around 9 tons. If needed, the satellite would shoot one of these rods out of orbit and send it plummeting down to earth at about Mach 11, too fast to stop and almost invisible to radar. When it hit the ground, it would have energy equivalent to about 11 tons of TNT. That’s not something I’d want to be near.
But it’s not a nuclear bomb. The US Air Force already has a guided missile with 11 tons of TNT-equivalent explosive power, and Russia has one four times as powerful. Compared to accidental explosions like the Halifax disaster and deliberate explosions like the Heligoland explosion, which both involved thousands of tons of explosives, it’s small, and it’s less than 0.1% of the power of the Hiroshima bomb, with 15,000 tons (or 15 kilotons) TNT-equivalent.
So to get hundreds of nuclear bombs, we need to scale up. First things first – what happens if we launch from the Moon?
The Moon is much further from Earth than the low-Earth orbits Rods from God would use, which means that projectiles can potentially pick up a lot more energy as they fall to Earth. Unfortunately, the Moon will steal a bit of that energy away – after all, shoot something from the Moon, and the Moon’s gravity will try to pull it back. In other words, when we shoot our rock into space, it’s slowing down. In order to get it to hit the Earth, we therefore need to get it close enough that the Earth’s gravity will catch it and take over. This point is roughly 15% of the way between the Moon and the Earth – the exact position will vary, because the Moon’s orbit is a bit eccentric, but it’s roughly 325,000 km from Earth. Drop a ton of rock from there, and it will hit the ground with a kinetic energy of about 55 GJ. This is roughly as much energy as it might take to heat a house or run a car for a year. It’s quite a lot of a energy to release in an instant.
In fact, it’s as much energy as 13 tons of TNT releases in an instant. So we’re still a long way off even a single nuclear weapon.
We can give the rock a bit more energy by shooting it faster, but this doesn’t help much. Energy is always conserved, so if we want to add some energy to an explosion on Earth with our rock gun, we need to subtract an equal amount of energy from an explosion on the Moon (or put explosive amounts of energy into the rock some other way, like a powerful rail gun). This is the same principle guns work on, incidentally – they create an explosion inside a metal tube in order to transfer that energy to a metal pellet that will cause an explosion in a living creature.
The only real answer is to fire more stuff. Every ton of rock adds another 13 tons of TNT, so to get a hundred Hiroshima bombs (1.5 megatons of TNT) we need 115,000 tons of rock. To make 100 of the largest nuclear bomb ever built, the 100 megaton Tsar Bomba (which was never tested at full power), we need 770,000,000 tons. It’s a lot, but hey, the Moon weighs 70,000,000,000,000,000 tons. It can spare it.
Drop a big enough rock, and you really can create an explosion with the force of a hundred nuclear bombs. Case closed.
Except…
Launch time
…like a big pizza pie
If it was this simple, why hasn’t it been done already? The US landed on the Moon when it was on the brink of nuclear war with its technological rival. The ability to bombard Moscow with rocks at will would have been incredibly useful to the States – it would have turned the principle of mutually-assured destruction on its head. So why didn’t they try it?
The biggest rocket the US ever built was the Saturn V that took astronauts to the Moon. It was able to lift into low-Earth orbit the Apollo spacecraft and its fuel, the heaviest things ever sent to space… at 140 tons. The rocket itself weighed 3,000 tons, but most of that was fuel which got burned off during the journey, so if fired from the Moon it wouldn’t have much impact on Earth (relatively speaking!) when it hit Earth. It also needed a giant space port with tens of thousands of employees to launch it. It’s not a practical way to get your hundreds of thousands of tons of rock back to Earth.
Maybe there’s a more high-tech way. In Heinlein’s The Moon is a Harsh Mistress, lunar rebels bombard the Earth with chunks of rock – maybe this is where Wu got the idea. They use a railgun – a long tube lined with electric coils, which uses electromagnetism to accelerate rocks to very high speeds. This is more feasible – Nasa takes the idea seriously. However, it’s still difficult to make it work with rocks.
Again, as Heinlein said, there There Ain’t No Such Thing As A Free Lunch. The energy to run your gun has to come from somewhere. Getting 1 ton of rock up to the point where Earth’s gravity takes over takes 2.5 GJ of energy, or about half a ton TNT equivalent. That’s not too bad – a nuclear reactor produces that much energy in a second. But if we want to launch our 115,000 tons, we need 115,000 times more energy. In other words, we need as much energy as a 60 kiloton nuclear bomb produces, or the energy of all the world’s power stations all plugged together running for two minutes solid. If we’re want to launch 770,000,000 tons, you need the world’s electricity for 23 years. That’s right out.
If you want to, you can think of this as a good investment. 60 kilotons TNT of energy on the Moon to get you into space, but then 1,500 kilotons TNT of gravitational energy converted to explosive energy on Earth. Not a free lunch, but a cheap one. However, shutting down your entire economy to scrape together enough energy to fire the gun seems counterproductive. And unnecessary. Why are we shooting rocks if we have all these nuclear reactors?
Stick a Tsar Bomba in your rail gun and shoot it at the Earth. It will have a lot more explosive power than your 115,000 tons of rock, and probably actually cost you a lot less to do.
Through the keyhole
If you’re shooting thousands of tons of rock at the Earth, you probably have an enemy or two. Will you hit them?
You don’t have to be dead accurate when your weapon has the power of a hundred Hiroshima bombs, but how close do you have to hit?
For one thing, you have to get close to the ground. Asteroids have a habit of exploding high in the atmosphere, and our moon rock is likely to do the same. The Chelabynsk meteor – which was equivalent to about 30 Hiroshima bombs – exploded about 25-30 km up in the atmosphere. As a result, all it actually did damage-wise was break some windows and cause some sunburn. Our 100 Hiroshima bomb wouldn’t do much better.
A much bigger rock would do damage on the ground even if it did explode high up. According to NUKEMAP, a 100 megaton explosion at 25 km altitude would flatten much of London and shatter windows across the Home Counties. (This should be taken with a punch of salt – using nuclear explosions to guess how much damage an asteroid explosion will do overestimates blast damage). So, let’s say you’re a moon-based Guy Fawkes, and you want to blow up the Houses of Parliament. This means that you need to hit somewhere with a 10 kilometre radius of it. That’s the target. How easy is that?
Here, I have to confess the answer is “I’m not sure”. Orbital mechanics is incredibly hard, as you’ll know if you’ve seen Hidden Figures. There are tricks like make it easier, like the patched conic approximation that makes the game Kerbal Space Program possible, but it still takes a lot of work.
When plotting the path of asteroids, astronomers talk about the “gravitational keyhole“. This is the patch of space that, if the asteroid passes through it, will set it on a collision course with Earth. Protecting the Earth from asteroids means bumping them so they go off course and miss the keyhole. There will be something similar here – you’ll want to ensure that the rock is in just the right place when the Earth’s gravity grabs it. Get it wrong, and it will go off course.
Let’s ignore gravity for a moment, and focus solely on the straight line path from the Moon to Earth. You’re setting up your gun – where do you point it? The difference between hitting the centre of your 10 km target circle and missing it completely is equivalent to letting your gun slip by an angle of 0.0015 degrees. That’s not much – thermal expansion of the railgun in sunlight might deform it by more than that. Gravity will distort that keyhole, but that’s the order of magnitude of precision we’re talking about. Hitting the keyhole could be made easier by adding boosters to your rock to nudge it into the correct path, although you’d need a lot of fuel to push such a heavy rock around quickly enough.
Not only do you have to be precise where you aim in space, you also have to be precise where you aim in time. The Earth rotates fast enough that at the equator, the ground is moving at 1000 mph, or about 460 metres per second. If your gun is pointed at Singapore, it’ll just take 20 seconds for the city to slip out of your crosshairs. London, further from the equator, would be a bit slower, but you’d still need to ensure that the missile reached the Earth at the exact minute you needed it to. Is that possible? Well, I don’t know how precise a railgun would be. We’re talking about sci-fi technology here.
That said, there’s a reason Nasa didn’t simply shoot astronauts straight at the Moon. Spaceflights between worlds typically start with orbit around Earth and end with orbit around the target world. This way you have much more control over your trajectory, and less chance of zooming off into deep space, never to return.
Worse things happen in space
So in all, the Moon rock bombardment threat is not a worry – a rock thrower would need too much power to be feasible, and it would take incredible precision to hit its target. This is not to say that the militarisation of space is nothing to worry about, but the threats are less dramatic. A military space power – even one that doesn’t have a giant moon base – could take satellites out of orbit and disrupt communications, GPS, weather forecasting and military surveillance. One with a space station can drop nuclear bombs (or tungsten rods) with near-impunity while shooting down enemy missiles. A space terrorist could attempt to block orbital space entirely by filling it with debris, as shown in Gravity and Planetes. A moon base could be used to harvest helium-3, used in nuclear weapons.
But falling rocks shouldn’t be a worry. At least, not ones dropped by humans.