Could you launch rocks from the Moon to hit Earth?

Question

In the Robert A. Heinlein novel, The Moon is a Harsh Mistress, the plot famously revolves around sending rocks from the Moon to Earth, launched via electromagnetic rail gun and the impacts looked like atomic-levels of force.

Is this plausible from an engineering standpoint? In the future, do we need to fear a Moon colony, "throwing rocks" at us?

From what I understand, if your speed was off by even 20 miles an hour, you could get atmospheric rebound, or burn up in re-entry. With Earth's atmosphere, the considerable distance to Earth, and the simple size of Earth relative to the small surface area of cities and other effective military targets, it seems the plan is pure lunacy?

Answer 1

You could, but it wouldn't be super easy.

First of all, you have to get off of the Moon. The escape velocity of the Moon is around 2.38 km/s, which is a good estimate of what you would need to leave the Moon's sphere of influence. About 700 m/s of that is the orbital velocity. If you launch the right direction, you would only need another 300 m/s of speed to completely cancel out the orbital velocity of the Moon around the Earth, which is about 1 km/s. Thus, the minimum velocity is 2.68 km/s. There are some nuances that might reduce this velocity slightly, but it should be close enough to get a rough guess.

Okay, so is that even possible? There are rail guns that have demonstrated 2.4 km/s when shooting a 3 kg slug on Earth. With low gravity, and no atmosphere, that can probably be scaled to something a bit higher for use at the Moon. Artillery on Earth typically is somewhat slower, maxing out at around 1 km/s for a larger round, and 1.5 km/s for a smaller round.

All that being said, it is easier to build a cannon on the Moon. The largest cannons on Earth, such as Project Babylon, require supports to keep the barrel from bending in the middle, which would cause the projectile to go off course.

Next to consider is the accuracy. A difference in only 1 m/s, when taken over the 3 days the Apollo mission took to return from the Earth results in a total distance of over 250 km, without taking into account gravity and the Earth's rotation. Realistically, at least some ability to tun the path in flight is required.

Next, would it survive? If a chunk of refined dense material, like Tungsten, was sent, it could survive. Titanium is quite common on the Moon, and would probably survive. Aluminum, which is the most common element on the Moon, would not survive, unless in a very large chunk.

Lastly, how much force would it impart? The velocity at Earth varies, but will be around 11 km/s. Let's say a small nuclear weapon is our benchmark, 20 kilotons. 1 kiloton is about 4.18 GJs. The kinetic energy is $\frac{1}{2}mv^2$. At the speed indicated, it would thus require a rock of about 1380 kg to have the force of a nuclear weapon. This is larger then any cannon type projectile we have launched on Earth, but isn't completely out of the realm of possibility.

Bottom line, if lunar citizens are really wanted to bomb Earth, they could do it using some kind of a cannon or electromagnetic rail. Most likely the projectiles would require at least a little guidance, and of very dense metals. It would also take considerable calculation to make it work as intended.

Answer 2

Heinlein's plot postulates regular grain shipments from Luna to Terra in 100-(metric) tonne batches via an "electromagnetic induction catapult" - what today we might call a mass-driver. Lunar Authority's catapult was specified as "almost 100 kilometers long" with an acceleration of 3g. A second catapult, built by the Loonies as an ace in the hole -- "Little David's Sling" was a 30 km, 10g job.

Said grain shipments occur in cylindrical steel containers ("barges") as "an induction field won't grab bare rock." Each grain barge was fitted with maneuvering and braking thrusters, and a transponder; the braking thrusters were removed and repurposed to other rocks when the barges became weapons. Heinlein's math for the KE of a 100-tonne grain barge at 11 km/sec is 6.25x10^12 joules, which "approaches the yield of a two-kilotonne atomic bomb."

Is this feasible? Gerard O'Neill and his merry band of experimenters at the Space Studies Institute built a prototype mass-driver in the late 1980s with 10g acceleration on a tabletop.

The questioner's concerns about rebound and precision of velocity have to do with shallow re-entry angle physics (say from orbit) rather than Heinlein's plot requirement of bombing from Luna, which for practical purposes are perpendicular to surface. 100 tonnes of rock should survive the short trip through the atmosphere largely intact.

From the book's perspective, whether you have to fear a future Lunar settlement throwing rocks depends entirely on whether Terran governments will exploit the colony and force the issue. (Vote wisely!) Further, it should be noted that the doctrine for Operation Hard Rock was to avoid killing anyone (except, as described, the "empty-headed swarms" who sat on the X announced three days prior). Cities were explicitly NOT targets:

"If we could prove to all Terra that we could drive home a sustained attack on strongest Gibraltar of their space defense, it would save having to prove it by smashing Manhattan or San Francisco.

Which we would not do even if losing. Why? Hard sense. If we used our last strength to destroy a major city, they would not punish us; they would destroy us. As Prof put it, 'If possible, leave room for your enemy to become your friend.'"