‘I may disagree with what you say but I will defend to my death your right to say it’.
Earth is big and, as a result, it has a strong gravity. By comparison, the moon is smaller and has less gravity, roughly one-seventh of Earth’s. If someone on the moon wants to attack a spot on the Earth, all they need to do is to throw a moon rock hard enough to leave the moon’s weak gravity well. The rock will then pass into Earth’s gravity well and fall down it, finally striking its appointed target on the Earth’s surface. This process is like a giant on a mountain tossing a boulder on to a fertile valley below. This is a kinetic weapon, as the damage it causes is entirely down to the speed at which it strikes the target, due to the extreme height from which the object has fallen.
To make such a weapon work on the moon, the attacker needs ammunition - rocks - of which the moon has loads, and some means to toss those projectiles in a guided way, in order for them to hit their intended target. Previous science-fiction stories have explored this idea, such as Robert Heinlein’s ‘The Moon is a Harsh Mistress’, in which rocks coated in iron are launched from the Moon, at Earth, by an electromagnetic cannon. Although Heinlein’s book was a masterwork of speculative fiction, wrapping such rocks in iron as a way to propel them is a dated method and unfeasible. Iron is heavy and rare on the moon. There is a better alternative and it involves more modern technology, that of lasers and solar power.
To launch a rock from the Moon to the Earth, you need a) a power source of some kind for the launching and b) something that launches the rocks out of the moon’s gravity. The first requirement, power, can be supplied by solar power. The moon can receive the full intensity of the sun’s rays, uninterrupted, for long periods of time, making this an ideal spot for solar power generation.
The next thing needed is something to launch the rock. Lasers can carry out this task. A possible mechanism is as follows:
On the far side of the moon, a solar array is installed on its surface, along with a robot and several lasers. The solar array charges up the robot. The robot then digs a rock out of the lunar surface and places the rock in a harness hung from poles above the ground, placed in the centre of a circle of lasers. The robot retreats and the lasers, powered by the solar array, fire beams at the rock in the harness. The heat of the laser beams on the rock causes material on its surface to heat up and boil off. This emission of gases pushes the rock in the opposite direction to the gases it emits. Using this ‘action and reaction’ effect, the lasers ‘push’ the rock upwards, against the moon’s weak gravity. By altering the intensity of their beams and where they hit the rock, the lasers guide the rock upwards and entirely away from the lunar surface, accelerating it out of the moon’s gravity well. Once the rock is free of the lunar gravity, the lasers are turned off and the rock is left to fall down the Earth’s gravity well until it finally hits the intended target.
There are many practical benefits to investing in this type of weapon. It runs entirely from its own power source. It also has effectively limitless ammo. If it is placed on the far side of the moon, it is not even vulnerable to any Earth-based lasers’ attempts to disable it. It effectively becomes the most powerful catapult ever created, firing its shot from the highest-ever castle, behind the thickest-ever wall. Although the weapon’s location would make communication with it from an Earth-based command centre very difficult, the weapon’s computer could be semi-autonomous, or even receive its instructions from probes located further away from Earth than the moon, for example at one of the Sun’s Lagrange points, that have relayed instructions to it from an Earth-based command centre.
Is such a weapon on the minds of the super-states racing to explore and colonise the moon? I don’t know, but I would very be surprised if none of them have done a feasibility study. The idea isn’t new to science-fiction and recent developments in laser efficiency, solar power efficiency and robotics make it far more achievable than when Heinlein wrote about it, fifty years ago. Knowing what we do about human-kind, it's sensible to believe that one or more super-states will install such a weapon if they think it's worth the cost. Civilisation has followed a logical path for millennia and there’s no reason to think that will change, at least until natural factors bring it to a painful end. I think the moon will be a key piece in our next global war. Someone will establish a weapon on our moon and use this new high ground to devastating effect.
Note: Thinking about this again, a day later, I'm keen to check through some more of the technical aspects. For example, how big does a lump of rock that's travelled from the moon need to be to avoid being burnt up in Earth's atmosphere? This could be tricky to work out but I'll see what I can do.