Neither dropping the stones from orbit nor diverting asteroids would be optimal strategy for the moon nazis. Assuming they have anti-gravity technology, their best strategy is to simply hover over the Earth and release the stone a few minutes before the target city rotates beneath them.
This makes aiming easy while reducing the energy absorbed by Earth's atmosphere, since the stone will start at hovering v = 0 kph instead of orbital v = 27,400 kph.
In quick, rough terms:
Suppose the moon nazis want to hit the city with the same energy as the Hiroshime bomb, about 8.370 x 10^13 Joules. If they want a rock to hit a city with with that much energy, when they drop it the rock must have at least that much potential energy.
PE = mgh
solving for mass:
m = PE/(gh)
Let's give the moon nazis two simple scenarios. In the first they want to release the rock from a high altitude of 2,000,000 meters.
(8.370 x 10^13 J)/(9.8 ms/s*2000000 m) = 4,270,408 kilograms.
In the second scenario the moon nazis want to drop a bigger rock from a lower altitude of 400,000 meters:
(8.370 x 10^13 J)/(9.8 ms/s*400000 m) = 21,352,040 kilograms.
Note that I have assumed a rock of infinite density so friction will be ignored. I leave it to you to decide on the density of the rock the moon nazis will choose.
I think the second scenario is better because:
a) It starts with a bigger rock closer to Earth, appearing more terrifying.
b) The rock will be visible from the ground for a longer time, again more terrifying.
c) The bigger rock needs less velocity, so friction is less of a factor.
In my next message I'll go into more detail.
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