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this post was submitted on 17 Jul 2024
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Someone's already given an answer for a non-illuminated structure, but the necessary brightness of a light to be visible is also an interesting question.
We'll assume the light is located on the dark portion of the Moon. From experience, the dimmest stars clearly visible with the naked eye when right next to the Moon are around magnitude 1, which is about 3.6x10^9 photons/sec/m^2.
If we focus the light on the near hemisphere of the Earth (which has an area of 2.5x10^14 m^2) we need to produce 9x10^23 photons/sec. A green photon has an energy of around 3.7x10^-19 joules, so the total power output is 9x10^23 x 3.7x10^-19 = 333 kW.
For reference, this is roughly comparable to the wattage of the fastest electric car chargers. It's a lot of power, but well within the capability of a small lunar solar farm.