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The most efficient reactor on Earth (Hanul) uses 3.1kg of fuel per gigawatt-hour. Shipping cost to the moon is currently $1.2 million per kilogram. So that's $3.27 per kilowatt-hour *just in transportation costs*. Earth-based solar costs $0.08 per kilowatt-hour, all costs included.

The only way I can see it working is if the power generated on the moon’s used on the moon. Like for lunar data centers.

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Lunar data centers are also a dumb idea, for different reasons -- but even if they decided to build them, solar would be a better option than nuclear.