Solar eclipses are fun and interesting. Alter the orbit of the moon so that they happen more frequently.
Nuclear weapons are of course the first (and last) possible solution to all problems. Set off a few on the moon to shift its orbit. (Previously, other recreational uses for nuclear weapons.)
The other famous method (for moving asteroids) is to use radiation pressure from the sun. Maybe large fields of steerable mirrors on the moon? This might have the advantage that the necessary raw materials for making mirrors might be readily available on the moon, unlike nuclear weapons which require heavy metals for their primary and tamper, which might not be easily available on the surface of the moon (or they might be).
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