The first footprints put on the moon will probably be there a long, long time — maybe almost as long as the moon itself lasts.
Unlike on Earth, there is no erosion by wind or water on the moon because it has no atmosphere and all the water on the surface is frozen as ice. Also, there is no volcanic activity on the moon to change the lunar surface features. Nothing gets washed away, and nothing gets folded back inside.
However, the Moon is exposed to bombardment by meteorites, which change the surface. One little spacerock could easily wipe out a footprint on the moon. And since the Moon has no atmosphere, it is exposed to the solar wind, a stream of charged particles coming from the sun, and over time this acts almost like weather on Earth to scour surfaces on the moon, but the process is very, very slow.
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