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In the meantime, here are some of the suggestions by NASA.
Radio astronomyPut a radio telescope on the far side of the Moon so that it would be shielded from Earth's copious radio noise, and would be able to observe low radio frequencies blocked by Earth's atmosphere. Observe at these frequencies and there may be a chance of it leading to many exciting new discoveries.
Study the cosmos in greater depthThe moon would also be an excellent place to study the high-energy particles of the solar wind, as well as cosmic rays from deep space. Earth's magnetic field and atmosphere deflect many of these particles, so even satellites in low-Earth orbit can't observe them all. The moon has virtually no atmosphere, and it spends most of its 28-day orbit outside of Earth's magnetosphere. Detectors placed on the moon could get a complete profile of solar particles, which reveal processes going on inside the sun, as well as galactic cosmic radiation from distant black holes and supernovas.
Bonus: These particles are trapped by lunar regolith, the layer of crushed rock and dust covering the moon's surface. This means that lunar regolith contains a historical record of solar output: core samples could tell us about changes in solar output over billions of years. "We believe that the moon's preservation of this solar record is unique and can provide us with insights on how past fluctuations in the solar output have affected, for example, the history of life on Earth," says Volosin. In particular, it could shed light on the extent to which solar variability and galactic cosmic radiation influence climate change.
Some other suggestionsLunar power from solar cells, protected data archives, mining of lunar metals, and research under conditions of low gravity and high vacuum.
Full list of things to do.