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by sho_hn 78 days ago
It's doable (and has been done), but is not entirely easy or cheap. Without getting into the orbital mechanics/whys, a "geostationary" orbit around the moon is not available (it exists but is further out than the Hill sphere and not stable). You can park a relay semi-stably at Earth-Moon L2, but still need station-keeping burns. The moon has has a very lumpy gravity field, so any kind of orbit needs station-keeping eventually.

It's just not super worth it.

If you want to look at a mission that did this, see China's Queqiao.