The Gensoukyan Moon (幻想郷 の 月 "Gensoukyou No Tsuki; Lit: Moon of Gensoukyou) is a Moon that holds the population of both Lunarians and Moon Rabbits alike, it is suggested that while the Moon isn't Gensoukyo's specific, and instead, the actual moon that revolves around Earth, it would then be plausible that the Moon itself is not of Gensoukyou's own location. Though expeditions to the Moon had never yielded positive life sightings by it's own governments, either that, or the life upon the Moon were real clever at hiding themselves, or may as well just sabotaged the discovery all together. It is the home of the Lunar Republic and The Lunar Defense Corps.
The term of 'Gensoukyan Moon' was applied by the residents of Gensoukyou were more of the ones to discover and then acknowledge the existence of Lunarians, particularly through Reimu Hakurei's discovery of Eientei and the Imperishable Night Incident, although this term is incorrect, it's what outsiders that are from Gensoukyou still refer it to. Where other terms have been used by others, such as simply The Moon. It's also known that with the incident mentioned before hand, a few Lunarians tried to hide the path of the Moon that started only from Gensoukyou, connecting the two ways. Which may also provide more to the misnomer. It could be the Near Side of this moon would be the one that most see, the one where Lunarians and Moon Rabbits don't tread, the Moon that is within Earth's thought bubble, where the Far Side would be the misnomer "Gensoukyan Moon"
It is said that the Moon is an artificial Pure Land, by that meaning, that those on it could not age or become sick, and the impurity of life and death do not exist, though the taint can be spread by others..According to Yamato Furea, the concept of such purity is that Lunarians and Moon Rabbits live much longer compared to their counterparts down on Earth, and the impurity is of the fact that Humans age and die in a normal case, but he wasn't entirely sure what entirely the purity of one meant, even though he his magical aura is considered pure, his immortality is considered impure, though it may also be that Humans simply spread death where they go, and seeing death is an impurity, they would threaten the Moon's said purity.
It's also said that magic originates from the Moon, though it's not entirely clear, as other realms are without the Moon and have their own magic, it could be possible that the Lunarians have developed their own concept of magic that Gensoukyou has ended up using, and it's likely that the study of magic has ended up being the primary course of magic, and may've ended up creating the Species: Youkai, though this is only another theory developed by other people. The concept of the Moon is not well known, and vague. It's assumed that the history said, both by Yamato and the origin of magic and youkai, would be such theories.
One thing is for certain, though, Gensoukyou does use the magic that was developed.
The Moon's timeframe seems to have better technology than that of Gensoukyou itself, though it is said that there is an interdimensional Organization that has similar technology, enough to rival, but not surpass or be equal to the one on the Moon, as well as the thought that the Kappa have also taken their strides and developments to be of similar way.
(RampantToyo may correct this after a review, or leave it be if determined correct)