The Quantum Moon, known to the Hearthians as the 'Wandering Moon,' phases between positions in your solar system when not being observed. It can exist in orbit around Giant's Deep, Brittle Hollow, the Hourglass Twins, and Timber Hearth, and a fifth position is alluded to by numerous inscriptions.
Landing and Surface
The best way to land is to take a photo of the surface from space, using the Probe (this is explained here in more detail). This locks the moon in place. Then, you land as normal. The surface is shrouded in a thick layer of fog, and is barren except for a sign post, a hut, and three trees, all of which move when you look away from them. This is similar to the statue in the Observatory, and the Moon itself.
Curiously, upon entering the atmosphere every feature of the game is in photo-negative for a short time, before reverting to normal. Also, every attempt to enter the moon's atmosphere will usually result in looking at the ground, even when entering from different angles (though on occasion, one may accidentally ram into the bottom of the land platform.)
Physics
In the game's universe, the moon exists in a quantum superposition, where it exists only as a probability across every location. When it is observed, the probability disappears and the moon is in only one place. Looking away from it puts it back in the superposition, and hence is why it moves. Thus the moon can be represented as a wavefunction. Taking a photo of it with the probe forces it into one position, locking it in place even when you yourself are not directly looking at it.
Note that, from the purposes of the game's code, it's not actually in a superposition - try targeting the moon, looking away and trying to find it again. You'll sometimes see the relative velocity arrows pointing you to where the moon is. This indicates that the moon's position is simply changed every time you look away, instead of being determined when you look at one of its positions.
Trivia
The moon may be where the ancient statue came from. The sign post is the same one as is in the village on Timber Hearth, as is the grass, vegetation, and the house. If you stand close to the edge, inside the shroud preventing you from seeing the surface from space, the chromatic inversion effect will affect everything except for the ground you're standing on.
The Fifth Position
The moon's fifth position's possibility exists within the planetary system for about the first 60 seconds of a session, making it very difficult to trigger. Its path in this position does not appear to be in relation to any other body, and quickly takes it out into deep space, reaching approximately 270km from the sun at the moment of supernova. Those attempting to trigger the fifth position should look for it coming out of the sun at the very start of a session. Not long after this, the moon will be far enough away from the sun that no light reaches it to reflect, making it as dark as the backdrop and impossible to detect, unless you target it beforehand.
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