The Moon is a myth and an Easter Egg in all GTA games from GTA III up.
The Moon is the Earth's only natural orbiting satellite and is the sixth largest natural satellite in the solar system. The moon first appeared in Grand Theft Auto III, and has been included in every game since then, excluding Grand Theft Auto: Advance and Grand Theft Auto: Chinatown Wars (because of them being top-down games.) It is assumed that the moon revolves around the Earth, just like in real life. However, the moon is never referred to as doing so in any game, and it only shows as a static image in all games since GTA III, fading into view at dusk and disappearing in the same way in the morning. Also, the moon never goes through phases as it always appears as a full moon.
There is no possible way of breaking through the atmosphere in the game to get to the moon (unless a modification is installed) because it is just an image, and because of the height limit. The moon is a helpful tool to navigate since it gives some light to dark rural areas such as Back O' Beyond in Grand Theft Auto: San Andreas. It should be noted the Grand Theft Auto IV version of the moon is not as detailed and bright as in past games.
In Grand Theft Auto V, the moon is much more detailed and realistic than its previous iterations. Also, the moon now cycles through phases, and it appears to be smaller than before, much like it is in real life. In Lester's home, there is a magazine that mentions an "Alien Moonbase."
Shooting at the Moon
In the 3D Universe, shooting the moon with a sniper rifle will change its size (Normal Size-Bigger-Bigger-Smaller-Bigger-Normal Size) but using other firearms will not work. It's unknown whether Rockstar did it intentionally or if it was a bug.
Connections with UFOs
It is possible to see a UFO cross the moon. It will create a black shadow on the Moon, some users believe that it could be E.T: The Extra Terrestrial. This most likely happens when players sight a bird flying adjacent to the moon, due to the dark texture of the bird, it may seem like a UFO. The Moon can also help the player to search for UFOs in its light, but it doesn't help when it is foggy or stormy, or a mixture of best known as "swampy" weather.