The land is literally called EORZEA. It's supposed to be like Earth.
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Putting aside the fact that Eorzea had two moons for a moment...
Hate to break it to you, but Earth's moon is perfectly visible during the day nearly every single day and its orbit is such that its position in the sky relative to us and the sun varies thus giving us the phases. Eorzea's moon is quite exotic compared to that given that it always follows the same path in the sky in perfect opposition to the sun from our vantage point, is only ever visible at night, and yet still manages to have phases rather than always being in either a state of lunar eclipse or full moon depending on how perfect the opposition to the sun is.
Why do we see the moon in daylight? - http://www.space.com/7267-moon-daylight.html
http://www.space.com/images/i/000/00...r090912-02.jpg