Here's why:
* Lunar Phases: The moon's phases are caused by the changing angles of sunlight reflecting off its surface as it orbits Earth. A full moon appears bright and high in the sky because it's reflecting the most sunlight. As the moon phases through its cycle (waxing gibbous, waning gibbous, etc.), it rises and sets later in the night.
* Earth's Rotation: The Earth rotates on its axis, causing day and night. As the Earth turns, the position of the moon in the sky changes relative to our viewpoint.
* Our Perception: We tend to associate the full moon with late nights because we're more likely to be awake and notice it when the sky is dark.
So, the moon's visibility isn't about being *late* at night, but rather about the combination of its phases and our planet's rotation.