The moon is a satellite because it moves around Earth. Earth and the moon are called "natural" satellites. Satellites fly high in the sky, so they can see large areas of Earth at one time.
Earth is a satellite of the Sun and the Moon is a sub-satellite orbiting Earth.If the Moon somehow ended up outside Earth's Hill sphere, the Moon would orbit the Sun instead of the Earth just like all the other planets, asteroids, and comets.
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