The moon is in a stable orbit around Earth. In simple terms, the means that it is attracted to Earth by gravity, but its "sideways" motion relative to Earth keeps it from hitting us. As a result the moon goes around Earth in an almost circular fashion. The sun is far more massive than Earth, so instead of the sun orbiting Earth, Earth orbits the sun. The stars are themselves distant suns, some even bigger than our own, but so far away they appear as mere dots in the sky. These stars are far enough away that they do not experience any significant effect from the sun, but instead orbit the center of the galaxy.
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