How long does moon rotate the sun?

The Moon does not rotate around the Sun independently; rather, it orbits the Earth, and together they both orbit the Sun. The Moon takes approximately 27.3 days to complete one orbit around the Earth, and during this time, both the Earth and the Moon are moving in their respective orbit around the Sun. Thus, the Moon indirectly participates in the Earth's annual orbit around the Sun, which takes about 365.25 days.