How long does it take the moon to go through an entire set of phases?.

It take approximately 29.5 days for moon to do its entire set of phases.

Explanation

The Moon is the only natural satellite of the Earth which undergoes three motions, that is :

Rotating on its own axisEvolving around the EarthTogether with the Earth evolving around the sun as the center of the solar system

With that, the moon has two periods of revolution, namely:

Sidereal revolution, which is the original revolution of the Moon. This sidereal revolution is really the time it takes the Moon to orbit the Earth. The sidereal revolution of the moon has a time span of 27.3 days or more accurate is approximately 27 days, 7.72 hours.Synodic revolution, namely the revolution of the Moon as seen from Earth as a series of moon phases (from the new moon phase, to the next new moon phase). The synodic revolution is slower, because the Moon needs to catch up with the Earth rotating in the same direction as the Moon. The synodic revolution of the moon has a time span of 29.5 days or to be more accurate approx 29 days, 12.734 hours.

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The fuzzy edges of shadows are a result of  diffraction