The Moon in Orbit

use diagrams to explain why the lunar phase cycle is (2.2 days) longer than the orbit period of the Moon

The Moon orbits the Earth every 27.3 days. Like the Earth the Moon is also spinning but with a period of 27.3 days. The result of this is that the same side of the Moon is always facing the Earth. Until man made probes were sent to orbit the Moon we had never seen the far side.

How long does a cycle last?

Although it takes 27.3 days for the Moon to orbit the Earth the lunar cycle above actually takes 29.5 days, more than two days longer.

This is because as the Moon orbits the Earth the Earth moves relative to the Sun, so an extra couple of days are needed for the Moon to get into the position it was in, relative to the Earth, when the cycle started.