What determines how long the Moon takes to complete one
cycle of phases?

It takes 27 days 7 hours and 43 minutes for the Moon to complete one full orbit around Earth. it's called the sidereal month it's measured by our Moon's position relative to distant fixed stars. but it takes our Moon about 29.5 days to complete one cycle of phases from new Moon to new Moon.

Explanation:

learned about it in 5th grade

the truman doctrine was an american foreign policy whose stated purpose was to counter soviet geopolitical expansion during the cold war. it was announced to congress by president harry s. truman on march 12, 1947, and further developed on july 12, 1948, when he pledged to contain threats to greece and turkey.