In 340 BC the Byzantines and their allies the Athenians were under siege by the troops of Philip II of Macedon. On a particularly dark and wet night Philip attempted a surprise attack but was thwarted by the appearance of a bright light in the sky in the middle of the crescent. To commemorate the event the Byzantines took as their emblem the sky and the crescent.
When St. Constantine the Great moved the seat of the Empire to Byzantium, he changed the name of the city to Constantinople and took out the star and put the cross instead as you can see in many places on Mount Athos.
The Ottoman Empire, considering itself the follower of the Byzantine Empire took the cross out and put the star back and till today this is the flag of the Turkish state.
This photo shows the actual astronomical phenomenon occuring on the Holy Mountain over Vatopaidi’s main church (katholikon).