Luna Moths are members of the Saturniidae family, also known as the Giant Silkworm Moths.. Luna Moths are huge moths, with a wingspan of four and a half inches. They have a white body, pinkish legs, and huge pale green wings.The hindwings have eyespots and long tails.They fly, only at night, in Spring and early Summer. The female Luna Moth lays eggs on the bottom of Black Walnut leaves.hey only live for about a week, and their only purpose is to mate. The caterpillars will continue to eat and grow, molting their skins as they grow. They will do this five times over a period of three to four weeks. When the caterpillar is fully grown, it will be 2 1/2 inches long and ready to become a pupa.