What does this moth eat?

It is indeed a Luna Moth, and you are correct. They don't eat anything, because as adults they have no mouths. They have to do all of their eating as caterpillars, storing up enough energy to keep them going as adults long enough to breed, find the right spot, and lay eggs.

As a child, I found a luna moth and put it in a large jar to observe. It laid eggs and died. I looked it up in the World Book encyclopedia, and discovered that the caterpillars would eat sweet gum leaves. When the eggs hatched, I started collecting leaves. Every day, I would pick fresh leaves for them. One of them lived, and pupated. When it emerged, I took the beautiful moth outside and released it. The moth fluttered away....for about 10 feet before a Mockingbird swooped down and grabbed it for lunch. That day I learned a lot about the food chain.

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