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Actias luna
Actias luna, commonly known as the Luna Moth, is a lime-green, Nearctic Saturniid moth in the family Saturniidae, subfamily Saturniinae. It has a wingspan of up to 114mm (4.5 inches),[2] making it one of the largest moths in North America.
Yours is Antheraea polyphemus, which is indeed very similar to Actias luna. But note the stripe and spots on the side of the caterpillar. In Polyphemus and yours they are in "one line", whereas in Luna they are separated, meaning there is no spot on or directly at the line. The darker "triangular"-like marking is also missing in Luna.
Luna: http://bugguide.net/node/view/74130/bgim...
Polyphemus: http://bugguide.net/node/view/722625/bgi...
http://bugguide.net/node/view/427/bgimag...