Factual error: The Apollo 11 lander Eagle detaches from command module Columbia with its landing legs already extended. Neil is then shown saying "the Eagle has wings" as if to mean the ship is flying on its own. Actually, the ship's legs wouldn't be extended until after the undocking. It was the extension of the legs that prompted Neil's quote about the Eagle having wings.
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Suggested correction: The legs were, in fact, extended prior to undocking. I was comparing it to the "From the Earth to the Moon" depiction.
