General Smith served as Eisenhower's chief of staff from 1942 through 1945. In 1946, Smith wrote a series of six magazine articles for the Saturday Evening Post to explain the reasoning behind the Allied actions for major events in the European Theater including the D-Day landing. He erroneously wrote :-
"For the airborne landings … we needed a late-rising full moon, so the pilots could approach their objectives in darkness, but have moonlight to pick out the drop zones."
Subsequently, Cornelius Ryan in his book "The Longest Day" used the phrase 'a late-rising moon' and many authors subsequently used the same phrase.
Texas State University Professor Donald Olson has set the record straight on the phase of the Moon during the D-Day invasion and the influence it and its timing made.
Article here by Donald Olson, June 2nd 2019, Sky & Telescope :-
https://www.skyandtelescope.com/astr...un-moon-tides/