According to Tolkien's final chronology, the full moon occurred on (S.R.) Jan 8, Feb 8 and Mar 8. He wasn't being lazy, he was using the lunar calendar of 1942, advanced 5 days and converted to Shire Reckoning, and it happened that the January full moon happened not long before midnight, almost on the 9th, and that of March was just after midnight on the 8th, just missing the 7th (as in the opening of Minas Tirith, when Pippin sees the moonrise from the back of Shadowfax. (Since a lunar month is slightly more than 29.5 days, the divergence over two thirty-day months is a bit less than 24 hours)
Tolkien spent a LOT of time getting his calendar right, and the lunar issue was an additional problem every time he adjusted his timeline, which didn't reach its final form until well after the book was finished (and naturally required some rewriting). The full moon of (eventually) March 8 was the linchpin of his synchronization- the marker for the Muster of Rohan, the moon Pippin saw from Shadowfax and Frodo from Henneth Annun.
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The entire plot of The Lord of the Rings could be said to turn on what Sauron didn’t know, and when he didn’t know it.
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