Eärendil, the Evening Star, most beloved of the Elves, shone clear above. So bright was it that the figure of the Elven-lady cast a dim shadow on the ground.
J.R.R. Tolkien, The Fellowship of the Ring, “The Mirror of Galadriel“
Frodo and Sam are shown the Mirror of Galadriel on the evening of T.A. 3019 February 15 (S.R. 1419 Solmath 15). Tolkien correctly makes no mention of the Moon during this scene because this event happens to fall on the evening of the third quarter moon (just like today 2021 February 4), which means the Moon set around noon and would not rise again until around midnight. So there would have been no moonlight to interfere with the light of Eärendil, the Evening Star. The Star of Eärendil is associated with Venus, and it really is possible for Venus to be bright enough to cast a shadow.
Incidentally, when aligning the Shire Calendar’s Mid-year’s Day with the modern summer solstice (as was done for this Lunar Read-along), then New Year’s Day in the Shire Calendar usually aligns with the modern winter solstice, and this date (or the following date when the Fellowship departs Lothlórien) would fall about half way between the winter solstice and the spring equinox.
The Shire Reckoning Project 
The Moon is not mentioned for the following day, the day that the Fellowship departs Lothlorien (corresponding with today, Feb. 5 in this Lunar Read-along), so I don’t have a blog post for it. But it will take only 40 more days (including that day) to complete the Quest and destroy the One Ring!
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