" The Sickle was swinging bright above the shoulders of Bree-hill. "
A footnote explains that the Sickle is the Hobbits’ name for the Plough or Great Bear. Also known as the Big Dipper
, this is a star constellation made up of seven stars that does indeed look more like a sickle, or a saucepan, than anything else. A sickle is a tool with a curved blade, used for cutting crops.
This is another very strong hint that Middle-earth is meant to be understood as a past or alternate version of our own world (see bookmark for page 209).
" It is part of the lay that is called The Fall of Gil-galad "
The Fall of Gil-galad tells the story of the Last Alliance of Men and Elves, where Gil-galad aids in the overthrow of Sauron and is himself slain. Written in an ancient tongue, it was translated by Bilbo Baggins and taught by him to a young Samwise Gamgee.