Thursday, 11 May: Bilbo, Gandalf and the Company enter Rhudaur

On this day, in 2941 T. A., the Company awakened in its camp on the east side of Weathertop, 80 miles east of the Last Inn, to slowly progress into Rhudaur. This is the next entry in the 1960 timeline quoted in full by John Rateliff in "The History of the Hobbit".

Karen Fonstad, in "The Atlas of Middle-earth", scheduled the camp on the east side of Weathertop on 15 May, rather: a compromise between the LotR map and the incongruent revisions of the 1966 Hobbit that are, alas, not based on the consistent 1960 timeline.

My own calculations published in "The Moon in 'The Hobbit'" add that a full moon was shining on Weathertop that night, agreeing with (most of) the observations of the lunar phases reported in the published Hobbit and with the real syzygy of about 29.5 days, which young Mr. Tolkien for some reason believed to be 28 days long only, according to Rateliff. I find it wondrous that a man who romantisised Nature so much would be so ignorant of the way it works. 

Bilbo no doubt asked about the significance of the facilities seen on Weathertop's summit, which may have inspired Gandalf to give a brief lecture on Arnorian history. It can be summarised in the way my illustration shows.