Saturday, 22 October 2941 T. A.: HAPPY NEW (dwarf) YEAR!

"He issued from the Gate, the waters
rose in fierce whistling steam ..."
(Dragon awakens, by Theodor Kittelsen (1857-1914))

On this day, the first day of the last week of autumn in 2941 T. A., the last young moon of autumn and the sun were visible in the sky together, announcing Durin's Day, the Secret Door opened, Bilbo made his investigations and aroused Smaug from his slumber. This was also, unbeknownst to him, the last full day of Smaug's life.

‘Soon [Bilbo] saw the orange ball of the sun sinking towards the level of his eyes. He went to the opening and there pale and faint was a thin new moon above the rim of Earth. ... The sun sank lower and lower, and their hopes fell. It sank into a belt of reddened cloud and disappeared. ... The little moon was dipping to the horizon. Evening was coming on. Then suddenly when their hope was lowest a red ray of the sun escaped like a finger through a rent in the cloud.’ ("The Hobbit, chap. 11)

The constraints of celestial mechanics, communication speeds and atmospheric conditions suggest that Durin’s Day did not mean the same thing for any dwarf in the world. Consider that next time you decide to set up your residence at a place that is called the Misty Mountains for a reason.

(Maybe that was why Khazad-dûm installed the outpost on Zirak-zigil, called – wonder why - ‘Durin’s Tower’. Even dwarves may have been aware that the best place for watching the heavens is high up in the mountains.)

"In theory and under ideal conditions, Durin’s Day could have been observed as short as 12 hours after conjunction. But the sun’s brightness and the moon’s proximity to its disk would forbid this daring adventure most of the time. Experienced observers have reported that they managed to descry a crescent 1.5 to 2 days after conjunction under exceptionally good conditions, i. e. high transparency of the atmosphere and favourite positioning of the celestial luminaries. But only a crescent that is at least 3 days old would have been easily visible to a layhobbit like Bilbo in autumn. 

Gandalf’s remark after Thorin had confessed his lack of astronomical education, ‘That remains to be seen’, was certainly made with some restraint not to insult the honourable dwarf. Wizard and half-elf may have thought of the ephemeris that Elrond no doubt kept in his house and that would have predicted the last new moon of autumn rather accurately. However, Elrond may have preferred to keep his head low that shortly after revealing that despite having lived since the Elder Days he had never heard of Durin’s Day before, inadvertently providing Thorin with the chance to retort his ‘as all should know’."

(Excerpt from "The Moon in 'The Hobbit', slightly amended for clarity)

A simulation of the view from the Doorstep on Durin's Day.
The yellow line marks the ecliptic. Notice the position of
the young moon to the left of the image.

The ‘thin new moon’ of Durin’s Day would not have been more than three days after new moon, set by Tolkien to have occurred on 19 October though more coherent with the other recorded observations is an early 20 October. The visibility of such a young moon is supported by the fact that in autumn, the crescent of a two days old moon is thicker than in, say, early summer.

With these data in hand, it is possible to set time and place precisely. Accepting that Hobbiton is at the latitude of Oxford, Erebor is located at about 54°N. This permits running a simulation of the configuration of the heavens at Durin's Day with a modern planetarium software. "Stellarium" was used to generate this image.

The simulation reveals a surprising fact that Tolkien could not have been aware of: At the northern latitude of Erebor, the crescent moon and the setting sun are almost at the same height of the horizon!

"This may seem hard to understand at first. The reason is the orientation of the ecliptic, which is the projection of the earth’s orbit on the sky or the virtual path that the sun seems to travel on. In October, the ecliptic assumes a very low angle respective to the horizon .... Even worse, the moon’s orbit is tilted against the ecliptic by 5°, and in autumn, it is located in the lower section of its course. Fortunately for Bilbo and the dwarves, the sun takes as well a very long time to vanish beneath the horizon.

This example should demonstrate that an almanac of lunar phases is not fully sufficient for a story-writer who wants to use the moon as a plot element. Any modern astronomy simulation software will do, though, but such tools had not been available in Tolkien’s time. And if he had known about them, he would probably have abhorred them."

(Excerpt from "The Moon in 'The Hobbit'")

It is not clear from the description whether or not Tolkien was aware of this particular constellation of the celestial luminaries. His wording does not conflict with that view.