Note from D.J. – I am pleased to post this on behalf of guest author Iduna.

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Predicting Durin’s Day
by Iduna

“The first day of the dwarves’ New Year is, as all should know, the first day of the last moon of Autumn on the threshold of Winter. We still call it Durin’s Day when the last moon of Autumn and the sun are in the sky together. But this will not help us much, I fear, for it passes our skill in these days to guess when such a time will come again.” – Thorin Oakenshield (The Hobbit)

Durin’s Day is one of the most important dates on the Dwarvish calendar. It is a festival day, and it signals the beginning of the New Year.

In The Hobbit, Durin’s Day is of critical importance to Thorin’s Company, because it’s the only day of the year when the light will fall at just the right angle to shine on the keyhole of the secret door.

Durin’s Day is their one and only chance to enter the Lonely Mountain.

So it’s surprising to discover that the dwarves don’t know when, exactly, Durin’s Day will be. Why is it so impossible?

Two Steps: Finding Autumn, Finding the Last Moon

One problem with establishing Durin’s Day is that it depends on two completely unrelated planetary cycles – the earth’s annual trip around the sun, and the monthly lunar cycle.

The earth travels around the sun in about 365 days. The moon travels around the earth in roughly 29.5 days. But there is no predictable relationship between the two, so some years could have more lunar months than others. And the beginnings and ends of the lunar months don’t match up evenly with the solstices and equinoxes.

Finding Autumn: It’s September 20 to December 21 (ish)

Durin’s Day happens in autumn. So first, let’s figure out what is meant by autumn.

As the earth moves around the sun over the course of a year, it passes over four points: the two times when the sun crosses the Earth’s equator (Equinoxes), and the moments when the Sun reaches its highest or lowest point in the sky (Solstices).

On the equinoxes, the Sun crosses Earth’s equator, and day and night are of equal length. This usually happens around March 20 and September 20 every year.

On the solstices, Sun reaches its highest or lowest point in the sky, marking the longest day (the summer solstice, usually around June 21) and the shortest day (the winter solstice, around December 21).

In the Northern hemisphere, our four seasons generally occur like this: Spring runs from the spring equinox (March 20, give or take a day) to the summer solstice (around June 22). Summer lasts from the summer solstice to the autumn equinox (September 20, roughly). Autumn generally runs from the autumn equinox to the winter solstice, about December 21, and winter lasts from the winter solstice to the spring equinox.

Middle-earth Calendars: Did Tolkien Do It Differently? No.

Several of the peoples of JRR Tolkien’s Middle-earth had their own calendars – elves, humans and hobbits all have systems for reckoning the dates. But if the dwarves had a separate calendar system, it’s not mentioned in the Appendices to the Lord of the Rings (perhaps the Royal Astronomers of Erebor were victims of the dragon and all their knowledge lost, so that the dwarven refugees ended up adopting the calendars of the people among whom they lived).

In the appendices, we discover that Elves’ and Hobbits’ calendars paid special attention to the middle of the year – a day corresponding to the Summer Solstice (around June 22). For Hobbits, the celebration of Mid-year’s Day was a chief holiday, and it corresponded with the summer solstice, marking the beginning of summer.

Therefore, the seasons according to Tolkien are the same as the seasons in the real world. Autumn runs from the autumn equinox, around September 20, to the winter solstice, around December 21.

Finding the Last Moon

The next step in figuring out when Durin’s Day occurs is to find out when the Last Moon in autumn is.

If we look at Thorin’s speech above, a “moon” must mean an entire 29.5-day lunar cycle, or from a new moon to a new moon, because he talks about the dwarves’ New Year beginning on the first day of the last moon of autumn.

During autumn, a period of about 91 days, there can be between two and three entire moons, with portions of up to two additional moons, depending on the phase of the moon at the autumn equinox.

For instance, in 2013, the moon will be full on September 19^th, right before the autumnal equinox on Sunday, September 22, 2013.

The last moon of autumn, meaning the beginning of the last lunar cycle of autumn in 2013, will fall on Tuesday, December 3. So that day will mark the beginning of the dwarves’ New Year.

But is that Durin’s Day? Not quite.

Last Step: Sun and Moon in Sky Together

On Durin’s Day, both the moon and the sun have to be visible in the sky at the same time. This means that the moon can’t be full or new — it’s got to be in the first or last quarter in the sky.

Source: http://www.universetoday.com/88956/how-can-you-see-the-sun-and-the-moon-at-the-same-time/

The diagram above shows that, to see the moon in the sky during the day (when the sun is also visible), the moon must be on the same side of the earth as the sun. Since there is very little sun shining on the moon when it’s brand-new, the best time for the moon to be seen in the sky is when the sun is illuminating it as much as possible.

That means the best time to see it in the daytime sky is between the waxing crescent and the first quarter moon.

Moonrise tables show us when the moon rises in the sky. Here is a link to moonrise tables for the Eastern US:

In December 2013, the moon and the sun will be visible in the sky together sometime between December 9, when the quarter moon will rise a little after noon, and December 17, when the full moon will rise around 5:30 in the evening (and possibly night will have fallen by then).

So between the 9^th and 17^th of December, the moon and the sun will be visible in the afternoon sky – and the first day when they can be seen together is Durin’s Day.

Now, was that so hard? Um, yes.

It’s not too surprising to think that the dwarves of Thorin’s generation might have had a hard time calculating the moment when Durin’s Day actually came to pass. A dispossessed people, wandering from place to place with only the items they could carry, might not have had access to an observatory or other tools needed to keep track of the planetary cycles.

Even with all the astronomical information at our disposal today, it’s not so easy to figure out when Durin’s Day has arrived, because it depends on what you can see – an overcast day, for example, would make it hard to detect the moon’s presence in the sky.

No wonder the dwarves celebrated Durin’s Day!