Introduction

Tolkien gave three quotes about the events of Middle-earth. The first is in Letters, #211:

... I hope the, evidently long but undefined, gap(*) in time between the Fall of Barad-dur and our Days is sufficient for 'literary credibility', even for readers acquainted with what is known or surmised of 'pre-history'. (*) I imagine the gap to be about 6000 years: that is we are now at the end of the Fifth Age, if the Ages were of about the same length as S.A. and T.A. But they have, I think, quickened; and I imagine we are actually at the end of the Sixth Age, or in the Seventh.

The second one is in one of the The History of the Lord of the Rings books (part of The History of Middle-earth):

The moons and suns are worked out according to what they were in this part of the world [i.e. England or thereabouts] in 1942 actually.... I mean I'm not a good enough mathematician or astronomer to work out where they might have been 7,000 or 8,000 years ago, but as long as they correspond to some real configuration I thought that was good enough.

The third one comes from a rejected note from the Chapter 11 of The Lhammas, in The Lost Road, volume V of The History of Middle-earth:

From the great war and the overthrow of Morgoth by Finwë and the ruin of Beleriand, which is computed to have happened about the year 397 of the Sun, are now very many ages passed; and the tongues of the waning Elves in different lands have changed beyond recognition of their kinship one to another, or to the languages of Valinor, save in so far as the wise among them use still Qenya, the Elf-latin, which remains in knowledge among them, and by no means of which they yet at whiles hold converse with emissaries from the West. For many thousands of years have passed since the Fall of Gondolin. (...) (Christopher note to Chapter 11): In the words of Rúmil here that 'many thousands of years have passed since the fall of Gondolin' an obliterated reading lies beneath 'many thousands of'; this was very probably '10,000', which is the reading of Lhammas A.

It should be noted that, since from the Fall of Gondolin to the Fall of Barad-dur there are approximately 6,000 years, and that the Lhammas was dictated by Pengolodh to Ælfwine around Year 1,000 AD, this 10,000 years estimate agrees with the above dates.

My purpose here is to prove those dates using astronomical data.

Duration of the Year

	THE CALENDARS
	The Calendar of the Shire differed in several features from ours. The year no doubt was of the same length,1 for long ago as those times are now reckoned in years and lives of men, they are not very remote according to the memory of the Earth. (...)
	1 365 days, 5 hours, 48 minutes, 46 seconds

Appendix D of The Lord of the Rings is written in the persona of Tolkien The Translator, so this comment is subject to criticism. The value of 365.2422 days per year is obviously a contemporary data!

The duration of the Year in that Age, measured in atomic seconds, might be the same as the duration of the Year in the current Age; however, the duration of the day has changed measurably, so that, in counting the duration of the Year in Days:

Year in Days =	Year in Atomic Seconds
	
	Day in Atomic Seconds

it is possible to arrive at a different answer depending on the date we choose. I have written a Javascript page to implement this formula.

The Eldar in Middle-earth, who counted in base 12, used the yén as their long period unit. It had 52,596 days, or 144 years (of which one in each 12 was a leap year, with additional 3 days; 144 * 365 + 12 * 3 = 52,596). The last year of the third yén was not a leap year, so that three yéns (432 years) had 157,785 days, or 365.2430 days per year. This is the actual duration of the Year in 10,000 BC - the date when the Noldor came to Middle-earth.

The Numenoreans used a system similar to the Gregorian calendar: normal years had 365 days, leap years had 366 days. The leap years were those that were multiple of 4, except those multiple of 100, but including those multiple of 1000 - or 365000 + 250 - 10 + 1 days per millenia, for an average of 365.2410 days per year. Too bad, this will only happen in 20,000 AD!

However, Boris Shapiro noticed that:

The millenium addition was 2 days, not 1. Tolkien wrote that while the Gregorian year is ~26 seconds faster than the tropical year, the Numenorean one was 17.2 seconds slower. That is 365.2420 days (17.2 sec ~ 0.0002 days). To make the average N. year (without millenium addition: 365.2400 days) equal to 365.2420 days (17.2 seconds slower that the tropical year) one should add 0.002 days every year or _2_ days every 1000 years.

365.2420 days per year still points to a future date (5000 AD, calculated in page yeardays.htm). Could this millenium addition be _3_ days?

The duration of the Day (measured in atomic seconds) is increasing in time due to the tidal friction caused by the Moon (this is compensated by a transfer of rotational angular momentum from the Earth to Moon's orbit, slowly raising Moon's orbit; this will go on until the Earth-Moon system rotates synchronously in 1200 hours per revolution, in Year 146,000 million AD)

Links:

• Origin of the Moon and tidal friction

• Tidal Friction

Precession of the Equinoxes

In The Fellowship of the Ring, Chapter II.4 A Journey in the Dark, there's the following song:

The world was young, the mountains green, No stain yet on the Moon was seen, No words were laid on stream or stone When Durin woke and walked alone. He named the nameless hills and dells; He drank from yet untasted wells; He stooped and looked in Mirrormere And saw a crown of stars appear; As gems upon a silver thread; Above the shadow of his head. (...) The world is grey, the mountains old, The forge's fire is ashen-cold; No harp is wrung, no hammer falls: The darkness dwells in Durin's halls; The shadow lies upon his tomb In Moria, in Khazad-dûm. But still the sunken stars appear In dark and windless Mirrormere; There lies his crown in water deep, Till Durin wakes again from his sleep.

The constellation that has an approximate form of a crown is Corona Borealis. The song speaks clearly of two times when Durin's crown is exactly in the Zenith. This happens when the declination of the stars of the constellation are identical to the latitude of the observer.

The precession of the equinoxes makes the declination of Corona Borealis change with time. The two most recent epochs when its declination corresponds to _MORIA = 51^o are around 12,000 BC and 5,000 BC - the two epochs mentioned in the song (when Durin found Khazad-dum and when Khazad-dum was lost)

Census of Middle-earth

The Noldor

(a) of the Noldor in Valinor, one tithe didn't go to Beleriand [I suppose it's one tithe of the males - those that count in War]

(b) the Edain in Beleriand were less numerous (at least in the beginning) than the Elves. And there were some thousands of them.

(c) At arrival, Turgon's folk was 1/3 of the total of Fingolfin's folk (that also included Fingon's folk)

(d) At arrival, Feanor's folk was close to (but less than) 1/2 of the total number of Noldor

(e) Turgon's army in the Nirnaeth was composed of 10,000 elves

From these data, and supposing that the Elves doubled their numbers in Beleriand [*], I propose the following numbers, at arrival:

• Feanor: 7,000 to 9,000 Noldor (how many ships?)

• Fingolfin total: 7,500

  • Fingon: 5,000 Noldor

  • Turgon: 2,500 Noldor

• Finrod Felagund: 1,500 Noldor

From the initial 144 elves that awoke roughly 1/3 were Noldor, and roughly half of them went to Valinor, and half of them were male.

So, the initial 12 male Noldor were multiplied to 17,000 males in 4300 Years. If we suppose a constant number (k) of children per couple, and a period of 100 years between generations, we have:

• Sun Year 1050: 12 male Noldor pre-Eldar

• Sun Year 1060: 12 + 12 * k

• Sun Year 1070: 12 + 12 * k + 12 * k²

• ...

After 43 generations: 12 * (1 + k + ... + k⁴³) = 12 * (k⁴⁴ - 1) / (k - 1)

So: 12 * (k⁴⁴ - 1) = 17000 * (k - 1)

The solution to this is around k = 1.10, or 2.2 children per couple. So, at the start of the trip, there would be from 600 to 900 elves, of which half of them went to Valinor, and half of them were male.

One problem mentioned in the list was that Orome had given weapons to the travelling elves. Orome had to bring 150 to 225 weapons - not a great feat of strength for a Demiurgic Creature!

[*] Of couse, now I must revise this statement. From the 17,000 Noldor that arrived, 12 * k⁴³ = 700 are young (and fertile). Supposing that they married Sindar Elf-maidens, in the 5 generations in Beleriand they would add more 1400 * (k + k² + ... + k⁵) elves, or 9500, of the order of the initial estimate.

Tolkien Timelines

In order to build a timeline for the Age of the Trees and the Fourth Age (and I suppose Stephen Geard had the same problem to make the Second and Third Age) we have to select among several usually contradictory texts. The standard procedure is: published material is "Canon", everything else should be made valid unless a latter material contradicts it.

Example: in the Book of Lost Tales, the Valar could reproduce. In Morgoth's Ring, Tolkien denied them this biological feature. So, any timeline should *not* include Valar reproduction.

In my opinion, this is not the only way to write Timelines: it's also possible to fix a time - say, 1930 - and try to reconstruct a timeline for Middle-earth *as it was imagined by Tolkien at that time*. To do this, we must consider as "Canon" everything that he wrote *before* that time, the latter the best, and then add what he wrote *after* that time, the earliest the best.

As an example, let's imagine that we have texts A, B, C, D and E, written in 1920, 1930, 1940, 1950 and 1960. If we want to make an "early" Timeline, the order should be A, B, C, D and E. If we want to make a 1945 Timeline, the order should be C, B, A, D and E. If we want to make a "final" Timeline, the order should be E, D, C, B and A.